Patent Publication Number: US-10782382-B2

Title: RFID antenna array for gaming

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present application is a continuation-in-part of U.S. patent application Ser. No. 16/402,776 filed May 3, 2019 for “RFID Antenna Array For Gaming”, which is a continuation of U.S. patent application Ser. No. 16/114,018 filed Aug. 27, 2018 for “RFID Antenna Array For Gaming”, which is a continuation of U.S. patent application Ser. No. 15/814,170 filed Nov. 15, 2017 for “RFID Antenna Array For Gaming”, all of which are incorporated herein by reference. 
    
    
     BACKGROUND 
     The present invention relates to gaming, and in particular, to a radio frequency identification (RFID) system with an antenna array for detecting the locations of RFID tags on a gaming table. 
     Unless otherwise indicated herein, the approaches described in this section are not prior art to the claims in this application and are not admitted to be prior art by inclusion in this section. 
     Tracking the location of gaming tokens in real-time on a gaming table has the potential to revolutionize the gaming industry by providing cash management and improved security. Tying this data to specific players allows casinos to create accurate player profiles while simultaneously alleviating the pit boss of mundane tasks that take years of training to hone. 
     Traditional RFID systems have tried to address the gaming market with limited success. In a typical RFID system, the excitation antenna defines a “working volume” within which the energy projected by the antenna is sufficient to power the RFID tag. This “working volume” is generally poorly defined with the only option to increase/decrease power to adjust the read range. But doing so extends the read range in ALL directions, introducing cross-talk errors when multiple antennas are in close proximity. Existing products on the market suffer from multiple shortcomings. First, they are limited to discrete betting spots. Second, they are limited in the chip stack heights they can read. Third, they have very poor discrimination between adjacent betting spots. Fourth, they have higher than acceptable read errors. Fifth, they have slow read rates that miss important events (e.g., placement and removal of chips, etc.). 
     These shortcomings limit the available technology to games where the betting spots are widely separated (e.g. a single “pot”), to detecting initial bets only (not capturing transient events such as payouts), and identifying counterfeit tokens only prior to their use on a table (not during gameplay). 
     U.S. Application Pub. No. 2013/0233923 discusses a ferrite core technology. The ferrite core technology overcomes many of the above-noted shortcomings, but does not address the need to track multiple separate bets placed by different bettors on a single larger betting spot (such as when “back bettors” share a betting spot with seated bettors on traditional Baccarat “racetrack” layouts). Also needed is the ability to discriminate the location of very closely spaced bets (such as can be found on a roulette table). 
     U.S. Application Pub. No. 2017/0228630 discusses a solution involving two intersecting antenna arrays. One array of horizontal antennas provides one coordinate, and a second array of vertical antennas provides a second coordinate. Signal strength information comparing adjacent antennas may then be used to interpolate a higher fidelity set of coordinates. 
     Although the approach of U.S. Application Pub. No. 2017/0228630 does work, it suffers from the simple fact that reading RFID tags takes time—and reading tags multiple times for purposes of interpolation multiplies the required time such that capturing an accurate “snapshot” of transient events with large numbers of tags may not practical in certain gaming environments. 
     The typical RFID system addresses the question, “Who&#39;s there?” The response is a series of unique item identifiers (e.g., serial numbers). As discussed above, the ferrite core technology discussed in U.S. Application Pub. No. 2013/0233923 is directed to addressing the additional question “Where are you?” as a way to track individual bets. 
     U.S. Application Pub. No. 2016/0217645 discusses using a network analyzer device prior to an RFID read, thereby being able to direct the RFID reader to only those antennas with tags present. This describes a serial approach that eliminates the “overhead” of looking for tags using an RFID reader where none are present, as using the network analyzer device takes less time than using the RFID reader. 
     Both U.S. Application Pub. No. 2013/0233923 and U.S. Application Pub. No. 2016/0217645 involve the placement of bets in specific areas (the betting spots). RFID tags not placed in one of the defined areas will not be read correctly. Neither of these disclosures addresses the need to detect bets placed anywhere on a larger bounded area. The additional disclosure of U.S. Application Pub. No. 2017/0228630 does address placing multiple bets within a larger bounded area. However, the system disclosed therein involved multiple RFID reads to define the coordinates of each bet, which is a time consuming process. 
     All three of U.S. Application Pub. No. 2013/0233923, U.S. Application Pub. No. 2016/0217645 and U.S. Application Pub. No. 2017/0228630 describe systems to identify and locate RFID tags by using signal strength information as measured by the RFID reader to determine proximity to a specific antenna. U.S. Application Pub. No. 2013/0233923 describes a system that increases the signal strength at the proper antenna, which further improves accuracy. 
     SUMMARY 
     One issue with existing systems that use an array of antennas to locate a tag within the array is the time involved in energizing each antenna, in order to read the RFID tags in the vicinity of each antenna and then repeat this process for each subsequent antenna. There is a need for a faster method to accurately locate and track individual closely spaced bets that can be placed anywhere within a defined boundary on a gaming table. There is a need for increased speed in a system that applies game rules to calculate the amounts and positions of the original bets, and also to correlate transient events such as payouts to winning bets. 
     Given the above, embodiments are directed toward using phase information of the detected RFID signals in order to improve the operation of the system. 
     According to an embodiment, a system determines the locations of objects in a gaming environment. The system includes a main antenna associated with an area on a gaming table, a first plurality of antennas oriented in a first direction and associated with the area on the gaming table, a second plurality of antennas oriented in a second direction, a main radio frequency identification (RFID) transmitter coupled to the main antenna, a main RFID receiver coupled to the main antenna, a first plurality of RFID receivers coupled to the first plurality of antennas, a second plurality of RFID receivers coupled to the second plurality of antennas, and a controller that controls the main RFID transmitter to generate an RFID inventory command. The second direction differs from the first direction, the second plurality of antennas overlaps the first plurality of antennas, the first plurality of antennas and the second plurality of antennas intersect at a plurality of locations within the area, and each of a plurality of RFID tags in the area responds to the RFID inventory command according to an anti-collision process. In response to the RFID inventory command, the main RFID receiver receives a first plurality of responses from the plurality of RFID tags, the first plurality of RFID receivers receives a second plurality of responses from the plurality of RFID tags, and the second plurality of RFID receivers receives a third plurality of responses from the plurality of RFID tags. The controller determines an identifier for each of the plurality of RFID tags using at least one of the first plurality of responses, the second plurality of responses, and the third plurality of responses, and the controller determines a position of each of the plurality of RFID tags by correlating amplitude information and phase information of the first plurality of responses, amplitude information and phase information of the second plurality of responses, and amplitude information and phase information of the third plurality of responses. 
     For a particular RFID tag of the plurality of RFID tags, the controller may simultaneously determine the identifier and the position of the particular RFID tag. 
     The RFID inventory command may be a single RFID inventory command that results in the controller determining the identifiers and the positions of all the plurality of RFID tags. 
     The first plurality of antennas and the second plurality of antennas may be overlapping and intersecting to define the position of each of the plurality of RFID tags in two dimensions within the area. The first plurality of antennas and the second plurality of antennas may intersect orthogonally and define the position of each of the plurality of RFID tags in an x dimension and a y dimension within the area. 
     The first plurality of antennas and the second plurality of antennas may define the position of each of the plurality of RFID tags using polar coordinates within the area. 
     The first plurality of antennas may be formed as a first non-overlapping, single layer, and the second plurality of antennas may be formed as a second non-overlapping, single layer. The first plurality of antennas may be formed as an overlapping, dual layer. 
     The controller may determine the position of each of the plurality of RFID tags using interpolation of the amplitude information of the second plurality of responses and the amplitude information of the third plurality of responses. 
     The controller may determine that a subset of the plurality of RFID tags are grouped together when the position of each RFID tag of the subset is within a defined range of at least one other RFID tag of the subset. 
     The controller may determine that a first subset of the plurality of RFID tags corresponds to a bet, and that a second subset of the plurality of RFID tags corresponds to a payout associated with the bet, according to the position of the first subset and the position of the second subset. 
     The controller may determine the identifier for each of the plurality of RFID tags using at least one of the second plurality of responses and the third plurality of responses. 
     The controller may use the first plurality of responses as reference information to normalize the second plurality of responses and the third plurality of responses. The controller may use the amplitude information of the first plurality of responses to normalize the amplitude information of the second plurality of responses and the amplitude information of the third plurality of responses. 
     The controller may use the phase information of the first plurality of responses to determine relative phase information for the second plurality of responses and relative phase information for the third plurality of responses. 
     When a first set of the plurality of RFID tags are associated with a first position, and when a second set of the plurality of RFID tags are associated with a second position, the controller may determine that the first set and the second set are a group when the first position and the second position are within a threshold distance. 
     According to an embodiment, a system determines the locations of objects in a gaming environment. The system includes a main antenna associated with an area on a gaming table, a first plurality of antennas oriented in a first direction and associated with the area on the gaming table, a second plurality of antennas oriented in a second direction, a main radio frequency identification (RFID) transmitter coupled to the main antenna, a main RFID receiver coupled to the main antenna, a first plurality of RFID receivers coupled to the first plurality of antennas, a second plurality of RFID receivers coupled to the second plurality of antennas, and a controller that controls the main RFID transmitter to generate an RFID inventory command. The second direction differs from the first direction, the second plurality of antennas overlaps the first plurality of antennas, and the first plurality of antennas and the second plurality of antennas intersect at a plurality of locations within the area. Each of a plurality of RFID tags in the area responds to the RFID inventory command according to an anti-collision process. In response to the RFID inventory command, the main RFID receiver receives a first plurality of responses from the plurality of RFID tags, the first plurality of RFID receivers receives a second plurality of responses from the plurality of RFID tags, and the second plurality of RFID receivers receives a third plurality of responses from the plurality of RFID tags. The controller determines an identifier for each of the plurality of RFID tags using at least one of the first plurality of responses, the second plurality of responses, and the third plurality of responses. The controller determines a position of each of the plurality of RFID tags by correlating amplitude information of the first plurality of responses, amplitude information and phase information of the second plurality of responses, and amplitude information and phase information of the third plurality of responses. 
     The details of this embodiment may otherwise be similar to the details of the previous embodiment. 
     According to an embodiment, a method determines the locations of objects in a gaming environment. The method includes generating, by a main radio frequency identification (RFID) transmitter coupled to a main antenna, an RFID inventory command, where the main antenna is associated with an area on a gaming table. The method further includes responding, by each of a plurality of RFID tags in the area, to the RFID inventory command according to an anti-collision process. The method further includes receiving, by a main RFID receiver coupled to the main antenna, a first plurality of responses from the plurality of RFID tags in the area in response to the RFID inventory command. The method further includes receiving, by a first plurality of RFID receivers coupled to a first plurality of antennas, a second plurality responses from the plurality of RFID tags in response to the RFID inventory command, where the first plurality of antennas is oriented in a first direction and is associated with the area on the gaming table. The method further includes receiving, by a second plurality of RFID receivers coupled to a second plurality of antennas, a third plurality of responses from the plurality of RFID tags in response to the RFID inventory command, where the second plurality of antennas is oriented in a second direction that differs from the first direction, where the second plurality of antennas overlaps the first plurality of antennas, and where the first plurality of antennas and the second plurality of antennas intersect at a plurality of locations within the area. The method further includes determining, by a controller, an identifier for each of the plurality of RFID tags using at least one of the first plurality of responses, the second plurality of responses, and the third plurality of responses. The method further includes determining, by the controller, a position of each of the plurality of RFID tags by correlating amplitude information of the first plurality of responses, amplitude information and phase information of the second plurality of responses, and amplitude information and phase information of the third plurality of responses. 
     The step of determining the position of each of the plurality of RFID tags may further include determining, by the controller, the position of each of the plurality of RFID tags by correlating the amplitude information and phase information of the first plurality of responses, the amplitude information and phase information of the second plurality of responses, and the amplitude information and phase information of the third plurality of responses. 
     The details of this embodiment may otherwise be similar to the details of the previous embodiments. 
     According to an embodiment, a system determines the locations of objects in a gaming environment. The system includes a main antenna associated with an area on a gaming table, a first plurality of antennas oriented in a first direction and associated with the area on the gaming table, and a second plurality of antennas oriented in a second direction, a main radio frequency identification (RFID) transmitter coupled to the main antenna, a first plurality of RFID receivers coupled to the first plurality of antennas, a second plurality of RFID receivers coupled to the second plurality of antennas, and a controller. The second direction differs from the first direction, the second plurality of antennas overlaps the first plurality of antennas, and the first plurality of antennas and the second plurality of antennas intersect at a plurality of locations within the area. The controller controls the main RFID transmitter to generate an RFID inventory command, where each of a plurality of RFID tags in the area responds to the RFID inventory command according to an anti-collision process. In response to the RFID inventory command, the first plurality of RFID receivers receives a first plurality of responses from the plurality of RFID tags, and the second plurality of RFID receivers receives a second plurality of responses from the plurality of RFID tags. The controller determines an identifier for each of the plurality of RFID tags using at least one of the first plurality of responses and the second plurality of responses. The controller determines a position of each of the plurality of RFID tags by correlating amplitude information of the first plurality of responses, and amplitude information of the second plurality of responses. 
     The controller may determine the position of each of the plurality of RFID tags by correlating the amplitude information and phase information of the first plurality of responses, and the amplitude information and phase information of the second plurality of responses. 
     The details of this embodiment may otherwise be similar to the details of the previous embodiments. 
     According to an embodiment, a method determines the locations of objects in a gaming environment. The method includes generating, by a main radio frequency identification (RFID) transmitter coupled to a main antenna, an RFID inventory command, where the main antenna is associated with an area on a gaming table. The method further includes responding, by each of a plurality of RFID tags in the area, to the RFID inventory command according to an anti-collision process. The method further includes receiving, by a first plurality of RFID receivers coupled to a first plurality of antennas, a first plurality responses from the plurality of RFID tags in response to the RFID inventory command, where the first plurality of antennas is oriented in a first direction and is associated with the area on the gaming table. The method further includes receiving, by a second plurality of RFID receivers coupled to a second plurality of antennas, a second plurality of responses from the plurality of RFID tags in response to the RFID inventory command, where the second plurality of antennas is oriented in a second direction that differs from the first direction, where the second plurality of antennas overlaps the first plurality of antennas, and where the first plurality of antennas and the second plurality of antennas intersect at a plurality of locations within the area. The method further includes determining, by a controller, an identifier for each of the plurality of RFID tags using at least one of the first plurality of responses, and the second plurality of responses. The method further includes determining, by the controller, a position of each of the plurality of RFID tags by correlating amplitude information of the first plurality of responses, and amplitude information of the second plurality of responses. 
     The step of determining the position of each of the plurality of RFID tags may include determining, by the controller, the position of each of the plurality of RFID tags by correlating the amplitude information and phase information of the first plurality of responses, and the amplitude information and phase information of the second plurality of responses. 
     The details of this embodiment may otherwise be similar to the details of the previous embodiments. 
     In one or more of the embodiments discussed herein, the system may determine the position of the RFID tags using phase information, relative phase information, amplitude information, or a combination thereof. 
     In one or more of the embodiments discussed herein, the main antenna may have a “figure 8” shape. The main antenna may have a first loop and a second loop, where the main antenna is associated with a field, where the first loop is associated with a first phase of the field, where the second loop is associated with a second phase of the field, and wherein the first phase is opposite the second phase. The system may further include a second main antenna located where a first loop of the main antenna crosses a second loop of the main antenna, where the controller controls the main RFID transmitter to generate a second RFID inventory command associated with the second main antenna. The second main antenna may be associated with a null of the main antenna, where the controller controls the main RFID transmitter to selectively generate the RFID inventory command and the second RFID inventory command to overcome the null. One or more of the first plurality of antennas and the second plurality of antennas may cross over both the first loop and the second loop of the main antenna. One or more of the first plurality of antennas and the second plurality of antennas may have the “figure 8” shape. The system may further include conductive traces, where the conductive traces are associated with an interior border of a loop of the main antenna. 
     One or more of the embodiments discussed herein may include a multiplexer coupled to two or more antennas, and coupled to the RFID receiver, where the two or more antennas are selected from the first plurality of antennas and the second plurality of antennas. The controller may control the multiplexer to selectively connect one of the two or more antennas to the RFID receiver. 
     In one or more of the embodiments discussed herein, the system may further include one or more outside antennas that are outside of the area, where the controller uses the responses from the outside antennas to exclude a subset of the plurality of RFID tags from being associated with the area. 
     The following detailed description and accompanying drawings provide a further understanding of the nature and advantages of embodiments of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of an RFID system  100 . 
         FIG. 2  is a flowchart of a method  200  of operating an RFID system (e.g., the RFID system  100  of  FIG. 1 ). 
         FIG. 3  is a graph showing a plot  300  of amplitude and phase information detected by one of the antennas  104  or  106  (see  FIG. 1 ) as the chip is moved across it. 
         FIG. 4  is a graph showing plots  400  and  402  of amplitude and phase information detected by two of the antennas  104 , or by two of the antennas  106  (see  FIG. 1 ). 
         FIG. 5  is an overhead view of the antennas  104  and  106  of  FIG. 1 . 
         FIG. 6  is a block diagram of an RFID system  600 . The RFID system  600  shows a specific implementation of the RFID system  100  (see  FIG. 1 ). 
         FIG. 7  is a block diagram of a receiver  700 . 
         FIG. 8  is a block diagram of an RFID system  800 . 
         FIG. 9  is an overhead view of a set of overlapping antennas  900  in one direction. 
         FIG. 10  is an overhead view of an antenna array  1000 . 
         FIG. 11  is an overhead view of a polar antenna array  1100 . 
         FIG. 12A  is an overhead view of a Baccarat table  1200 , and  FIG. 12B  is an overhead view of a portion of the Baccarat table  1200  showing a corresponding portion of an antenna array  1202 . 
         FIG. 13  is an overhead view of a roulette table  1300  having an antenna array  1302 . 
         FIG. 14  is an overhead view of the antennas  104  and  106  of  FIG. 1   
         FIG. 15  is an overhead view of an antenna  1500  having a “figure 8” shape. 
         FIG. 16  is an overhead view of antennas  1604 . 
         FIG. 17  is an overhead view of antennas  1706 . 
         FIG. 18  is an overhead view of conductive traces  1800 . 
         FIG. 19  is a block diagram of a multiplexer  1900 . 
         FIG. 20  is an overhead view of an antenna arrangement  2000 . 
     
    
    
     DETAILED DESCRIPTION 
     Described herein are techniques for location determination of RFID tags. In the following description, for purposes of explanation, numerous examples and specific details are set forth in order to provide a thorough understanding of the present invention. It will be evident, however, to one skilled in the art that the present invention as defined by the claims may include some or all of the features in these examples alone or in combination with other features described below, and may further include modifications and equivalents of the features and concepts described herein. 
     In the following description, various methods, processes and procedures are detailed. Although particular steps may be described in a certain order, such order is mainly for convenience and clarity. A particular step may be repeated more than once, may occur before or after other steps (even if those steps are otherwise described in another order), and may occur in parallel with other steps. A second step is required to follow a first step only when the first step must be completed before the second step is begun. Such a situation will be specifically pointed out when not clear from the context. 
     In this document, the terms “and”, “or” and “and/or” are used. Such terms are to be read as having an inclusive meaning. For example, “A and B” may mean at least the following: “both A and B”, “at least both A and B”. As another example, “A or B” may mean at least the following: “at least A”, “at least B”, “both A and B”, “at least both A and B”. As another example, “A and/or B” may mean at least the following: “A and B”, “A or B”. When an exclusive-or is intended, such will be specifically noted (e.g., “either A or B”, “at most one of A and B”). 
     In this document, the terms “RFID tag”, “RFID gaming tag”, “RFID chip”, “RFID gaming chip”, “gaming chip”, and “gaming token” are used. Such terms are to be read as being broadly synonymous. (More precisely, an “RFID chip” may be used to refer to the integrated circuit components of the “RFID tag”, which also includes additional components such as an antenna, a rigid housing, etc. However, this document is mostly concerned with the broad usage for these terms.) The RFID tag responds to a radio frequency signal from the RFID reader, generally with its serial number or other identifier, enabling the RFID reader to obtain an inventory of the RFID tags in the vicinity. In a gaming context, the RFID gaming tags may be placed on, removed from, or moved around on a gaming table as bets and payouts, according to various game rules. The RFID gaming tags may be marked with a value identifier (e.g., $1). 
       FIG. 1  is a block diagram of an RFID system  100 . The RFID system  100  includes a main antenna  102 , a first set of antennas  104   a - 104   d  (collectively antennas  104 ), a second set of antennas  106   a - 106   d  (collectively antennas  106 ), a main RFID transmitter  108 , a main RFID receiver  112 , a first set of RFID receivers  114   a - 114   d  (collectively RFID receivers  114 ), a second set of RFID receivers  116   a - 116   d  (collectively RFID receivers  116 ), and a controller  120 . In general, the main RFID transmitter  108  generates radio frequency energy that is radiated by the antenna  102  and received by any RFID tags; the responses from the RFID tags are then received by the antennas  102 ,  104  and  106 . The responses from the RFID tags may be amplitude and phase information. The amplitude information may be in the form of received signal strength (RSSI) information, and the phase information may be in the form of in-phase (I) and quadrature (Q) information. 
     The RFID system  100  may be implemented as part of a gaming table (see, e.g., the roulette and Baccarat examples of  FIGS. 12A-12B and 13 ). For example, the antennas  102 ,  104  and  106  may be embedded below the playing surface of the gaming table (in order to detect the locations of the RFID gaming tags during play on the gaming table), and the rest of the components of the RFID system  100  may be embedded within the structure of the gaming table. The gaming environment may have a number of gaming tables, each including an RFID system  100 ; the multiple RFID systems  100  may be connected to each other or to other components via a network. 
     The main antenna  102  is located under the playing surface of the gaming table. As part of playing games using the gaming table, RFID gaming tags are placed on, removed from, and moved around on the area above the main antenna  102 . This area on the gaming table may be marked to show various subareas according to the particular game being implemented (see, e.g., the roulette and Baccarat examples of  FIGS. 12A-12B and 13 ). The main antenna  102  may be implemented on a printed circuit board. The main RFID transmitter  108  and the main receiver  112  are coupled to the main antenna  102 . 
     The antennas  104  are located under the playing surface of the gaming table and, like the main antenna  102 , are associated with the gameplay area. The antennas  104  are oriented in a first direction. As shown in  FIG. 1 , the antennas  104  are oriented in the north-south (or y) direction. In other implementations, the antennas  104  may be oriented in other directions. The antennas  104  may be implemented on a printed circuit board, or as a layer of a multilayer circuit board that also includes the main antenna  102 . The RFID receivers  114  are coupled to the antennas  104 . 
     The antennas  106  are located under the playing surface of the gaming table and, like the main antenna  102 , are associated with the gameplay area. The antennas  106  are oriented in a second direction that differs from the first direction of the antennas  104 . As shown in  FIG. 1 , the antennas  106  are oriented in the east-west (or x) direction. In other implementations, the antennas  106  may be oriented in other directions. The antennas  106  may be implemented on a printed circuit board, or as a layer of a multilayer circuit board that also includes the main antenna  102  or the antennas  104 . The RFID receivers  116  are coupled to the antennas  106 . 
     The antennas  106  overlap the antennas  104 ; this overlap is shown using dotted lines in  FIG. 1 . This overlap generally allows both the antennas  104  and  106  to be associated with the gameplay area, in addition to the main antenna  102 . In general, this allows at least three antennas (e.g., the main antenna  102 , one of the antennas  104 , and one of the antennas  106 ) to be associated with each location within the gameplay area. The spacing between each of the antennas  104 , and the spacing between each of the antennas  106 , may be adjusted as desired. 
     Collectively, the antennas  104  and  106  form what may be referred to as an antenna array. As shown in  FIG. 1 , the antennas  104  and  106  intersect at right angles. In other implementations, the antennas  104  and  106  may intersect at other angles. As shown in  FIG. 1 , the antennas  104  and  106  are rectangular in shape. In other implementations, the antennas  104  may have other shapes, such as ring shapes, pie shapes, curved shapes, rounded rectangular shapes, etc. The sizes of the antennas  104  and  106  may be adjusted as desired. 
     Four antennas  104  and four associated RFID receivers  114 , and four antennas  106  and four associated RFID receivers  116 , are shown in  FIG. 1 . These quantities may be adjusted as desired to cover larger or smaller areas and/or to increase or decrease spatial resolution. 
     In general, the main RFID receiver  112  is used to generate reference amplitude and phase information that the controller  120  uses when processing the amplitude and phase information from the antennas  104  and  106 . Although the main RFID receiver  112  is shown as a separate component in  FIG. 1 , the main RFID receiver  112  may be a subcomponent of the main RFID transmitter  108 . 
     The controller  120  generally controls the operation of the RFID system  100 . The controller  120  may be connected to, or may be a component of, a computer (e.g., a personal computer). The controller  120  may connect to other components, or may itself include components, that implement other functions such as RFID tag identification, RFID tag location determination, game rules verification, etc. The controller  120  may access various data stores or databases such as a game rules database, an RFID tag database, etc. 
     The RFID system  100  generally operates as follows. The transmitter  108  generates a radio frequency signal that is transmitted by the main antenna  102 . Any RFID gaming tags in the gameplay area respond to the radio frequency signal. The responses from the RFID gaming tags are received by the main receiver  112  (via the main antenna  102 ), at least one of the receivers  114  (via at least one of the antennas  104 ), and at least one of the receivers  116  (via at least one of the antennas  106 ). The controller  120  determines the position of each RFID gaming tag by correlating the responses received by each of the receivers. More details are provided with reference to  FIG. 2 . 
     According to another embodiment, the main receiver  112  may be omitted. 
       FIG. 2  is a flowchart of a method  200  of operating an RFID system (e.g., the RFID system  100  of  FIG. 1 ). The method  200  may be controlled by a controller (e.g., the controller  120  of  FIG. 1 ), for example, according to the execution of a computer program. In general, the method  200  describes a single RFID read cycle. Between read cycles, the RFID gaming tags are unpowered and do not send signals. During the RFID read cycle, each RFID gaming tag in the gameplay area responds. The RFID read cycle ends after each RFID gaming tag has responded. Thus, each RFID read cycle results in all the RFID gaming tags in the gameplay responding once but being read by multiple receivers. 
     At  202 , the controller controls a main RFID transmitter (e.g., the main RFID transmitter  108  of  FIG. 1 ) to generate an RFID inventory command. In general, the main RFID antenna is energized, and the RFID inventory command is one of a number of commands that may be included in the radio frequency energy generated by the main RFID transmitter. Further details of the RFID inventory command are provided below. A main antenna (e.g., the main antenna  102  of  FIG. 1 ) coupled to the main RFID transmitter transmits the RFID inventory command. The main antenna is associated with an area on a gaming table that contains one or more RFID tags (e.g., RFID gaming tags). 
     At  204 , each of the RFID tags responds to the RFID inventory command according to an anti-collision process. In general, the anti-collision process helps ensure that only one of the RFID tags is responding at a given time. Further details of the anti-collision process are provided below. 
     At  206 , a main RFID receiver (e.g., the main RFID receiver  112  of  FIG. 1 ) coupled to the main antenna receives a first set of responses from the RFID tags in the area in response to the RFID inventory command. 
     At  208 , a first set of RFID receivers (e.g., the RFID receivers  114  of  FIG. 1 ) coupled to a first set of antennas (e.g., the antennas  104  of  FIG. 1 ) receives a second set of responses from the RFID tags in the area in response to the RFID inventory command. The first set of antennas is oriented in a first direction and is associated with the area on the gaming table. 
     At  210 , a second set of RFID receivers (e.g., the RFID receivers  116  of  FIG. 1 ) coupled to a second set of antennas (e.g., the antennas  106  of  FIG. 1 ) receives a third set of responses from the RFID tags in the area in response to the RFID inventory command. The second set of antennas is oriented in a second direction that differs from the first direction, the second set of antennas overlaps the first set of antennas, and the first set of antennas and the second set of antennas intersect at a number of locations within the area. 
     As mentioned above, each RFID tag responds once, but each response is received by multiple antennas. For ease of description, these received responses are referred to as the “first set of responses”, the “second set of responses” and the “third set of responses” in  206 - 210  above. In general, each of the multiple antennas receives a particular response simultaneously. 
     Due to the anti-collision process, ideally only one of the RFID tags is responding at a given time, so controller is able to associate the responses received by each of the antennas at that given time with that one responding RFID tag. So generally  206 - 210  occur in parallel, with each RFID tag (ideally) responding at a given time and being detected by multiple receivers. For example, at a given time, the response from one RFID tag is received by the main RFID receiver, at least one of the first set of RFID receivers, and at least one of the second set of RFID receivers. 
     A brief description of the anti-collision process is as follows. The controller puts out a start of inventory command which includes a 5 bit cyclic redundancy check (CRC). This command also defines how many slots there are. The tag creates a random number and compares it to the particular slot number. If it matches then the tag responds with the 5 bit CRC from the command along with the 16 bit CRC of its serial number. If the controller receives this without detecting a collision then it resends the 5 bit CRC and the 16 bit CRC to the tags. The tag then responds by sending out its serial number and sets its flag so it does not respond to more queries until the flag is reset when RF power is removed. Thus, sending the CRC before the actual data speeds things as it is a shorter message to determine if there is a collision. 
     At  212 , a controller (e.g., the controller  120  of  FIG. 1 ) determines an identifier for each of the RFID tags using at least one of the first set of responses, the second set of responses, and the third set of responses. As discussed above, when a given tag responds with its serial number according to the anti-collision process, this response may be received by multiple RFID receivers (e.g., the main RFID receiver receives the first set of responses, including the response from the given tag; the first set of RFID receivers receives the second set of responses, including the response from the given tag; etc.). The controller may use one of the RFID receivers (e.g., the main RFID receiver) to determine the identifiers, and may use the information from the other RFID receivers for verification or confirmation purposes. When the current read cycle ends, the RFID tag loses power, the flag is cleared, and that RFID tag is free to respond during the next read cycle. 
     At  214 , the controller determines a position of each of the RFID tags by correlating amplitude and phase information of the first set of responses with amplitude and phase information of the second set of responses and amplitude and phase information of the third set of responses. Further details of this correlation process are provided below. In general, the controller uses the information from the first set of responses to modify the second set of responses in order to determine one dimension of the position (e.g., the x dimension), and uses the information from the first set of responses to modify the third set of responses in order to determine another dimension of the position (e.g., they dimension); the intersection of the x dimension and the y dimension then indicates the position of the RFID tag in the gaming area. 
     As an alternative in  214 , the controller may determine a position of each of the RFID tags by correlating amplitude information only (not phase information) of the first set of responses with amplitude and phase information of the second set of responses and amplitude and phase information of the third set of responses. In this alternative, the main RFID receiver just performs excitation, and its amplitude information is used for normalization purposes; the phase information from the first and second sets of antennas is used to determine the position. 
     As another alternative in  214 , the controller may determine a position of each of the RFID tags by correlating amplitude information of the first set of responses with amplitude information of the second set of responses and amplitude information of the third set of responses. 
     The controller may perform  212 - 214  in parallel, or may perform  214  prior to  212 . 
     Once all of the RFID tags have responded, the current read cycle is complete. When the controller performs the next read cycle, the controller performs the method  200  again. 
     The controller may then use the identifier and position of each of the RFID tags to perform other gaming functions such as verifying the amounts and placements of bets and payouts, verifying conformance of the RFID tag placements with various game rules, etc. Further details of these gaming functions are provided below. 
     As discussed above with reference to  FIG. 1 , an alternative embodiment omits the main RFID receiver. In such an embodiment, the controller determines the identifier (see  212 ) and the position (see  214 ) without using the first set of responses. 
       FIG. 3  is a graph showing a plot  300  of amplitude and phase information detected by one of the antennas  104  or  106  (see  FIG. 1 ) as the chip is moved across it. The plot  300  represents the amplitude and phase information resulting from the response of a single RFID tag at each given x position. For visualization purposes, imagine that we are using the antenna  104   a  (see  FIG. 1 ) to detect the RFID tag at each position. In  FIG. 3 , the antenna  104   a  has a width of approximately 2 inches, positioned between approximately 1.8 and 3.8 inches from the zero position  302 . So imagine that the RFID tag starts at the zero position  302 . This is outside the antenna  104   a  and has a zero amplitude, corresponding to the RFID tag not being detected. The left side of the antenna  104   a  begins at  304 . As the RFID tag moves from  302  to  304 , the antenna  104   a  detects the amplitude of the response from the RFID tag, which increases as the RFID tag nears the antenna  104   a . (The amplitude shown in  FIG. 3  is normalized using the response received by the main antenna  102  of  FIG. 1 .) Note that the amplitude of the plot  300  is negative between  302  and  304 ; this is due to the comparison of the phase information for the RFID tag detected by the main antenna  102  versus the antenna  104   a . Specifically, the phase information detected by the main antenna  102  is out-of-phase with the phase information detected by this antenna  104   a ; this out-of-phase result is shown as the negative amplitude in  FIG. 3 . The negative phase information indicates that the RFID tag is detected outside of the antenna  104   a.    
     When the RFID tag reaches  304  (directly above the left-side loop of the antenna  104   a ), the amplitude information is zero, corresponding to the RFID tag not being detected. As the RFID tag moves toward the center of the antenna  104   a , the amplitude increases, reaching a maximum of about 0.75 at  306 . Since the phase information detected by the main antenna  102  is in-phase with the phase information detected by the antenna  104   a , this indicates that the RFID tag is inside both antennas, and is shown by the positive amplitude curve of the plot  300  between  304  and  308 . As the RFID tag moves toward the right-side loop of the antenna  104   a , the amplitude decreases down to zero at  308 . 
     As the RFID tag continues past  308 , the antenna  104   a  detects that the amplitude information increases (negatively) for a bit before returning to zero at  310 . As before, the amplitude is shown as a negative value due to the phase information comparison between the main antenna  102  and the antenna  104   a . Since the RFID tag is inside the main antenna  102  but outside the antenna  104   a  between  308  and  310 , the comparison result is out-of-phase, and the amplitude of the plot  300  is shown as a negative between  308  and  310 . 
     As an example, imagine that the antenna  104   a  detects an amplitude of 0.2. Using just the amplitude information, the RFID tag could be at the position corresponding to one of six points:  320 ,  322 ,  324 ,  326 ,  330  or  332 . If the phase information indicates out-of-phase, the RFID tag could be at the position corresponding to one of the four points  320 ,  322 ,  324  or  326 . If the phase information indicates in-phase, the RFID tag could be at the position corresponding to one of the two points  330  or  332 . Next,  FIG. 4  shows how adjacent antennas can be used to narrow these multiple positions down to a single position. 
       FIG. 4  is a graph showing plots  400  and  402  of amplitude and phase information detected by two of the antennas  104 , or by two of the antennas  106  (see  FIG. 1 ). For illustrative purposes, assume that the plot  400  corresponds to the signal received by the antenna  104   a , similar to the plot  300  (see  FIG. 3 ); the plot  402  corresponds to the signal received by the nearby antenna  104   b . The antennas  104   a  and  104   b  may be referred to as adjacent antennas. The plots  400  and  402  are otherwise similar to the plot  300  (see  FIG. 3 ). 
     Due to the distance between the antennas  104   a  and  104   b , there is some overlap among the plots  400  and  402 . This overlap provides the RFID system  100  (see  FIG. 1 ) with the ability to correlate the amplitude and phase information detected by each antenna with the position of the RFID tag. 
     Returning to the example discussed above regarding  FIG. 3 , imagine that the antenna  104   a  detects an in-phase amplitude of 0.2, which indicates the RFID tag could be at the position corresponding to one of two points:  430  or  432 . Imagine that the antenna  104   b  detects an out-of-phase amplitude of 0.2, which indicates that the RFID tag could be at the position corresponding to one of four points:  450 ,  452 ,  454  or  456 . By correlating these measurements, the RFID system  100  determines that the position of the RFID tag is the one that corresponds to point  432  (antenna  104   a ) and point  450  (antenna  104   b ); on the gaming table, this position is slightly inside the right-hand side of the antenna  104   a . (Note that  FIG. 4  corresponds to a side view of the antenna  104   a , so in the overhead view of  FIG. 1 , the position of the RFID tag corresponds to one on a line slightly inside the right-hand side of the antenna  104   a .) Next,  FIG. 5  shows how to extend this example to two dimensions. 
       FIG. 5  is an overhead view of the antennas  104  and  106  of  FIG. 1 . Continuing the thought experiment discussed above regarding  FIG. 4 , imagine that the RFID system  100  uses the antennas  104  to determine that the RFID tag is on a position corresponding to the line  502 , due to the amplitude and phase information detected by the antennas  104   a  and  104   b . Further imagine that the RFID system  100  uses the antennas  106  to determine that the RFID tag is on a position corresponding to the line  504 , due to the amplitude and phase information detected by the antennas  106   a  and  106   b  (in a manner similar to that discussed above regarding the antennas  104   a  and  104   b ). The RFID system  100  is then able to determine the position of the RFID tag as the intersection of the lines  502  and  504 , position  506 . In this manner, the RFID system  100  is able to determine the positions of one or more RFID tags in the vicinity of the antenna array. 
       FIG. 6  is a block diagram of an RFID system  600 . The RFID system  600  shows a specific implementation of the RFID system  100  (see  FIG. 1 ). The RFID system  600  includes a main antenna  602 , a first set of antennas  604   a - 604   d  (collectively antennas  604 ), a second set of antennas  606   a - 606   d  (collectively antennas  606 ), an RFID reader  608 , a main RFID receiver  612 , a first set of RFID receivers  614   a - 614   d  (collectively RFID receivers  614 ), a second set of RFID receivers  616   a - 616   d  (collectively RFID receivers  616 ), and controllers  620   a  and  620   b  (collectively controllers  620 ). These components are similar to the components discussed above regarding the RFID system  100  (see  FIG. 1 ). The RFID system  600  also includes an oscillator  630 , a signal divider  632 , microprocessors  640   a - 640   i  (collectively microprocessors  640 ), a dual-directional coupler  650 , and a diode detector  652 . 
     The RFID reader  608  includes an RFID transmitter and a RFID receiver. The RFID transmitter is similar to the main RFID transmitter  108  (see  FIG. 1 ). The RFID receiver enables the RFID reader  608  to read the identifiers of the RFID tags, if so desired. The RFID reader  608  may be a “stock” or “off the shelf” RFID reader. The RFID reader  608  generates a radio frequency signal that is provided to the dual directional coupler  650 . The RFID reader  608  may also read the identifiers of the responses from any RFID tags in the area. 
     The oscillator  630  generates a first local oscillator signal at a desired frequency. For the RFID system  600 , the RFID tags are designed to operate at a frequency of 13.56 MHz. This frequency may be adjusted as desired in other embodiments. The oscillator  630  provides this first local oscillator signal to the receivers  612 ,  614  and  616  (as also shown in  FIG. 7 ), and to the signal divider  632 . 
     The signal divider  632  divides the first local oscillator signal from the oscillator  630  in order to generate a second local oscillator signal. For the RFID system  600 , the RFID tags are designed to operate with a modulation frequency of 424 kHz. Thus, the signal divider  632  divides the 13.56 MHz signal by 32 to get 424 kHz. The modulation frequency may be adjusted as desired in other embodiments. The signal divider  632  provides this second local oscillator signal to the receivers  612 ,  614  and  616  (as also shown in  FIG. 7 ). 
     The microprocessors  640  process the amplitude and phase information from the receivers  612 ,  614  and  616 , and provide the amplitude and phase information from each of the receivers to the controller  620   b . The microprocessors  640  receive an enable signal from the controller  620   b  to selectively enable them. 
     The dual-directional coupler  650  generally couples the RFID reader  608 , the main antenna  602 , the main RFID receiver  612 , and the controller  620   b  (via the diode detector  652 ). The dual-directional coupler  650  couples the radio frequency energy transmitted by the RFID reader  608  to the main antenna  602 , and directs a portion of the transmitted radio frequency energy to the controller  620   b  (via the diode detector  652 ). The dual-directional coupler  650  couples the radio frequency energy received by the main antenna  602  to the RFID reader  608 , and directs a portion of the received radio frequency energy to the main RFID receiver  612 . 
     The diode detector  652  generally functions as an envelope detector. The controller  620   b  uses the output of the diode detector to determine the time at which a tag may be responding. This allows the controller  620   b  to have the receivers  614  and  616  start sampling the antenna signals. 
     The controllers  620  generally control the operation of the RFID system  600 , as discussed above regarding the controller  120  (see  FIG. 1 ) and the method  200  (see  FIG. 2 ). The controller  620   a  generally controls the RFID reader  608 , and processes the data collected by the controller  620   b  in order to determine the positions of the RFID tags. The controller  620   a  may connect to the RFID reader  608  via an Ethernet connection, and may connect to the controller  620   b  via a universal serial bus (USB) connection. The controller  620   a  may be implemented with a computer (e.g., a personal computer) that is connected via a network to other devices. The controller  620   b  generally collects the amplitude and phase information received by the receivers  612 ,  614  and  616 . The controller  620   b  may be implemented with a microprocessor or a programmable logic device. 
     The RFID system  600  generally operates as follows. The controller  620   a  instructs the RFID reader  608  to transmit an inventory command. The RFID reader  608  turns on its radio frequency output and sends a signal to the RFID tags (e.g., by amplitude modulating the carrier signal of its radio frequency output). The dual-directional coupler  650  directs a portion of this signal to the diode detector  652 . The controller  620   b  monitors the output of the diode detector  652  in order to determine when to have the receivers start sampling for an RFID tag which may be responding to the RFID reader  608 . At this time, the controller  620   b  instructs the microprocessors  640 , using the enable signal, to begin sampling the RSSI information. When the controller  620   b  determines the end of the RFID tag response, the controller  620   b  uses the enable signal to instruct the microprocessors  640  to sample the I and Q levels from the receivers  612 ,  614  and  616 , and to process the RSSI information to determine the data returned by the RFID tag. (This data is generally the serial number of the RFID tag, in response to the inventory command.) The I and Q information determine the phase of the modulated second local oscillator signal of the response from the RFID tag (e.g., at 424 kHz). Note that the phase of the modulated second local oscillator signal is indeterminate when using a single one of the receivers  614  or  616 . However, by comparing the phase detected by one of the receivers  614  or  616  and the phase detected by the receiver  612 , the controller  620   b  is able to determine whether or not the RFID tag is inside of, or outside of, a given antenna loop. 
     The oscillator  630  provides the first local oscillator signal (e.g., 13.56 MHz) to the receivers  612 ,  614  and  616 , and to the signal divider  632 . The signal divider  632  generates the second local oscillator signal (e.g., 424 kHz) and provides this second local oscillator signal to the receivers  612 ,  614  and  616 . The RFID tags respond to the inventory command by load modulating a subcarrier signal onto the carrier signal transmitted by the RFID reader  608 . The receivers  612 ,  614  and  616  determine the modulated subcarrier signal from the RFID tags by first mixing the antenna signal first with the first local oscillator signal. After filtering and amplifying, the signal is mixed with the second local oscillator signal to demodulate the modulated subcarrier signal to baseband to determine the I and Q components. 
     The controller  620   b  analyzes the data from the receivers  614 , and the data from the receiver  612 , to determine the location of the RFID tag on the x axis. Similarly, the controller  620   b  analyzes the data from the receivers  616 , and the data from the receiver  612 , to determine the location of the RFID tag on the y axis. The controller  620   b  may use the RSSI from the receiver  612  to normalize the signals received from the other receivers  614  and  616  so that higher fidelity position information can be attained. 
     Although four sets of antennas  604  and antennas  606  (and their associated receivers  614  and  616 ) are shown, these numbers may be adjusted as desired. Similarly, the shapes of the antennas  604  and  606  may be adjusted. 
       FIG. 7  is a block diagram of a receiver  700 . The receiver  700  may be a specific implementation for one or more of the receivers  612 ,  614  or  616  (see  FIG. 6 ). The receiver  700  includes a mixer  702 , a band-pass filter  704 , an amplifier  706 , a band-pass filter  708 , a limiting amplifier  710 , mixers  712   a  and  712   b , a phase shifter  714 , resistors  716   a  and  716   b , and capacitors  718   a  and  718   b.    
     The receiver  700  is connected to one of the antennas (e.g., one of the antennas  602 ,  604  or  606  of  FIG. 6 ). The receiver  700  receives a first local oscillator (LO) signal  730  (e.g., at 13.56 MHz) from the oscillator  630  (see  FIG. 6 ), and receives a second local oscillator signal  732  (e.g., at 424 kHz) from the signal divider  632  (see  FIG. 6 ). 
     The mixer  702  mixes the radio frequency signal received by the antenna (e.g., one of the antennas  602 ,  604  or  606  of  FIG. 6 ) with the first local oscillator signal  730 , in order to generate a modulated subcarrier signal  734  (e.g., at 424 kHz). (The subcarrier signal  734  is a modulated subcarrier signal due to the radio frequency energy from the RFID reader (e.g.,  608  in  FIG. 6 ) being modulated by the RFID tag in the area.) 
     The band-pass filter  704  performs band-pass filtering on the modulated subcarrier signal  734  to reduce the noise, and generates a modulated subcarrier signal  736 . The band-pass filter  704  has a center frequency around the expected frequency of the subcarrier signal (e.g., 424 kHz). 
     The amplifier  706  amplifies the modulated subcarrier signal  736 , and generates a modulated subcarrier signal  738 . The band-pass filter  708  performs band-pass filtering on the modulated subcarrier signal  738  to further reduce the noise, and generates a modulated subcarrier signal  740 . The band-pass filter  708  has a center frequency around the expected frequency of the subcarrier signal (e.g., 424 kHz). 
     The limiting amplifier  710  drives the modulated subcarrier signal  740  into limiting (e.g., by having a high gain) so that the I and Q phase signals are independent of signal amplitude, resulting in a modulated subcarrier signal  742 . The limiting amplifier  710  also outputs a RSSI signal  744  that is proportional to the level of the modulated subcarrier signal  740  (e.g., in dB). The RSSI signal  744  is then provided to the controller  620   b  of  FIG. 6 , and corresponds to the RSSI or amplitude information discussed above. 
     The mixer  712   a  mixes the modulated subcarrier signal  742  with the second local oscillator signal  732  in order to extract a modulated signal  746 . The modulated signal  746  corresponds to the modulation of the subcarrier signal (e.g., at 424 kHz) performed by the RFID tag in the area. The resistor  716   a  and the capacitor  718   a  form a low-pass filter that performs low-pass filtering on the modulated signal  746 , resulting in an in-phase (I) signal  748 . The in-phase signal  748  is then provided to the controller  620   b  of  FIG. 6 , and corresponds to the in-phase (I) signal component discussed above. 
     The phase shifter  714  performs phase-shifting by 90 degrees on the second local oscillator signal  732  to generates a phase-shifted second local oscillator signal  733 . 
     The mixer  712   b  mixes the modulated subcarrier signal  742  with the phase-shifted second local oscillator signal  733  in order to create a demodulated signal  750 . The demodulated signal  750  corresponds to an unfiltered quadrature (Q) signal. The resistor  716   b  and the capacitor  718   b  form a low-pass filter that performs low-pass filtering on the demodulated signal  750 , resulting in a quadrature (Q) signal  752 . The quadrature signal  752  is then provided to the controller  620   b  of  FIG. 6 , and corresponds to the quadrature (Q) signal component discussed above. 
     As discussed above, the controllers  620  (see  FIG. 6 ) are able to determine whether a given RFID tags is inside of, or outside of, one or more of the antennas  604  and  606  by comparing the I and Q components received by that antenna with the I and Q components received by the main antenna  602 . 
     According to another embodiment, instead of the receiver  700 , the receiver may be implemented as a software defined radio. In general, a software defined radio samples the signal from the antenna with a high speed analog to digital converter, then processes the signals digitally, in order to detect the amplitude and phase. 
       FIG. 8  is a block diagram of an RFID system  800 . The RFID system  800  shows a specific implementation of the RFID system  100  (see  FIG. 1 ). The RFID system  800  includes a main antenna  802 , a first set of antennas  804   a - 804   d  (collectively antennas  804 ), a second set of antennas  806   a - 806   d  (collectively antennas  806 ), an RF transmitter  808 , a main RFID receiver  812 , a first set of RFID receivers  814   a - 814   d  (collectively RFID receivers  814 ), a second set of RFID receivers  816   a - 816   d  (collectively RFID receivers  816 ), controllers  820   a  and  820   b  (collectively controllers  820 ), an oscillator  830 , and a signal divider  832 . These components are similar to the components discussed above regarding the RFID system  100  (see  FIG. 1 ) or the RFID system  600  (see  FIG. 6 ). The RFID system  800  also includes a directional coupler  850 . 
     The RFID system  800  is similar to the RFID system  600  (see  FIG. 6 ), with the main differences being replacing the RFID reader  608  (see  FIG. 6 ) with the RF transmitter  808 , replacing the controller  620   b  with the controller  820   b , and replacing the dual-directional coupler  650  with the directional coupler  850 . In brief, the RFID system  600  (see  FIG. 6 ) is directed to using a “stock” or “off the shelf” RFID reader (the RFID reader  608 ), and the RFID system  800  is directed to using a controllable RF transmitter (the RF transmitter  808 ). 
     The oscillator  830  generates a first local oscillator signal at a desired frequency. For the RFID system  800 , the RFID tags are designed to operate at a frequency of 13.56 MHz. This frequency may be adjusted as desired in other embodiments. The oscillator  830  provides the first local oscillator signal to the receivers  812 ,  814  and  816 . The receivers  812 ,  814  and  816  may be implemented in a manner similar to the receiver  700  (see  FIG. 7 ), in which case this signal corresponds to the first local oscillator signal  730 . 
     The signal divider  832  divides the first local oscillator signal from the oscillator  830  in order to generate a second local oscillator signal. For the RFID system  800 , the RFID tags are designed to operate with a modulation frequency of 424 kHz. Thus, the signal divider  832  divides the 13.56 MHz signal by 32 to get 424 kHz. The modulation frequency may be adjusted as desired in other embodiments. The signal divider  832  provides this second local oscillator signal to the receivers  812 ,  814  and  816  (as also shown in  FIG. 7 ), in which case this signal corresponds to the second local oscillator signal  732 . 
     The directional coupler  850  generally couples the RF transmitter  808 , the main antenna  802  and the main RFID receiver  812 . The directional coupler  850  couples the radio frequency energy transmitted by the RF transmitter  808  to the main antenna  802 . The directional coupler  850  couples the radio frequency energy received by the main antenna  802  to the RF transmitter  808 , and directs the received radio frequency energy to the main RFID receiver  812 . 
     The controllers  820  generally control the operation of the RFID system  800 , as discussed above regarding the controller  120  (see  FIG. 1 ) and the method  200  (see  FIG. 2 ). The controller  820   a  generally acts as an interface to the other components. The controller  820   a  may connect to the controller  820   b  via an Ethernet connection. The controller  820   a  may be implemented with a computer (e.g., a personal computer) that is connected via a network to other devices. The controller  820   b  generally controls the RF transmitter  808 , collects the amplitude and phase information received by the receivers  812 ,  814  and  816 , and processes the amplitude and phase information to determine the positions of the RFID tags. The controller  820   b  may be implemented with a microprocessor or a programmable logic device. 
     The RFID system  800  generally operates as follows. The controller  820   b  controls the RF transmitter  808  using a modulation signal  860 . The RF transmitter  808  applies the modulation signal  860  to its RF carrier signal to command the tags (e.g., to transmit an inventory command using amplitude modulation of a subcarrier signal on the carrier signal of its radio frequency output). The directional coupler  850  directs this signal to the main antenna  802 . The controller  820   b  receives the amplitude and phase information (RSSI, I and Q) from the receivers  812 ,  814  and  816 . (This data is generally the serial number of the RFID tag, in response to the inventory command.) The I and Q information determine the phase of the modulated subcarrier of the response from the RFID tag (e.g., at 424 kHz). Note that the phase of the modulated subcarrier is indeterminate when using a single one of the receivers  814  or  816 . However, by comparing the phase detected by one of the receivers  814  or  816  and the phase detected by the receiver  812 , the controller  820   b  is able to determine whether or not the RFID tag is inside of, or outside of, a given antenna loop. 
     The oscillator  830  provides the first local oscillator signal (e.g., 13.56 MHz) to the receivers  812 ,  814  and  816 , and to the signal divider  832 . The signal divider  832  generates the second local oscillator signal (e.g., 424 kHz) and provides this signal to the receivers  812 ,  814  and  816 . The RFID tags respond to the inventory command by load modulating a subcarrier signal onto the carrier signal transmitted by the RF transmitter  808 . The receivers  812 ,  814  and  816  determine the modulated subcarrier signal from the RFID tags by mixing the detected subcarrier signal with the first local oscillator signal from the oscillator  830 . The receivers  812 ,  814  and  816  demodulate the modulated subcarrier signal to baseband to determine the I and Q components. 
     The controller  820   b  analyzes the data from the receivers  814 , and the data from the receiver  812 , to determine the location of the RFID tag on the x axis. Similarly, the controller  820   b  analyzes the data from the receivers  816 , and the data from the receiver  812 , to determine the location of the RFID tag on the y axis. The controller  820   b  may use the RSSI from the receiver  812  to normalize the signals received from the other receivers  814  and  816  so that higher fidelity position information can be attained. 
     Although four sets of antennas  804  and antennas  806  (and their associated receivers  814  and  816 ) are shown, these numbers may be adjusted as desired. Similarly, the shapes of the antennas  804  and  806  may be adjusted. 
       FIG. 9  is an overhead view of a set of overlapping antennas  900  in one direction. The overlapping of the antennas  900  increases the number of antennas that may receive the response from a given RFID tag, which increases the amount of data available to the RFID system and possibly increases the accuracy of the position determination of the RFID tag. The antennas  900  include antennas  900   a ,  900   b ,  900   c ,  900   d ,  900   e ,  900   f  and  900   g . The antennas  900  are associated with RFID receivers (not shown); these RFID receivers may be similar to the RFID receivers  114 ,  116  (see  FIG. 1 ),  614 ,  616  (see  FIG. 6 ),  700  (see  FIG. 7 ),  814 , or  816  (see  FIG. 8 ). Note that the antennas  900   e ,  900   f  and  900   g  are shown slightly offset, for illustrative clarity. 
     The antennas  900  may be used in place of one of the sets of antennas in a particular direction. For example, the antennas  900  may be used in place of the antennas  104  (see  FIG. 1 ) for the x direction, or the antennas  106  (see  FIG. 1 ) for the y direction. The antennas  900  may be used in place of the antennas  604  (see  FIG. 6 ) for the x direction, or the antennas  606  (see  FIG. 6 ) for the y direction. The antennas  900  may be used in place of the antennas  804  (see  FIG. 8 ) for the x direction, or the antennas  806  (see  FIG. 8 ) for the y direction. 
     The antennas  900  may be printed as dual layers on a printed circuit board. The number, and shape, of the antennas  900  may be adjusted as desired. 
       FIG. 10  is an overhead view of an antenna array  1000 . The antenna array  1000  includes a first set of antennas  1004   a ,  1004   b ,  1004   c  and  1004   d  (collectively antennas  1004 ), and a second set of antennas  1006   a ,  1006   b ,  1006   c ,  1006   d ,  1006   e ,  1006   f ,  1006   g ,  1006   h ,  1006   i  (collectively antennas  1006 ). As compared to other of the antenna arrays (e.g., the antennas  104  and  106  of  FIG. 1 ), the antennas  1004  and  1006  do not intersect at right angles. The antenna array  1000  may be used in place of the antennas  104  and  106  (see  FIGS. 1 ),  604  and  606  (see  FIGS. 6 ), or  804  and  806  (see  FIG. 8 ). The antennas  1004 , the antennas  1006 , or both, may be overlapping in a manner similar to that of the antennas  900  (see  FIG. 9 ). 
     The number, and shape, of the antennas  1004  and  1006  may be adjusted as desired. 
       FIG. 11  is an overhead view of a polar antenna array  1100 . The polar antenna array  1100  includes overlapping circular antennas  1104   a ,  1104   b ,  1104   c  and  1104   d  (collectively circular antennas  1104 ), and radial antennas  1106   a ,  1106   b ,  1106   c  and  1106   d  (collectively radial antennas  1106 ). The antennas  1104  are shown with dotted lines. As compared to other of the antenna arrays (e.g., the antennas  104  and  106  of  FIG. 1 ), the antenna array  1100  does not generate x and y position information, but instead generates polar position information (e.g., magnitude and direction). The circular antennas  1104  are used to determine the distance from the center point  1110 , and the radial antennas  1106  are used to determine the angle. The polar antenna array  1100  may be used in place of the antennas  104  and  106  (see  FIG. 1 ),  604  and  606  (see  FIG. 6 ),  804  and  806  (see  FIG. 8 ), or the antenna array  1000  (see  FIG. 10 ). 
     As an example, say that the system detects an RFID tag inside of the circular antenna  1104   d  and outside of the circular antenna  1104   c . If the system further detects that RFID tag outside of the radial antenna  1106   a , the system determines that the position of the RFID tag is in the vicinity of the point  1110 . The accuracy of the position determination can be determined according to the values of the signals detected, as discussed above regarding  FIGS. 3-4  (or as further detailed below in the section Determining the Positions). 
     As an option, the circular antennas  1104  need not be overlapping. Similarly, the radial antennas  1106  need not be overlapping. As another option, the circular antennas  1104  can be annular or ring-shaped, and overlapping or non-overlapping or partially overlapping. 
       FIG. 12A  is an overhead view of a Baccarat table  1200 , and  FIG. 12B  is an overhead view of a portion of the Baccarat table  1200  showing a corresponding portion of an antenna array  1202 . In  FIG. 12A , the entire antenna array  1202  is present, but not shown. In  FIG. 12B , the antenna array  1202  includes a first set of antennas  1204   a ,  1204   b ,  1204   c ,  1204   d ,  1204   e ,  1204   f ,  1204   g  and  1204   h  (collectively antennas  1204 ) and a second set of antennas  1206   a ,  1206   b ,  1206   c  and  1206   d  (collectively antennas  1206 ). The Baccarat table  1200  also includes one or more main antennas (not shown), similar to the main antenna  102  (see  FIG. 1 ). For one main antenna, it may surround the entire playing area of the Baccarat table  1200 . For two main antennas, each may cover a portion of the Baccarat table  1200 . For example, one may surround the betting positions on the left-hand portion of the Baccarat table  1200  (positions  7 - 12 ), and the other may surround the betting positions on the right-hand portion of the Baccarat table  1200  (positions  1 - 6 ). Alternatively, the main antenna can define a bounded area for some (or all) of a single type of bet (e.g. player or banker). Such an array can be used to track individual bets within the bounded area. 
     The antennas  1204  and  1206  (and the main antenna) are connected to RFID readers (not shown), in a manner similar to the RFID receivers  114  or  116  (see  FIG. 1 ). The antennas  1204  are wider at one end than at the other end. The antennas  1206  are slightly bent or curved, in order to conform to the Baccarat table  1200 . 
     As an option, the antennas  1204 , the antennas  1206 , or both may be overlapping in a manner similar to that of the antennas  900  (see  FIG. 9 ). 
       FIG. 13  is an overhead view of a roulette table  1300  having an antenna array  1302 . The antenna array  1302  includes a first set of antennas  1304   a ,  1304   b ,  1304   c ,  1304   d  and  1304   e  (collectively antennas  1304 ) and a second set of antennas  1306   a ,  1306   b ,  1306   c ,  1306   d ,  1306   e ,  1306   f ,  1306   g ,  1306   h ,  1306   i ,  1306   j ,  1306   k ,  1306   l ,  1306   m  and  1306   n  (collectively antennas  1306 ). The roulette table  1300  also includes a main antenna (not shown), similar to the main antenna  102  (see  FIG. 1 ), that surrounds the playing area. The antennas  1304  and  1306  (and the main antenna) are connected to RFID readers (not shown), in a manner similar to the RFID receivers  114  or  116  (see  FIG. 1 ). 
     As an option, the antennas  1304 , the antennas  1306 , or both may be overlapping in a manner similar to that of the antennas  900  (see  FIG. 9 ). 
     Finally, regarding the sizing of the antennas discussed herein, generally the width of each antenna should be less than the diameter of the RFID tags (or within around +/−0.5 inches of the diameter of the RFID tags), and the spacing between each antenna should also be less than the diameter of the RFID tags. 
     Reading the RFID Tags 
     As discussed above, the RFID reader (e.g., the RFID transmitter  108  of  FIG. 1 ) sends an inventory command (e.g.,  202  in  FIG. 2 ) that the RFID tags respond to (e.g.,  204  in  FIG. 2 ). The RFID tags include anti-collision features to mitigate interference resulting when two or more RFID tags respond at the same time. One anti-collision feature is a pseudo-random selection of the slot in which they respond. Statistically, the different pseudo-random slots among a plurality of RFID tags helps prevent them from all responding at the same time. 
     Another anti-collision feature is the 5 bit CRC that is added to the inventory command which is sent from the tag to the reader along with the 16 bit CRC of the serial number of the tag. If the CRCs are not correct then there is likely a collision. When all the RFID tags have been read, the RFID reader stops radiating energy, which causes the RFID tags to clear their flags; with the cleared flags, the RFID tags are free to respond when the RFID reader begins radiating energy again when sending the next inventory command. 
     The RFID reader may implement a slotted Aloha system or a binary tree search. In the slotted Aloha system, the RFID reader broadcasts an initialization command and a parameter that the tags individually use to pseudo-randomly delay their responses. In the binary tree search, the RFID reader sends an initialization symbol and then transmits one bit of identification data at a time; only RFID tags with matching bits respond, and eventually only one RFID tag matches the complete identification string. 
     Each RFID tag may include 96 bits of identification information, which allows for 2{circumflex over ( )}96 total RFID tags to be individually identified by the system. The RFID tags may send their responses using Manchester encoding of their modulation on the carrier signal from the RFID reader. 
     As a result of the anti-collision features, the system can generally operate as if only one RFID tag is responding at a given time. This allows all of the receivers (e.g., the receivers  112 ,  114  and  116  of  FIG. 1 ) that receive a response at a given time to associate together the respective responses received by each receiver. For clarity of illustration, the remainder of this document assumes that only one RFID tag is responding at a given time. 
     Determining the Positions 
     As discussed above, at least three receivers (e.g., the receiver  112 , at least one of the receivers  114 , and at least one of the receivers  116  of  FIG. 1 ) of the RFID system (e.g., the RFID system  100 ) receive the response from a given RFID tag. For a given antenna in the x direction (e.g., the antenna  104   b ), the RFID system can determine that the given RFID tag is inside of, or outside of, the given antenna by comparing the signal phases between the given antenna in the x direction and the main antenna (e.g., the main antenna  102 ). Similarly, for a given antenna in the y direction (e.g., the antenna  106   b ), the RFID system can determine that the given RFID tag is inside of, or outside of, the given antenna by comparing the signal phases between the given antenna in the y direction and the main antenna. When the RFID system determines that the given RFID tag is inside of both the x direction antenna and the y direction antenna, the RFID system determines the position of the given RFID tag on the gaming table as being at the position where those two antennas intersect. In a simple case, the RFID system assumes the position is at the midpoint of the intersection. 
     When the RFID system determines that the given RFID tag is outside of either the x direction antenna or the y direction antenna, the RFID system needs to determine which direction outside. As an example in the x direction, if the given RFID tag is detected outside of the antenna  104   b , the given RFID tag may be to the left of, or the right of, the antenna  104   b . At this point, the RFID system looks at the responses received by the antennas adjacent to the antenna  104   b  (e.g., the antennas  104   a  and  104   c ). If the antenna  104   a  received the response and the antenna  104   c  did not, then the RFID system determines the position of the given RFID tag as to the left of the antenna  104   b . Similarly, if the antenna  104   c  received the response and the antenna  104   a  did not, then the RFID system determines the position of the given RFID tag as to the right of the antenna  104   b . In a simple case, the RFID system assumes the position is at the midpoint between the two antennas ( 104   b  and  104   a , or  104   b  and  104   b ). In the y direction, a similar result occurs. 
     Interpolation 
     Instead of assuming the position at the midpoint, as discussed above, the RFID system (e.g., the RFID system  100  of  FIG. 1 ) may interpolate the position based on the amplitude of the received signal. For example, the RFID system may store the plot  300  of  FIG. 3  as a lookup table (e.g., in the controller  120 ). TABLE 1 is an example lookup table with 7 entries, corresponding to 7 segments of the plot  300  (where segment 1 is from point  302  down to the maximum negative value of the plot  300 ; segment 2 is from that point up to point  304 ; segment 3 is from point  304  up to near the maximum positive value of the plot  300 ; segment 4 is the portion around the maximum positive value; segment 5 is from near the maximum value down to point  308 ; segment 6 is from point  308  down to the maximum negative value of the plot  300 ; and segment 7 is from the maximum negative value up to point  310 ): 
     
       
         
           
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Segment 
                 Amplitude 
                 Position 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 From 0 to −0.25 
                 0.5 (approx. point 320) 
               
               
                 2 
                 From −0.25 to 0 
                 1.4 (approx. point 322) 
               
               
                 3 
                 From 0 to 0.7 
                 1.9 
               
               
                 4 
                 Above 0.7 
                 2.5 
               
               
                 5 
                 From 0.7 to 0 
                 3.2 
               
               
                 6 
                 From 0 to −0.25 
                 3.75 (approx. point 324)  
               
               
                 7 
                 From −0.25 to 0 
                 4.2 (approx. point 326) 
               
               
                   
               
            
           
         
       
     
     (Since the plot  300  is symmetric, the data in TABLE 1 may be reduced to 4 entries, as offsets around a center point.) As discussed above, there may be multiple points for a given amplitude detected by a single antenna, so the RFID system uses adjacent antennas in order to eliminate the unlikely points. 
     The position data in TABLE 1 corresponds to the midpoint of each segment of the plot  300 . Instead of using the midpoint when the amplitude falls anywhere within the appropriate range, the RFID system can interpolate using the exact amplitude. For example, if the amplitude is at −0.125 and (using adjacent antennas) the position is determined to be within the first segment, instead of using 0.5 as the position, the RFID system interpolates the position as halfway to 0.5, which is 0.25. The RFID system may use linear interpolation. 
     The number of entries in the lookup table may be increased, or decreased, as desired. As more entries appear in the lookup table, the interpolation becomes more accurate to the actual position. 
     In general, the values in TABLE 1 are applicable to the uniform-width antennas, such as in  FIG. 5 . For other antennas, such as the radial antennas  1106  of  FIG. 11 , or the antennas of  FIG. 12B , the values in the corresponding lookup tables may be determined empirically. 
     Integration with Game Rules 
     The RFID system (e.g., the RFID system  100  of  FIG. 1 ) may use the determined RFID information (e.g., the detected RFID tag identifiers and positions) to control various events in the gaming environment. In general, these events are managed according to game rules, and different game rules apply in different gaming circumstances (referred to as game states). When the RFID system detects a violation of the game rules, the RFID system may generate an alert. The RFID system may use the RFID readers described herein to determine the detected RFID tag identifiers and positions (generally referred to as chip data), and may use an instrumented card shoe to determine the values of cards dealt (generally referred to as card data). 
     In general, the game states are tailored to a particular game. For example, Baccarat may have the following game states: pre-game, new game, bets locked, payout, and end of game. In the pre-game state, the RFID system is not monitoring RFID tag identifiers or locations. In the new game state, the RFID system may track RFID tag identifiers and locations (and may display and record the resulting data), but since the game rules allow chips to be freely moved around in this state, no illegal move alerts are generated. (An exception may be made for detecting an illegal chip, which may result an illegal chip alert.) In the bets locked state, chip movements are not allowed, so any RFID tag movements detected may result in an alert. In the payout state, the RFID system monitors that the correct payout amounts are made to the correct locations, and that the correct collections are made from the correct locations, by correlating the RFID tags placed at (or removed from) the various locations. In the end of game state, the RFID system logs the end of the current game, and returns to the new game state for the next game. 
     A particular game state may include one or more sub-states (that may also be referred to as game states). For example, in blackjack, the dealer is obligated to deal another card to the dealer&#39;s hand depending upon the point total of the dealer&#39;s hand (e.g., 17). So within the game state of “deal cards to dealer&#39;s hand”, there is a sub-state of “deal another card” and a sub-state of “deal no more cards”. Similar states and sub-states exist for each hand. Similarly, if the dealer is dealt an initial Blackjack, the RFID system may transition from the “deal” state to the “collection/payout” state. As another example, Baccarat has a variety of sub-states within the gameplay state that each play position transitions between, depending upon the cards dealt. For example, the transition from play to payout can be staggered for each player. 
     The RFID system is particularly helpful during the collection and payout states. For example, the RFID system determines that Location 1 is a winner, and Location 2 is a loser, based on the game results. The RFID system knows the identifiers of the RFID tags associated with the locations, and verifies that additional chips corresponding to a correct payout are made to Location 1, and that the chips associated with Location 2 are collected. 
     Further information regarding the game rules and game states can be found in U.S. Application Pub. No. 2015/0312517 and U.S. Application Pub. No. 2016/0217645, which are incorporated herein by reference. 
     Grouping 
     The RFID system (e.g., the RFID system  100  of  FIG. 1 ) may associate RFID tags that have similar positions into a single group. (These similar positions refer to the x-y plane; e.g., two RFID tags stacked on top of each other will have similar x-y positions but different z positions.) For example, if the determined positions of two RFID tags are less than approximately 0.75× diameters, the RFID system may consider those two RFID tags to be associated in a group. For example, for RFID tags having a diameter of 1.5 inches, a group results when two RFID tags are within about 1.125 inches. Similar groups may be formed from adjacent stacks of RFID tags. The controller may then consider that group of RFID tags as a single unit. For example, instead of interpreting a first RFID tag and a nearby second RFID tag as two separate bets (e.g., $100 and $200), the controller groups the two RFID tags as a single bet (e.g., $300). Generally, the RFID system may consider a set of RFID tags to be a group when the position of each RFID tag in the set is within a defined range (e.g., 0.75× diameters) of at least one other RFID tag in the set. For example, a “stack” of RFID tags will have similar positions (e.g., much less than 0.75× diameters), so the RFID system determines that stack to be a group. As another example, a “mound” of RFID tags may have positions that in the aggregate that are beyond the defined range, but as long as each RFID tag in the mound is within the defined range of at least one other RFID tag in the mound, the RFID system determines that mound to be a group. 
     Grouping may also be used in combination with the game rules (e.g., the game states and sub-states). For example, in Blackjack, a player is allowed to “double down” (to double the amount of the initial bet) in certain circumstances. In such a situation, the RFID system first uses the card data to determine that the double down is allowed. Second, the RFID system uses the RFID data to verify that an accurate doubled bet has been placed as a group with the initial bet. (The RFID system may determine the initial bet to be a first group and the doubled bet to be a second group.) Third, the RFID system uses the card data to determine if the player&#39;s hand is a winner or a loser; for a winner, the RFID system uses the chip data to verify that correct payouts have been placed as additional groups with the initial bet and the doubled bet; and for a loser, the RFID system uses the chip data to verify that all the groups (the initial bet and the doubled bet) are collected. If any of the data indicates a violation of the game rules, the RFID system may generate an alert. 
     The defined range that the RFID system uses to determine a group may be adjusted as desired. For example, when the defined range is 1.5× diameters, the RFID system determines that two adjacent stacks are a group. 
       FIG. 14  is an overhead view of the antennas  104  and  106  of  FIG. 1 . As compared to  FIG. 5 ,  FIG. 14  includes 5 RFID tags  1402 ,  1404 ,  1406 ,  1408  and  1410 . Assume that each RFID tag takes 10 milliseconds (ms) to respond. Assuming no collisions, the read cycle takes 50 ms (10 ms per RFID tag): During this time, the main antenna (not shown) is energized, and the RFID reader connected to the antenna  104   a  receives the responses from the RFID tags  1402  and  1404 ; the RFID reader connected to the antenna  104   b  receives the responses from the RFID tags  1402 ,  1404  and  1406 ; the RFID reader connected to the antenna  104   c  receives the responses from the RFID tags  1406 ,  1408  and  1410 ; and the RFID reader connected to the antenna  104   d  receives the responses from the RFID tags  1408  and  1410 . (These responses correspond to the “second set of responses” discussed above, at  208  in  FIG. 2 .) During the same time, the RFID reader connected to the antenna  106   a  receives the responses from the RFID tags  1402  and  1408 ; the RFID reader connected to the antenna  106   b  receives the responses from the RFID tags  1402 ,  1406  and  1408 ; the RFID reader connected to the antenna  106   c  receives the responses from the RFID tags  1404 ,  1406  and  1410 ; and the RFID reader connected to the antenna  106   d  receives the responses from the RFID tags  1404  and  1410 . (These responses correspond to the “third set of responses” discussed above, at  210  in  FIG. 2 .) 
     Compare the above to a system that energizes each antenna separately (e.g., without a main antenna). In such a system, the RFID reader connected to the antenna  104   a  takes 20 ms to perform a read (10 ms for each of the RFID tags  1402  and  1404 ), the RFID reader connected to the antenna  104   b  takes 30 ms to perform a read (10 ms for each of the RFID tags  1402 ,  1404  and  1406 ), the RFID reader connected to the antenna  104   c  takes 30 ms to perform a read (10 ms for each of the RFID tags  1406 ,  1408  and  1410 ), and the RFID reader connected to the antenna  104   d  takes 20 ms to perform a read (10 ms for each of the RFID tags  1408  and  1410 ); so reading the x direction takes 100 ms (20+30+30+20). Similarly, reading the y direction also takes 100 ms, for a total read time of 200 ms. This is significantly more than the 50 ms discussed above. 
     Thus, the RFID systems described herein result in a notable improvement in read times as compared to existing systems that energize each antenna separately. 
     Additional Antenna Options 
       FIG. 15  is an overhead view of an antenna  1500  having a “figure 8” shape. The antenna  1500  may be used in the RFID systems discussed herein, such as the RFID system  100  (see  FIG. 1 ), the RFID system  600  (see  FIG. 6 ), the RFID system  800  (see  FIG. 8 ), etc. In the RFID system, the antenna  1500  may be used in place of the main antennas, such as the main antenna  102  (see  FIG. 1 ), the main antenna  602  (see  FIG. 6 ), the main antenna  802  (see  FIG. 8 ), etc. The antenna  1500  may connect to the transmitter  108  and the receiver  112  (see  FIG. 1 ), to the RFID reader  608  and the receiver  612  (see  FIG. 6 ), to the RF transmitter  808  and the receiver  812  (see  FIG. 8 ), etc. The antenna  1500  may be used with the antenna arrays discussed herein, such as the array formed by antennas  104  and  106  (see  FIG. 1 ), the array formed by the antennas  604  and  606  (see  FIG. 6 ), the array formed by the antennas  804  and  806  (see  FIG. 8 ), the antenna array  1000  (see  FIG. 10 ), the polar antenna array  1100  (see  FIG. 11 ), the antenna array  1202  (see  FIG. 12B ), the antenna array  1302  (see  FIG. 13 ), etc. 
     The antenna  1500  includes two loops, referred to as the upper loop and the lower loop (corresponding to the orientation shown in  FIG. 15 ). Where the loops cross, the wire of the antenna  1500  from one loop passes over that of the other loop, such that the antenna  1500  forms a single conductive path. (For example, a side view would show a gap between the loops where they cross, which is not evident from the overhead view.) As a result of the “figure 8” shape, the phase of the field of one loop is opposite that of the other loop (e.g., a 180 degree phase difference). 
     The antenna  1500  results in a null in the field where the loops cross to form the “figure 8” (e.g., along the horizontal centerline of the antenna  1500  as shown in  FIG. 15 ). (In the null, the RFID tags cannot be read.) To overcome the null, an antenna  1502  may be placed where the loops cross on the antenna  1500 . The antenna  1502  may be connected to the transmitter and the receiver (e.g.,  108  and  112  in  FIG. 1 ), selectively with the antenna  1500  (e.g., using a switch, multiplexer, etc.), as controlled by the controller (e.g.,  120  in  FIG. 1 ). The controller (e.g.,  120 ) may control the transmitter and the receiver (e.g.,  108  and  112 ) to perform a first read (e.g., generating an RFID inventory command) using the antenna  1500 , and to perform a second read (e.g., generating a second RFID inventory command) using the antenna  1502 . Any RFID tags that do not respond to the first read due to the null instead respond to the second read, thereby overcoming the null. 
     Alternatively, the antenna  1502  may be omitted, for example if the null is associated with a location in which it is undesired to read RFID tags (e.g., the null occurs in an area without a betting spot). 
     The shape and size of the antenna  1500  may be varied as desired. Instead of two similarly-shaped and similarly-sized loops as shown in  FIG. 15 , the loops may have different sizes, different lengths, different widths, etc. For example, one loop may have a smaller width and the other loop may have a larger width. As another example, one loop may have a smaller length and the other loop may have a larger length. The number of loops may be varied in the “figure 8” antenna, for example to have four loops, six loops, etc. 
       FIG. 16  is an overhead view of antennas  1604  (6 shown:  1604   a ,  1604   b ,  1604   c ,  1604   d ,  1604   e  and  1604   f ). The antennas  1604  may be referred to as vertical antennas as this corresponds to the view in  FIG. 16 . The antennas  1604  may be used with the antenna  1500  (see  FIG. 15 , as well as optionally the antenna  1502 ). (The antennas  1500  and  1502  are shown in  FIG. 16  with dotted lines to reduce the number of line crossings.) The antennas  1604  may be used in the RFID systems discussed herein, such as the RFID system  100  (see  FIG. 1 ),  600  (see  FIG. 6 ),  800  (see  FIG. 8 ), etc. In the RFID system, the antennas  1604  may be used in place of similar antennas such as the antennas  104  (see  FIG. 1 ),  604  (see  FIG. 6 ),  804  (see  FIG. 8 ),  900  (see  FIG. 9 ), the set of antennas in a first orientation in  FIG. 10  (e.g.,  1004   a ,  1004   b ,  1004   c  and  1004   d ), the set of antennas in a second orientation in  FIG. 10  (e.g.,  1004   e ,  1004   f ,  1004   g ,  1004   h  and  1004   i ), the antennas  1204  or  1206  (see  FIG. 12B ), the antennas  1304  or  1306  (see  FIG. 13 ), etc. 
     A noteworthy feature of the antennas  1604  is that each one crosses over both loops of the antenna  1500 . As a result, the antenna  1500  cancels out the carrier signal (e.g., 13.56 MHz) received by the antennas  1604 , making the sideband signal (which has the tag ID) easier to detect. For example, the antenna  1604   a  has a much easier job of detecting the sideband responses from the RFID tags sitting atop the antenna  1604   a . In general, the antennas  1604  are not “figure 8” antennas. 
     In general, the width of the antennas  1604  corresponds to the size of the RFID tokens. According to an embodiment, the antennas  1604  have a width of 1.5 inches. The size of the antennas  1604  may be adjusted as desired. 
     As an alternative, the antennas  1604  may be overlapping in a manner similar to the antennas  900  (see  FIG. 9 ). For example, when the antennas  1604  have a width of 1.5 inches, adjacent antennas may overlap by 0.25 inches. 
       FIG. 17  is an overhead view of antennas  1704  (6 shown:  1704   a ,  1704   b ,  1704   c ,  1704   d ,  1704   e  and  1704   f ) and  1706  (6 shown:  1706   a ,  1706   b ,  1706   c ,  1706   d ,  1706   e  and  1706   f ). (To reduce the clutter, the antennas  1704  are shown dotted and slightly offset from the antennas  1706 .) The antennas  1704  and  1706  may be referred to as horizontal antennas as this corresponds to the view in  FIG. 17 . The antennas  1704  and  1706  may be used with the antenna  1500  (see  FIG. 15 , as well as optionally the antenna  1502 ), and with the antennas  1604  (see  FIG. 16 ). (The antennas  1500  and  1502  are shown in  FIG. 17  with dotted lines to reduce the number of line crossings; the antennas  1604  are not shown.) The antennas  1704  and  1706  may be used in the RFID systems discussed herein, such as the RFID system  100  (see  FIG. 1 ),  600  (see  FIG. 6 ),  800  (see  FIG. 8 ), etc. In the RFID system, the antennas  1704  and  1706  may be used in place of similar antennas such as the antennas  106  (see  FIG. 1 ),  606  (see  FIG. 6 ),  806  (see  FIG. 8 ),  900  (see  FIG. 9 ), the set of antennas in a first orientation in  FIG. 10  (e.g.,  1004   a ,  1004   b ,  1004   c  and  1004   d ), the set of antennas in a second orientation in  FIG. 10  (e.g.,  1004   e ,  1004   f ,  1004   g ,  1004   h  and  1004   i ), the antennas  1204  or  1206  (see  FIG. 12B ), the antennas  1304  or  1306  (see  FIG. 13 ), etc. 
     A noteworthy feature of the antennas  1704  and  1706  is that they are “figure 8” antennas like the antenna  1500 . Another noteworthy feature of the antennas  1704  and  1706  is that each one does not cross over both loops of the antenna  1500 . However, since both loops of each particular one of the antennas  1706  do cross over a single loop of the antenna  1500 , the carrier signal cancellation feature (described above for  FIG. 16 ) is also applicable to the antennas  1704  and  1706 . 
     However, the “figure 8” shape of the antennas  1706  results in a null in the field where the loops cross to form the “figure 8” along line  1750 , similar to the null discussed above for  FIG. 15 . However, different from the strategy employed in  FIG. 15  to use the antenna  1502 ,  FIG. 17  uses the antennas  1704 . The crossover points of the antennas  1704  are offset from the vertical center line  1750  of the antennas  1706 , where the loops cross and where the null occurs. Thus, where there is a null in one of the antennas  1706  there is not in the corresponding one of the antennas  1704 , and vice versa. In this manner, the nulls of both the antennas  1704  and  1706  may be overcome. 
     As with the antenna  1502  (see  FIG. 15 ), the antennas  1704  may be omitted, for example if the null of the antennas  1706  is associated with a location in which it is undesired to read RFID tags (e.g., the null occurs in an area without a betting spot). 
       FIG. 18  is an overhead view of conductive traces  1800 . The conductive traces  1800  may be made from copper. The conductive traces  1800  may be etched onto a printed circuit board (e.g., that may also contain one or more of the antennas, etc.) or may be formed using copper tape. The conductive traces  1800  may be used with the “figure 8” antenna  1500  (see  FIG. 15 , and also with the optional antenna  1502 ), shown in  FIG. 18  with dotted lines to reduce the number of line crossings. The field of the antenna  1500  is not uniform; it is concentrated near the null between the two loops and around the perimeter of each loop. The conductive traces  1800  generally correspond to an interior border of each loop of the antenna  1500 , shown as the portions  1800   a  and  1800   b . The conductive traces  1800  result in the field being more uniform with little loss in field strengths. The uniformity of the field allows the antenna power to be reduced while still being able to read RFID tags anywhere within the area of the antenna. 
     When the conductive traces  1800  are formed using copper tape, each conductive tape portion (e.g.,  1800   a ) may be formed from multiple tape portions as shown, e.g. as 4 tape portions arranged as the sides of a rectangle. When the conductive traces  1800  are etched onto a printed circuit board, each portion (e.g.,  1800   a ) may be etched as a single continuous trace, or as multiple traces (similar to the tape portions). 
     Multiplexer 
       FIG. 19  is a block diagram of a multiplexer  1900 . The multiplexer  1900  may be used with any of the RFID systems described herein (e.g., the RFID system  100  of  FIG. 1 , the RFID system  600  of  FIG. 6 , the RFID system  800  of  FIG. 8 , etc.). The multiplexer  1900  connects to two or more antennas  1905  (4 shown:  1905   a ,  1905   b ,  1905   c  and  1905   d ) and to an RFID receiver  1915 . The multiplexer  1900  is controlled by a controller  1920 . 
     The antennas  1905  may be similar to the antennas described herein, such as the antennas  104  or  106  (see  FIG. 1 ),  604  or  606  (see  FIG. 6 ),  804  or  806  (see  FIG. 8 ),  900  (see  FIG. 9 ),  1004  (see  FIG. 10 ),  1104  (see  FIG. 11 ),  1204  or  1206  (see  FIG. 12B ),  1304  or  1306  (see  FIG. 13 ),  1604  (see  FIG. 16 ),  1706  (see  FIG. 17 ), etc. The RFID receiver  1915  may be similar to the RFID receivers described herein, such as the RFID receivers  114  or  116  (see  FIG. 1 ),  614  or  616  (see  FIG. 6 ),  700  (see  FIG. 7 ),  814  or  816  (see  FIG. 8 ), etc. The controller  1920  may be similar to the controllers described herein, such as the controller  120  (see  FIG. 1 ),  620  (see  FIG. 6 ),  820  (see  FIG. 8 ), etc. 
     In general, the multiplexer  1900  allows the number of receivers to be reduced in the RFID system. Consider the RFID system  100  of  FIG. 1 . The main RFID receiver  112  reads the serial numbers of the RFID tag. The other receivers such as  114   a - 114   d  and  116   a - 116   d  only need to determine the amplitude and/or phase of the signal from the RFID tag. The amplitude and/or phase of the RFID tag signal can be determined in a small fraction of the total RFID tag transmission. This allows the use of a single receiver (e.g.,  1915 ) to read multiple antennas all within the transmission time of the RFID tag. The controller  1920  controls the multiplexer  1900  to selectively route the signals received by the antennas  1905  to the receiver  1915 . When the main RFID receiver  112  determines that a RFID tag may be transmitting, the controller  1920  selects one of the antennas (e.g.,  1905   a ) and measures the amplitude and/or phase received by the receiver  1915 . The controller  1920  dwells on that antenna for a fraction of the RFID tag transit time (e.g., about ⅛th the RFID tag transit time). The controller  1920  then does the same for the other antennas (e.g.,  1905   b - 1905   d ) in the following fractional time windows. At the completion of the RFID tag transmission, the controller  1920  then uses the received amplitude and/or phase from all the antennas  1905  to determine the location of the RFID tag. 
     For example, in the RFID system  100  (see  FIG. 1 ), one or more of the receivers (e.g., one or more of  114  and  116 ) may be removed, and the outputs from two or more antennas (e.g., two or more of  104 ,  106 ) may be routed through the multiplexer  1900  to the RFID receiver  1915 . The controller  1920  controls the multiplexer  1900  to selectively connect each of the antennas ( 104 ,  106 , etc.) to the receiver  1915 . In this manner, the single RFID receiver  1915  may connect through the multiplexer  1900  to selectively read each of the antennas (e.g.,  104  and  106 ). The multiplexer  1900  may be used in a similar manner regarding the RFID system  600  (see  FIG. 6 ), the RFID system  800  (see  FIG. 8 ), etc. 
     An example of using only phase information with the overlapping antennas  900  (see  FIG. 9 ) is as follows. (This example determines the position on the x-axis.) For a particular detected RFID tag, the RFID system normalizes the phase of the antenna with the largest signal strength (e.g.,  900   b ) to zero degrees and looks at the phase detected at the adjacent antennas (e.g.,  900   e  and  900   f ). If both the adjacent antennas have the opposite phase (e.g., 180 degrees), the position of the RFID tag is determined to be in the center of the antenna  900   b  (e.g., where the antennas  900   e  and  900   f  do not overlap with  900   b ). If one antenna (e.g.,  900   e ) has the same phase (e.g., zero degrees) and the other antenna ( 900   f ) has the opposite phase (e.g., 180 degrees), the position of the RFID tag is determined to be on the left side of the antenna  900   b  (e.g., where the antennas  900   b  and  900   f  overlap). The y-axis direction may be determined in a similar manner (e.g., using a set of antennas oriented in the other direction). 
       FIG. 20  is an overhead view of an antenna arrangement  2000 . The antenna arrangement  2000  includes one or more antennas (not individually shown) that are associated with an area  2003  and one or more antennas  2010  (4 shown:  2010   a ,  2010   b ,  2010   c  and  2010   d ). The antennas in the antenna arrangement  2000  may connect to other components of an RFID system discussed herein, such as an RFID reader (see, e.g.,  FIG. 1 ,  FIG. 6 ,  FIG. 8 , etc.), a multiplexer (see  FIG. 19 ), etc. 
     The area  2003  generally corresponds to a read area (e.g., a betting spot on a gaming table), and the antennas associated with the area  2003  may be similar to one or more of the antennas discussed herein (e.g., the antennas  102  or  104  or  106  of  FIG. 1 ; the antennas  602  or  604  or  606  of  FIG. 6 ; the antennas  802  or  804  or  806  of  FIG. 8 ; the antennas  900  of  FIG. 9 ; the antennas  1004  of  FIG. 10 ; the antenna array  1100  of  FIG. 11 ; the antenna array  1302  of  FIG. 13 ; the antennas  1500  or  1502  of  FIG. 15 ; the antennas  1604  of  FIG. 16 ; the antennas  1704  or  1706  of  FIG. 17 ; the antennas  1905  of  FIG. 19 ; etc.). 
     The antennas  2010  may be referred to as outside antennas because they are outside the area  2003 . The return flux path of the antennas associated with the area  2003  may extend outside of the area  2003 , and may thus energize RFID tags that are outside of the betting area. If an RFID tag outside the area  2003  is energized, one or more of the outside antennas  2010  receive the signal from that RFID tag. If the RFID system detects that the received signal level for that RFID tag is greater at one of the antennas  2010  than at one of the antennas associated with the area  2003 , then the system may exclude that RFID tag from being associated with the area  2003 . In this manner, the RFID system more accurately detects that the RFID tag is within the area  2003 , instead of nearby (but outside) the area  2003 . 
     The above description illustrates various embodiments of the present invention along with examples of how aspects of the present invention may be implemented. The above examples and embodiments should not be deemed to be the only embodiments, and are presented to illustrate the flexibility and advantages of the present invention as defined by the following claims. Based on the above disclosure and the following claims, other arrangements, embodiments, implementations and equivalents will be evident to those skilled in the art and may be employed without departing from the spirit and scope of the invention as defined by the claims.