Patent Publication Number: US-6663486-B2

Title: Gaming simulation program providing selection of betting and playing strategies

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims priority under U.S. Provisional Application Serial No. 60/294,483, filed May 30, 2001. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Technical Field 
     The present invention relates to a gaming simulation program and more particularly, to a gaming simulation program providing for user selection of gaming and betting strategies. 
     2. Background Information 
     A number of computer programs have been developed to permit a user to simulate the playing of various games of chance such as poker, blackjack, bingo and the like. Some programs are available on CD ROM or floppy diskettes and are adapted for installation and use on personal computers. Programs are also burned into integrated circuit memory chips installed in hand held electronic devices. Computer programs and hand held devices programed to simulate games of chance conveniently permit the user to simulate the playing of sequential hands or rounds of a selected game of chance and track the results of playing a given number of hands by displaying, for example, a running total of the user&#39;s “bankroll,” i.e., how much “money” the user has at any given time assuming the user started the playing session with an initial bankroll. 
     Lacking in prior art gaming simulation programs and devices is the ability to simulate the results of playing multiple rounds or hands of a selected game of chance using both a selected betting strategy and a selected playing strategy and displaying simulation result statistics so the user can intelligently analyze different combinations of playing and betting strategies. 
     What is needed is a gaming program and method for its use that allows the user to select between different games of chance and, for a selected game of chance, to further select a betting strategy from a set of betting strategies and a playing strategy from a set of playing strategies and to simulate the playing of a plurality of hands using the selected betting and playing strategies. What is further needed is a gaming program and method for its use that provides comprehensive statistics to enable a user to determine the results of the simulation of a plurality of hands using the selected betting and playing strategies to enable the user to determine the relative merits of the selected strategy vis-a-vis other strategies. What is further needed is a gaming program and method of use to enable a user to be taught various strategies and techniques in playing various games of chance and to enhance his skill in employing such strategies and techniques. What is also needed is a gaming program and method for its use that is relatively inexpensive and easy to use. 
     SUMMARY OF THE INVENTION 
     The present invention concerns a gaming simulation computer program for use on a personal computer. The program provides for user selection of both gaming and betting strategies. A betting strategy is a decision rule for deciding how much to bet on any given hand or game. For example, a simple betting strategy would be: if I won the last hand, I will double my previous et on the next hand, and if I lost the last hand, I will reduce my previous bet by half on the next hand. A gaming strategy is a decision rule or rules selecting a course of action to be taken when a non-betting amount question arises. For example, in the card game known as war, in a first hand, if the dealer and the player are both dealt cards that have the same numeric value, the player must choose to either surrender or not surrender. If the gaming strategy decision rule selected by the player is to surrender, the player loses one half of his or her current bet and a new hand is dealt. If the gaming strategy decision rule selected by the player is to not surrender, the player puts up additional money to match his current bet while the dealer does not. A second hand is dealt, the player and the dealer each receiving a card, the winner (i.e., the person receiving the card with the higher numeric value) of the new hand takes all of the money put up in the first and second hands. 
     In one operating embodiment of the present invention, the single step mode, the user selects a betting strategy and a playing strategy, selects a starting bankroll and determines the number of rounds or hands to be simulated. The simulation program, operating in single step mode, allows the user to step through the simulated playing of the hands on a one at a time basis prompting each hand to be played with a keystroke. Statistics are collected during the simulation gaming session. Upon completion of the simulation gaming session, statistics summarizing the results of the simulation are selectively displayed to the viewer, including occurrences of winning and losing streaks of different lengths and maximum and minimum bankroll values. 
     In a second operating embodiment of the present invention, the automatic mode, the user selects a betting strategy and a playing strategy, selects a starting bankroll and determines the number of hands to be simulated during a gaming session. Operating in automatic mode, the simulation program runs the simulation of the selected number of hands in automatic mode at a selected speed (hands dealt per time period) from a range of speeds, displaying each hand on a display screen of the computer monitor at a speed selected in terms of number of hands dealt per time period. Again, statistics are collected during the simulation gaming session. Upon completion of the simulation, statistics summarizing the results of the simulation are selectively displayed to the viewer, including occurrences of winning and losing streaks of different lengths and maximum and minimum bankroll values. 
     In a third operating embodiment of the present invention, the session operating mode, the user selects a betting and playing strategy, a starting bankroll, a maximum session winning amount cut-off, a maximum session losing amount cut-off, a bail out percent, and the maximum number of hands to be played in total. The simulation proceeds on a gaming session by gaming session basis. A gaming session consists of a simulation of successive hands until the maximum session winning amount or maximum session losing amount is achieved, or, if the user is on a winning streak, the session will continue until the current session bankroll declines by an amount greater than the maximum session bankroll amount multiplied by the bail out percentage. The current session bankroll is then carried over to the next gaming session. Upon completion of the total number of hands specified (or a current bankroll value of zero, whichever comes first), the simulation is completed and statistics are displayed for each session of the simulation. 
     These and other objects, features and advantages of the invention will become better understood from the detailed description of the preferred embodiments of the invention which are described in conjunction with the accompanying drawings. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The present invention is further described with reference to the accompanying drawings in which: 
     FIG. 1 is a conceptual diagram showing modules of the gaming simulation module; 
     FIG. 2 is a user interface block diagram of the war game of the gaming simulation program; 
     FIG. 3 is a block diagram showing the use of the application main screen for selecting play in the war game gaming simulation program shown in FIG. 2; 
     FIG. 4 is a block diagram of the application play logic for the war game of the gaming simulation program shown in FIG. 2; 
     FIG. 5 is a block diagram showing use of the multiple session screen for the gaming simulation program shown in FIG. 2; 
     FIG. 6 is a block diagram of the multiple session play logic for the gaming simulation program shown in FIG. 2; 
     FIG. 7 is a representation of a first screen display of a war game of the gaming simulation computer program of the present invention in which betting strategy is selected; 
     FIG. 8 is a representation of a second screen display of the war game of the gaming simulation program which is the game configuration screen for streak betting; 
     FIG. 9 is a representation of an alternate second screen display of the war game of the gaming simulation program which is the game configuration for variable betting; 
     FIG. 10 is a representation of a third screen display of the war game of the gaming simulation program which is the play screen for the selected configuration; 
     FIG. 11 is a fourth screen display of a war game of the gaming simulation program which is an advance statistics summary of a game; 
     FIG. 12 is a fifth screen display of a war game of the gaming simulation program which is the screen employed in the multiple session simulation mode; 
     FIG. 13 is a sixth screen display of a war game of the gaming strategy which is an hourly statistics summary of a game; 
     FIG. 14 is a user interface block diagram of a blackjack game of a preferred embodiment of the gaming simulation program of the present invention; 
     FIG. 15 is a block diagram showing the application main screen illustrating play selection in the gaming simulation program shown in FIG. 13; 
     FIG. 16A is a block diagram illustrating application play logic for the gaming simulation program shown in FIG. 13; 
     FIG. 16B is another block diagram showing application play logic for the gaming simulation program shown in FIG. 13; 
     FIG. 17 is a block diagram showing use of the multiple session screen for the gaming simulation program shown in FIG. 13; 
     FIG. 18 is a block diagram of the multiple session play logic for the gaming simulation program shown in FIG. 13; 
     FIG. 19 is a representation of a first screen display of a blackjack game of the gaming simulation computer program of the present invention in which betting strategy is selected; 
     FIG. 20 is a representation of a second screen display of the blackjack game of the gaming simulation program which is the game in configuration screen for street betting; 
     FIG. 21 is a representation of an alternative second screen display of the blackjack game of the gaming simulation program which is a game configuration for variable betting; 
     FIG. 22 is a third screen display of the blackjack game of the gaming simulation program which is the play screen for the selected configuration; 
     FIG. 23 is a fourth screen display of the blackjack game of the gaming simulation program which is a game configuration screen for adjusting playing strategies; 
     FIG. 24 is a fifth screen display of the blackjack game of the gaming simulation program which is an advanced statistic display; 
     FIG. 25 is a sixth screen display of the blackjack game of the gaming simulation program which is a multiple session simulation display; and 
     FIG. 26 is a seventh screen display of the blackjack game of the gaming simulation program which is an hourly statistics summary of a game. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to the drawings, the gaming simulation computer program of the present invention is shown conceptually at  10  in FIG.  1 . The program  10  consists of a simulation module  12 , a statistics module  14 , and gaming modules including a war game module  16  and a blackjack module  18 . One skilled in the art would recognize that other gaming modules such as craps, poker, keno, baccarat, etc. may be advantageously added to the program  10 . It should be understood that the present invention is not limited to the two specific games of chance noted. The program  10  preferably is stored on a computer readable media such as a compact disk (CD ROM)  20 , inserted in a CD device  22  in a personal computer (PC)  24  on which the program  10  is new. One skilled in the art, however, would recognize that the program  10  may be run on a dedicated electronic device, such as a hand held electronic game device, instead of the PC  24 . The PC has a monitor  26  along with a keyboard  28  and a mouse  30 . 
     The program  10  includes a war game module  12 . A block diagram of the war game simulation module  16  is shown in FIG.  2 . The module  16  and  18  are programed in the C++ programming language and are suitable to run in a WINDOWS 98 environment. Of course, those skilled in the art will recognize that there are other suitable programming languages that could be used to program the simulation concepts of the present invention. 
     Referring to FIG. 2, in step  32  of the game, the user selects a playing strategy. The user then selects a betting strategy in step  34 , either streak or function. In step  36 , streak betting amounts are selected. Alternatively, in step  38  variable betting amounts are selected. With either betting strategy in step  40  there is a selection of playing mode. Such playing mode may be a single hand mode as in step  42 , an automatic mode as in step  44 , or a session mode as in step  46 . If the session mode is selected, a bail out percentage is selected in step  48 . With either the automatic mode in step  44  or the session mode in step  46 , there is a selection of hands to be played in step  50 . There is also a selection of speed play in step  52  then a display of statistics in step  54 . 
     In the game of war, the playing strategy involves the selection of a surrender strategy or a no surrender strategy which is employed in the event that in a particular hand the numeric value of the card dealt to the “dealer” matches the numeric value of the card dealt to the user or “player”. A number card has a numeric value equal to the card number, e.g., a three of hearts has a numeric value of three. A face card, jacks, queens, kings and aces have the following numeric values, a jack has a numeric value of 11, a queen has a numeric value of 12, a king has a numeric value of 13, and an ace has a numeric value of 14. 
     A war would occur in a hand where the dealer and the player are dealt cards with identical numeric values. The surrender strategy, if selected by the player, means that when a war occurs, the player opts to complete the war hand by surrendering one half of his or her current bet to the dealer. The next hand is then dealt as if the war hand did not occur, that is, the war hand does not count as a win or a loss for purposes of computing the player&#39;s winning or losing streak length. The no surrender strategy, if selected, means that when a war occurs, tiebreaker or war breaker hand is dealt to decide the winner of the war hand, the player increases the “pot” by putting up an additional amount of money to match the current bet (in effect, doubling the current bet of the war hand). The winner of the tiebreaker hand takes the entire pot, that is, three times the player&#39;s current bet on the war hand. The total pot is determined as follows: total pot=the player&#39;s current bet for the war hand+the dealer&#39;s current bet for the war hand (which matches the player&#39;s current bet for the war hand)+the player&#39;s tiebreaker hand bet (which matches the player&#39;s current bet for the war hand). In the event that the tiebreaker hand results in another war, the same process is repeated. The outcome of the tiebreaker hand is counted as a win or a loss, as appropriate, in determining the player&#39;s winning or losing streak length. 
     In one preferred embodiment of the present invention, the player selects between a fixed betting strategy and a variable betting strategy. At a input block, the player inputs the winning and losing sequence length or number of hands that he or she wishes to enter bet amounts for. 
     Betting strategy involves selecting winning sequence lengths (WS) and associated bet amounts for winning streaks of length  1  through WS, selected losing sequence length and associated bet amounts for losing streaks for bet amounts. 
     Playing options include selecting the number of decks in shoe (list options). The cards dealt for each hand are selected via a random number generator subroutine in the program. The cards for the “dealer” and the user for each hand are concurrently displayed in a playing area. In the automatic and session modes, maximum speed of playing is a hand being dealt every 0.1 seconds. The statistics routine displays the results of the hands played. 
     Referring to FIG. 3, a single run application  56  initiates the application play logic  58  that is shown in FIG.  4 . Multiple session  60  initiates the multiple session screen  62  as is shown in FIG.  5 . Advanced statistics  64  initiates a page that displays statistical information concerning streak length and frequency of streaks  66  as is illustrated, for example, in FIG.  5 . 
     Referring to FIG. 4, the application play logic begins by determining at step  68  if the hand played is less than or equal to the number of hands to play. If it is not at step  70 , play stops and control is returned to the application. If it is, at step  72  the first card is dealt to the first player and dealer. The determination at step  74  is then made if the player wins. If the player does not win, the dealer wins at step  78  which at step  80  there is a increment value displayed loss. If the dealer does not win at step  78 , a determination at step  82  is made as to whether the player surrenders if a war occurs. If the player surrenders at step  84 , increment variables display loss of surrender and the next bet is adjusted based on betting strategy. If the player does not surrender at step  86 , a second card is dealt to player one and the dealer. If the player wins or ties dealer at step  88 , increment variables display winnings at step  90  and the next bet is adjusted based on betting strategy. If the player does not win or tie the dealer, increment values are displaying loss at step  92  and the next bet is adjusted based on betting strategy. 
     Referring to FIG. 5, the multiple session screen is shown generally at numeral  94 . This screen  94  has inputs for betting strategy to use  96 , number of times to play  98 , reset  102 , cancel  104 , and return to game  106 . There is also a display grid  108 . There is also a maximum winning amount entry  110  which at step  112  causes the session to quit when the amount won is greater than or equal to this amount. There is a maximum losing amount entry  114  which at step  116  causes the session to quit when the amount lost is greater than or equal to this amount. There is a starting bankroll  118  which enters a current bankroll when the session starts at step  120 . There is a bailout percent entry  122  which enters the percentage for bailout at step  124 . That is, if the winnings supersede the winning amount entered, play will continue until the player has lost this percentage of the maximum amount won. For example, if the maximum winnings are $400.00 and the bailout is 10% and current winnings are $600.00, there will be a stop play when the player loses $60.00 or 10% of maximum winnings. The deal input  126 , at step  128  refers to FIG. 6 which results in a determination at step  130  if current play is less than or equal to the number of times to play. Then, referring to FIG. 6, playing logic is initiated at step  132 . At step  134  after each hand is played, there is a check of maximum and minimum loss or bailout. If the amount has reached such maximum or minimum or bailout amounts, then at step  136  data is recorded for display on the grid  108  and continues to the next play at step  130  where it is again determined if current play is less than or equal to the number of times to play. If at step  134  it is determined that the amount won or lost of the percentage of loss is not outside the maximum or minimum amount or bailout amount, then play logic again begins at step  132 . 
     FIGS. 7-13 are representative illustrations of the displays or screen shots that would be seen on a display or monitor by the user playing the war game module  12 . FIG. 8 shows an initial screen entitled “Game Configuration” displayed to the user or player when the war game module is selected. Not shown is an initial menu screen in which the user selects the desired game by double clicking on an icon representative of the war game module which is displayed on the monitor. The initial screen called the Game Configuration Screen includes prompts for input of the playing strategy, the betting strategy and card deck options to be made by the user. 
     In the first screen shown, the player would select either a streak betting strategy or a variable betting strategy. On the great game configuration screen, the player will select both a playing strategy and a betting strategy. In the game of war, the playing strategy comprises of selection of either to surrender when a war occurs or to not surrender when a war occurs. A streak betting strategy may also be selected in which the player may select the length of a winning sequence and the length of a losing sequence. Depending on the length of the streak, a specific amount for a bet may also be selected. For example, if the winning streak has a length of 1, a bet of 5 may be selected. If the winning streak has a bet of 2, a bet of 10 may be selected. In the same way, winning streaks of 3, 4, and 5 may result in bets of 20, 30, and 40. Of course, different specific amounts for the bets may be selected for each of these winning streaks. Corresponding bets may be selected for the losing streak. It will be understood that the amount of bets for both winning and losing streaks may or may not be the same. In addition to a default playing strategy in which a decision is made only to as to whether to surrender or not surrender in event of war. A strategy may be followed in which an assumption is made that the dealer won&#39;t win four hands in a row. In another possible strategy, an assumption is made that the player will win the first two hands. The selection of either of these three strategies may result in variations in the number of decks in the shoe, the winning sequence, and the losing sequence. A preferred size of shoe in winning and losing sequence for each of a default strategy, and the other two strategies, is set forth in Table I. Preferred betting strategies are shown in Table II in which the amount to bet on the next hand for winning and losing streaks of various strengths when various assumptions are made. The abbreviation “W” herein means win or winning and the abbreviation “L” means losing. It will be understood, however, that within these strategies, the decks and the shoes and the winning and losing streaks may be adjusted. As an alternative to using the streak betting strategies as will be employed using the screen shown on FIG. 8, a variable betting strategy may be employed using the screen of FIG.  9 . Using this screen, variable betting configuration can be employed. Like the streak betting configuration screen used on FIG. 8, with the variable betting configuration, a playing strategy can be selected regarding whether to surrender when a war occurs. Specific initial bets, maximum bets, and minimum bets may also selected and a decision may be made regarding whether to maintain the maximum bets after that point is reached or to return to the initial bet. Similarly, after the minium bet is reached, a decision may also be made as to whether to maintain the minimum bet or use the initial bet. A flat dollar strategy is employed wherein a specific amount may be added to or subtracted from the bet in the event of either a winning hand or a losing hand. After either a streak betting configuration or a variable betting configuration has been selected in the way described above, the game has begun using the screen shown in FIG.  10 . On this screen, either a continuous deal or a single hand deal arrangement may be selected. The number of hands to be played as well as the speed of play may also be selected. On this screen, bankroll data, total hand data, and winning or losing streak data will also be displayed to the player. From the screen shown in FIG. 10, an advanced statistic screen shown in FIG. 11 may be viewed. On this screen, detailed winning streak and losing streak data is displayed so that the player will be able to ascertain the number of times and a total number of times winning streaks and losing streaks were stopped at particular numbers. From the game screen shown in FIG. 10, a multiple session simulation as shown in FIG. 12 may also be selected. From the multiple session simulation screen shown in FIG. 12, hourly statistics as shown in FIG. 13 may also be selected. 
     In the configuration for the blackjack game, a playing strategy may be selected in which the player selects whether to hit or stand on any combination of initial two cards based on the dealer&#39;s face card value. The player may also elect whether to split, double down, or take insurance in various situations. By the terms “hit” and “stand”, what is meant is that a player elects respectively to accept a card or to not accept a card. In a “split” an existing initial hand is divided into two hands. When a player “double downs” it is meant that he doubles his bet. An “insurance” bet is one against the player&#39;s own hand in various situations. Depending on house rules, the player may double down on any hand or on a 10 and an 11 only. The player may also double down on splits. House rules may also be elected as to whether the dealer must stand on a soft 17 or be hit on a soft 17. by the term “soft” it is meant that an initial two card hand includes an ace. It may also be decided if in a contingency when a player has 21 and the dealer has an ace up to take insurance, take even money, or play out the hand. In the blackjack game, betting strategy may also be elected as to bankroll data, total hand data, and winning streak or losing streak data. The rules for the game of blackjack are well known and are described, for example, in  Hoyle&#39;s Rules of Games , second edition (1983) by Albert H. Moorehead, et al. at pages 180-183. 
     Referring to FIG. 14, the employment of the blackjack module  18  in FIG. 1 is described. In the employment of this module  18 , a playing strategy is selected at step  140 . A betting strategy is then selected at step  142 . If a streak betting strategy is selected at step  144 , streak betting amounts will be decided. If a variable betting strategy is selected at step  146 , variable betting amounts will also be decided. A playing mode is then selected in step  148  wherein this playing mode will be either a single hand mode as in step  150 , an automatic mode as in step  152  or session mode as in step  154 . If a session mode is selected at step  156 , a bailout percentage will be selected. If automatic mode or session mode is chosen, the number of hands to be played will be selected in step  158 . In step  160 , the speed of play will be selected and at step  162  statistics will be displayed. 
     Referring to FIG. 15, on the main application screen, input  166  may be used to run the application as at step  168  which is further detailed in FIG.  16 A. There is also input  170  for selection of the multiple session mode at step  172  which is detailed in FIG.  16 . There is also input  174  for selection of the advanced statistics which display page  176  for statistical information concerning the length and frequency of streaks. 
     Referring to FIGS. 16A, and  16 B at step  178  it is first determined if the hands played is equal to or less than the hands to play. If it is not at step  180 , play is stopped and control returned to the application. If hands played is equal to or less than hands to play, cards are dealt to the player and the dealer at step  182 . At step  182 , it is thus determined if dealer has an ace showing. If the dealer has an ace showing, it is determined at step  186  if the total of the dealer&#39;s cars are 21. If the dealer&#39;s total is 21, it is determined at step  188  if the player has insurance. If the player does have insurance, he wins the insurance bet, but loses the bet and breaks even. Otherwise, the player loses the bet. If the dealer does not have a total of 21 at step  190 , it is determined if the player has insurance, and at step  192 , if he does have insurance, the player loses the insurance bet. If the player does not have insurance, at step  194  the logic proceeds to  196  where a determination is made if a player splits in which case if he does at step  198  the cards are broken into two separate hands and one hand is played at a time wherein the next card is dealt to the current hand. A determination is then made if under house rules, a player can double down on his split at step  200 . If he cannot, a determination is again made at step  196  if there is a split, and if so, if there are aces in which case only one split will be allowed. If house rules allow for double down on a split, a determination is made at step  202  if the player doubles down. If the player does not double down, a determination is made if the player stands at step  202 . Returning to step  196 , if there are no aces, a determination is made if the player further splits his hand at step  204 . If he does not, a determination is made if the player doubles down at step  202  and if he does further split his hand, a determination is made at step  204  if the player stands. After the player does double down on a split hand, one card is dealt to the player at step  208 . If the player does not stand at step  204 , one card is dealt to the player at step  210  and step  212 . A determination is made as to whether the player busts, and if he does not bust, a determination is again made at step  204  if the player stands. If the player busts, the player loses the bet at  214 . By the term “bust”, it is meant that the amount of the hand exceeds 21. If at step  216  the player had a split and if he does split, then he returns to step  198  to determine if cards will be broken into two separate hands and playing cards one hand at a time with a deal of a next card to the current hand. If at step  216  the player does not have a split, a determination is made at step  218  if the player busts. If the player does bust, reference is made to increment variables to display loss and the next bet is adjusted based on the strategy after which there is a return to step  178  on FIG. 16A to determine if the number of hands played is less than or equal to the number of hands to play. If at step  218  the player did not bust, reference is made at step  224  to the dealer&#39;s hand. If the dealer has a soft 17 or less than 17, he must, depending on house rules selected, hit and at step  226  one card is dealt to the dealer and reference again is made at step  224  to the dealer&#39;s hand. If the dealer has a soft 17 and under, depending on house rules, the dealer must stand or a 17 or greater. A determination is made at step  228  as to whether the player won, and if the player did win, reference is made at step  230  to increment values to display winnings and to adjust next bet based on strategy. If at step  228 , the player did not win, reference is made at step  220  to increment values to display loss and to adjust the next bet based on strategy and then at step  222  to return to step  178  on FIG. 16A to determine if the number of hands played is less than or equal to the number of hands to play. 
     Referring to FIG. 17, the operation of a multiple session mode is described wherein the multiple session screen is shown generally in numeral  232 . There is an input  234  for the betting strategy to use, and input  236  controls the number of hands to play and input  238  the number of times to play. There is an input  240  for reset, input  242  to cancel, and input  244  for a return to game. At input  248  the maximum winning amount may be entered so that when the amount won is equal to or greater than this amount, the game quits. At input  252  the maximum amount which is to be lost may be selected and entered so that at step  254  the game has quit when the amount lost is greater than or equal to this amount. At input  256  a starting bankroll is entered so that at step  258  a current bankroll at the time the procession starts is defined. Input  260  allows for the selection of a bailout percent to enable step  262  to be carried out by defining a percentage to bailout. That is, in step  262 , if the player&#39;s winnings supersede the winning amount entered, play will continue until this percentage of a maximum amount is won. There is a deal input  264  which in step  266  begins the sequence on FIG. 18 in which in step  268  a determination is made if the current play is less than or equal to the number of times to play, and if it is, in step  270 , playing logic begins on FIG.  16 A. After each hand is played, there will be a check of maximum winnings or losses and bailout percentage in step  272 . If such maximums have not been reached, step  270  will again be repeated in which playing logic will again be begun on FIG.  16 A. If such maximums have been reached in step  272 , data will be recorded for display on the grid and continued to the next play in step  272  after which step  268  will again be repeated and a determination will be made if current play is less than or equal to number of times to play. The multiple session screen will preferably be implemented for speed. The game will be played until any of the perimeters are matched, then it will continue to a new session until the number of times the play has been reached. A listing of the maximum winning amounts, maximum losing amounts, and hands played, time (in minutes), total for session, amount won or lost and total won or lost for all sessions will be made. 
     Referring to FIGS. 19-26, the screens employed in the blackjack module are shown. In FIG. 19, a betting strategy is selected between a streak betting strategy and a variable betting strategy. If a streak betting strategy is selected, the game configuration screen shown in FIG. 20 is used. On this screen, a playing strategy can be selected from a default strategy in which no assumptions or predictions are made with regard to streaks or from a strategy based on an assumption that the dealer will not win four games in a row or from a strategy based on an assumption that the player will win the first two games. Still another strategy can be selected which is known as “5 &amp; 5, 10, 20” in which it is assumed that losing streaks will not be of an extended length. In the “5 &amp; 5, 10, 20” if the player wins, the next bet will be 10. If the player loses the game or this 10 bet, the next bet will be 20. Bets on any further successive losing games will be 20 until there is a winning hand in which case the bet on the next game will again be 5. In Table III, a preferred number of decks in the shoes, winning sequence length, and losing sequence length is shown for each of these strategies for playing the blackjack game. In Table IV, preferred bets for a winning or losing streak of various lengths is shown for each of these four strategies for playing the blackjack game. It will be understood that on the game configuration screen shown in FIG. 20 that the player may make adjustments in the number of decks in the shoe, winning sequence lengths, losing sequence lengths, and amounts of bets for various winning streaks for each of these strategies. 
     The variable betting configuration screen is shown in FIG.  21 . On this screen, an initial bet, a maximum bet, and a minimum bet may be selected, and a betting strategy may also be employed in which the maximum bet is maintained after the maximum bet is reached or the initial bet is used. Similarly, after the minimum bet is reached, a strategy may be selected in which the minimum bet is maintained or the initial bet is again adopted. The betting strategy may also employ the option to add to a bet in the event of a winning hand or subtract from the bet in the event of a winning hand by a selectable amount. Similarly, if there is a losing hand, the player may also select an addition or a subtraction of a selected amount from the bet. 
     The game screen for the blackjack game is shown in FIG.  22 . On this screen, the player can select a continuous or a single-hand deal. The player can also select a number of hands to be played and speed of play. Betting strategy and playing strategy may also be employed. As will be discussed hereafter, advanced statistics and multiple sessions may also be selected. Bankroll data, total hand data, and winning and losing streak data are also displayed. 
     The screen shown in FIG. 23 is a configuration for blackjack in which various playing strategies may be selected. On this screen, for a default playing strategy, the player&#39;s action in response to his own hand and the card which the dealer has shown is displayed. That action may be to hit, stand, or split. Similar strategies for action in response to the dealer&#39;s face card are also shown on a “no bust” strategy, that is one in which the player would not have a total greater than 21. Such actions for the default strategy are shown on Table V. Such actions on the “no bust” strategy are shown on Table VI. On these Tables V and IV, “+1” means to take a card while the other abbreviations are shown in Table VII which also shows the possible actions for each possible one of the player&#39;s hands. For each of these situations, the player&#39;s hand and the action in response to the dealer&#39;s face card may be adjusted. The player may also select whether or not to take insurance. On this screen, house rules are also displayed and may be adjusted. That is, the player can elect to double down on any hand or on 10 and 11 only. The player may elect to double down on splits or not to double down on splits. House rules may be elected to either that the dealer must stand on the soft 17 or that the dealer must hit a soft 17. If a player has 21 and the dealer has an ace up, it can also be elected either could take insurance, take even money, or play out the hand. From the game screen shown in FIG. 22 an advanced statistics display screen as shown in FIG. 24 may be selected. A multiple session simulation screen as shown in FIG. 25 may also be selected from the game screen shown in FIG.  22 . From the multiple session simulation screen shown in FIG. 25 an hourly statistics summary screen as shown in FIG. 26 may also be selected. 
     The use of the gaming simulation program of the present invention is further illustrated with reference to the following examples. 
     EXAMPLE 1 
     The war game module was selected as described above. A “no surrender” playing strategy and a default streak betting strategy as described above were used. A single hand deal was selected and five hands were played. The results of these hands are shown in Table I. 
     EXAMPLE 2 
     The war game module again was again selected. A surrender playing strategy was elected. A default betting strategy was also selected. Five hands were played in which a single hand deal was selected. The results of the hands are shown in Table II. 
     EXAMPLE 3-6 
     In these examples, the war game was again played. The following betting and playing strategies were selected. 
     Example 3: streak, no surrender 
     Example 4: streak, surrender 
     Example 5: variable, no surrender 
     Example 6: variable, surrender 
     For each of these examples, 50 hands were played. The cumulative results of these hands are shown in Table IX. 
     EXAMPLE 7 
     The multiple session simulation for the war game was selected. The starting bank roll was 10,000. A streak betting and a no surrender default strategy was selected. Maximum winning and losing amounts were $1,000 and the bank out percent was 170. The number of hands to play was 5, and the number of times to play was 5. The results of these hands were compiled and are shown in Table X. Hourly statistics were compiled using this simulation and are shown in Table XI. 
     EXAMPLE 8 
     In this example, the blackjack simulation was used. The default playing strategy and streak betting strategies were selected. House rules selected were that a player may double down on any hand, a player may double down on splits, the dealer must stand on a soft 17. If a player has 21 and a dealer has an ace up, the player also will take even money. Continuous dealing was selected and the number of hands to play was set at 1,000. The results of this simulation of 1,000 hands were compiled and are shown in Table XII. 
     EXAMPLES 9-12 
     The simulation of Example 8 was repeated four times for 1,000 hands each except that the following changes were made from Example 8 in either playing strategy or in house rules, while the same streak betting strategy was maintained. 
     Example 9: the “no bust” playing strategy was used. 
     Example 10: house rules were that player may double down on 10 and 11 only. 
     Example 11: house rules were that dealer must hit on a soft 17. 
     Example 12: player takes insurance if player has 21 and dealer has an ace up. 
     The results of these simulations were compiled and are shown in Table XII. 
     EXAMPLE 13 
     In this example, the blackjack simulation was used. The default playing strategy and variable betting strategies were selected. House rules selected were that a player may double down on any hand, a player may double down on splits, the dealer must stand on a soft 17. If a player has 21 and a dealer has an ace up, the player also will take even money. Continuous dealing was selected and the number of hands to play was set at 1,000. The results of this simulation of 1,000 hands were compiled and are shown in Table XIII. 
     EXAMPLES 14-17 
     The simulation of Example 8 was repeated four times for 1,000 hands each except that the following changes were made from Example 8 in either playing strategy or in house rules, while the same streak betting strategy was maintained. 
     Example 14: the “no bust” playing strategy was used. 
     Example 15: house rules were that player may double down on 10 and 11 only. 
     Example 16: house rules were that dealer must hit on a soft 17. 
     Example 17: player takes insurance if player has 21 and dealer has an ace up. 
     The results of these simulations were compiled and are shown in Table XIII. 
     EXAMPLE 18 
     The multiple session simulation for the blackjack game was selected. The starting bank roll was 10,000. A streak betting and a no surrender default strategy was selected. Maximum winning and losing amounts were $850 and the bank out percent was 170. The number of hands to play was 5, and the number of times to play was 5. The results of these hands were compiled and are shown in Table XVI. Hourly statistics were compiled using this simulation and are shown in Table XVII. 
     It will be appreciated that a gaming program and method of its use has been provided which allows the user to select between different games of chance and, for a selective game of chance, to further select a betting strategy from a set of betting strategies, and a playing strategy from a set of playing strategies and to simulate a playing of hands using the selecting playing and betting strategies. 
     It will also be appreciated that a gaming program and method of its use has been provided which displays comprehensive statistics to enable the user to determine the results of the simulation of the plurality of hands using a selective betting and playing strategy to enable the user to determine the relative merits of the selected strategies, these are the other strategies. 
     If will also be appreciated that a gaming program and a method of its use has been provided which affords the above advantages while being relatively inexpensive and easy to use. 
     It will also be appreciated that a gaming program and a method of its use has been provided which enables a user to be taught various strategies in playing war, blackjack and other games of chance and to further enable the user to enhance his skill in employing such strategies and techniques. 
     While the invention has been described here in its currently preferred embodiment or embodiments, those skilled in the art will recognize that other modifications may be made without departing from the invention and it is intended to claim all modifications and variations as fall within the scope of the invention. 
     In the foregoing description, certain terms have been used for brevity, clearness, and understanding. No unnecessary limitations are to be implied therefrom beyond the requirement of the prior art because such terms are used for descriptive purposes and are intended to be broadly construed. 
     Moreover, the description and illustration of the invention is an example and the invention is not limited to the exact details shown or described. 
     
       
         
           
               
             
               
                 TABLE I 
               
             
            
               
                   
               
               
                 War Game Configuration 
               
            
           
           
               
               
               
               
               
            
               
                 Playing Strategy 
                 Surrender 
                 Deck in Shoe 
                 Winning Sequence 
                 Losing Sequence 
               
               
                   
               
               
                 Default 
                 yes/no 
                 1 
                 5 
                 5 
               
               
                 Dealer won&#39;t win 4 in a 
                 yes/no 
                 8 
                 1 
                 5 
               
               
                 row 
                   
               
               
                 Plan on winning first 2 
                 yes/no 
                 8 
                 3 
                 1 
               
               
                 hands 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE II 
               
             
            
               
                   
               
               
                 War Game Betting Strategies 
               
            
           
           
               
               
               
               
               
               
               
            
               
                 Playing Strategy 
                 Streak 
                 1 
                 2 
                 3 
                 4 
                 5 
               
               
                   
               
               
                 Default 
                 W 
                  5 
                 10 
                 20 
                 30 
                 40 
               
               
                   
                 L 
                  5 
                 10 
                 20 
                 30 
                 40 
               
               
                 Dealer won&#39;t win 4 
                 W 
                  5 
                 — 
                 — 
                 — 
                 — 
               
               
                 in a row 
                 L 
                  5 
                  5 
                  5 
                 25 
                  5 
               
               
                 Plan on winning 
                 W 
                 50 
                 25 
                  5 
                 — 
                 — 
               
               
                 first 2 hands 
                 L 
                  5 
                 — 
                 — 
                 — 
                 — 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE III 
               
             
            
               
                   
               
               
                 Blackjack Game Configuration 
               
            
           
           
               
               
               
               
            
               
                   
                   
                 Winning 
                   
               
               
                 Playing Strategy 
                 Deck in Shoe 
                 Sequence 
                 Losing Sequence 
               
               
                   
               
               
                 Default 
                 8 
                 5 
                 5 
               
               
                 Dealer won&#39;t win 4 in a 
                 8 
                 1 
                 5 
               
               
                 row 
                   
               
               
                 Plan on winning first 2 
                 1 
                 3 
                 1 
               
               
                 hands 
                   
               
               
                 5 &amp; 5, 10, 20 
                 8 
                 1 
                 7 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE IV 
               
             
            
               
                   
               
               
                 Blackjack Betting Strategies 
               
            
           
           
               
               
            
               
                   
                 Winning/Losing Streak Length 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Playing Strategy 
                 1 
                 2 
                 3 
                 4 
                 5 
                 6 
                 7 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
            
               
                 Default 
                 W 
                  5 
                 10 
                 15 
                 20 
                 25 
                 — 
                 — 
               
               
                   
                 L 
                  5 
                 10 
                 15 
                 20 
                 25 
                 — 
                 — 
               
               
                 Dealer won&#39;t win 4 
                 W 
                  5 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 in a row 
                 L 
                  5 
                  5 
                  5 
                 25 
                  5 
                 — 
                 — 
               
               
                 Plan on winning 
                 W 
                 50 
                 25 
                  5 
                 — 
                 — 
                 — 
                 — 
               
               
                 first 2 games 
                 L 
                  5 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                 5 &amp; 5, 10, 20 
                 W 
                  5 
                 — 
                 — 
                 — 
                 — 
                 — 
                 — 
               
               
                   
                 L 
                  5 
                 10 
                 20 
                 40 
                 80 
                 160 
                 7 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE V 
               
             
            
               
                   
               
               
                 Blackjack Default Playing Strategy 
               
               
                 Player&#39;s Action Based on Dealer&#39;s Hand Showing 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Player&#39;s Hand 
                 Example 
                 A 
                 Insurance 
                 K or 10 
                 9 
                 8 
                 7 
                 6 
                 5 
                 4 
                 3 
                 2 
               
               
                   
               
               
                  4 
                 2-2 
                 H 
                   
                 H 
                 H 
                 H 
                 SP/H 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
               
               
                  5 
                 2-3 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                  6 
                 3-3 
                 H 
                   
                 H 
                 H 
                 H 
                 SP/H 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
               
               
                   
                 3-4 
               
               
                  7 
                 2-5 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                  8 
                 4-4 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                   
                 3-5 
               
               
                  9 
                 3-6 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 10 
                 5-5 
                 H 
                   
                 H 
                 H 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
               
               
                   
                 4-6 
               
               
                 11 
                 5-6 
                 H 
                   
                 H 
                 H 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
               
               
                 12 
                 6-6 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 ST 
                 SP/ST 
                 ST 
                 ST 
                 ST 
               
               
                   
                 5-4-3 
               
               
                 Soft 12 
                 A-A 
                 SP + 1 
                   
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
               
               
                 13 
                 J-3 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 Soft 13 
                 A-Z 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 14 
                 7-7 
                 H 
                   
                 H 
                 H 
                 H 
                 SP/H 
                 SP/H 
                 SP/H 
                 SP/H 
                 SP/H 
                 SP/H 
               
               
                   
                 k-4 
               
               
                 Soft 14 
                 A-3 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 15 
                 7-8 
                 H 
                   
                 H 
                 H 
                 H 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                   
                 3-2-Q 
               
               
                 Soft 15 
                 A-4 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 16 
                 8-8 
                 H 
                   
                 H 
                 H 
                 SP/H 
                 SP/H 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
               
               
                   
                 K-4-2 
               
               
                 Soft 16 
                 AJ 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 17 
                 J-7 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                   
                 4-5-6 
               
               
                 Soft 17 
                 A-6 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 18 
                 9-9 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                   
                 K-8 
               
               
                 Soft 18 
                 A7 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 19 
                 9-J 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                   
                 3-5-A 
               
               
                 Soft 19 
                 A8 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 20 
                 K-K 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                   
                 A-4-5 
               
               
                 Soft 20 
                 A-9 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE VI 
               
             
            
               
                   
               
               
                 Blackjack “No Bust” Playing Strategy 
               
               
                 Player&#39;s Action Based on Dealer&#39;s Hand Showing 
               
            
           
           
               
               
               
               
               
               
               
               
               
               
               
               
               
            
               
                 Player&#39;s Hand 
                 Example 
                 A 
                 Insurance 
                 K or 10 
                 9 
                 8 
                 7 
                 6 
                 5 
                 4 
                 3 
                 2 
               
               
                   
               
               
                  4 
                 2-2 
                 H 
                 yes 
                 H 
                 H 
                 H 
                 SP/H 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
               
               
                  5 
                 2-3 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                  6 
                 3-3 
               
               
                   
                 3-4 
                 H 
                   
                 H 
                 H 
                 H 
                 SP/H 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
               
               
                  7 
                 2-5 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                  8 
                 4-4 
               
               
                   
                 3-5 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                  9 
                 3-6 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 10 
                 5-5 
               
               
                   
                 4-6 
                 H 
                   
                 H 
                 H 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
               
               
                 11 
                 5-6 
                 H 
                   
                 H 
                 H 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
                 DD 
               
               
                 12 
                 6-6 
               
               
                   
                 5-4-3 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 SP/ST 
                 ST 
                 ST 
                 ST 
               
               
                 Soft 12 
                 A-A 
                 SP + 1 
                   
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
                 SP + 1 
               
               
                 13 
                 J-3 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 Soft 13 
                 A-Z 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 14 
                 7-7 
               
               
                   
                 k-4 
                 SP/ST 
                   
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
               
               
                 Soft 14 
                 A-3 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 15 
                 7-8 
               
               
                   
                 3-2-Q 
                 H 
                   
                 H 
                 H 
                 H 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 Soft 15 
                 A-4 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 16 
                 8-8 
               
               
                   
                 K-4-2 
                 SP/ST 
                   
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
                 SP/ST 
               
               
                 Soft 16 
                 AJ 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 17 
                 J-7 
               
               
                   
                 4-5-6 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 Soft 17 
                 A-6 
                 H 
                   
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
                 H 
               
               
                 18 
                 9-9 
               
               
                   
                 K-8 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 Soft 18 
                 A7 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 19 
                 9-J 
               
               
                   
                 3-5-A 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 Soft 19 
                 A8 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 20 
                 K-K 
               
               
                   
                 A-4-5 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                 Soft 20 
                 A-9 
                 ST 
                   
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
                 ST 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE VII 
               
               
                   
               
               
                 Alternative Strategies for Blackjack 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
            
               
                 If player&#39;s hand is: 4, 8, 10, 12, 14, 16, 18, or 20 
               
               
                 Possible actions are: 
               
               
                 Hit (H) 
               
               
                 Stand (ST) 
               
               
                 Double Down (DD) 
               
               
                 Split or Hit (SP/H) 
               
               
                 Split or Stand (SP/ST) 
               
               
                 Split or Double Down (SP/DD) 
               
               
                 If player&#39;s hand is: 5, 6, 7, 9, 11, 13, soft 13, 14, soft 14, 15, soft 15, soft 
               
               
                 16, 17, soft 17, soft 18, 19, soft 19, soft 20 
               
               
                 Possible Actions are: 
               
               
                 Hit (H) 
               
               
                 Stand (ST) 
               
               
                 Double Down (DD) 
               
               
                 If player&#39;s hand is: soft 12 
               
               
                 Possible actions are: 
               
               
                 Hit (H) 
               
               
                 Stand (ST) 
               
               
                 Double Down (DD) 
               
               
                 Split or Hit (SP/H) 
               
               
                 Split or Stand (SP/ST) 
               
               
                 Split or Double Down (SP/DD) 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE VIII 
               
               
                   
               
               
                 Alternative House Rules for Blackjack 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
            
               
                   
                 Double Down 
               
               
                   
                 Player can double down on: 
               
               
                   
                 any hand 
               
               
                   
                 10 and 11 only 
               
               
                   
                 Player may double down on splits 
               
               
                   
                 Soft 17 
               
               
                   
                 Dealer must hit on soft 17 
               
               
                   
                 Dealer must stand on soft 17 
               
               
                   
                 If a player has 21 and dealer has an ace up: 
               
               
                   
                 Take insurance 
               
               
                   
                 Take even money 
               
               
                   
                 Play on the hand 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE IX 
               
             
            
               
                   
               
               
                 Example 1: Play of War Game With No Surrender Playing and Streak Betting Strategy 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Dealer 
                 AH 
                 10C 
                 AD 
                 3D 
                 3S 
                 6S 
               
               
                   
                 Player 
                 KV 
                 AC 
                 6D 
                 JH 
                 2H 
                 7H 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Bankroll data 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Current bankroll 
                 10,000 
                 9,695 
                 10,005 
                 9,995 
                 10,000 
                 9,995 
                 10,000 
               
               
                 Maximum bankroll 
                 0 
                 0 
                 10,005 
                 10,005 
                 10,005 
                 10,005 
                 10,005 
               
               
                 Minimum bankroll 
                 0 
                 9,995 
                 9,995 
                 9,995 
                 9,995 
                 9,995 
                 9,995 
               
               
                 Total Won on War 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Total Loss on war 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Total Hand Data 
               
               
                 Total hands won 
                 0 
                 0 
                 1 
                 1 
                 2 
                 2 
                 3 
               
               
                 Total hands lost 
                 0 
                 1 
                 1 
                 2 
                 2 
                 3 
                 3 
               
               
                 Total wars won 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Total wars lost 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Total wars 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Win/Loss Streak Data 
               
               
                 Current winning streak 
                 0 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
               
               
                 Current losing streak 
                 0 
                 1 
                 0 
                 1 
                 0 
                 1 
                 0 
               
               
                 Current Bet 
                 5 
                 10 
                 10 
                 5 
                 5 
                 5 
                 5 
               
               
                 Maximum winning streak 
                 0 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                 Maximum losing streak 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE X 
               
             
            
               
                   
               
               
                 Example 2: Play of War Games With War Surrender Playing and Variable Betting Strategy 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Dealer 
                 8D 
                 9H 
                 ZS 
                 QS 
                 Z 
                 AD 
               
               
                   
                 Player 
                 4C 
                 KD 
                 AD 
                 7C 
                 10 
                 3H 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 Bankroll data 
                   
                   
                   
                   
                   
                   
                   
               
               
                 Current bankroll 
                 10,000 
                 9,990 
                 10,010 
                 10,040 
                 10,000 
                 10,050 
                 10,000 
               
               
                 Maximum bankroll 
                 0 
                 0 
                 10,010 
                 10,040 
                 10,040 
                 10,050 
                 10,050 
               
               
                 Minimum bankroll 
                 0 
                 9,990 
                 9,990 
                 9,990 
                 9,990 
                 9,990 
                 9,990 
               
               
                 Total Won on War 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Total Loss on war 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Total Hand Data 
               
               
                 Total hands won 
                 0 
                 0 
                 1 
                 2 
                 2 
                 3 
                 3 
               
               
                 Total hands lost 
                 0 
                 1 
                 1 
                 1 
                 2 
                 2 
                 3 
               
               
                 Total wars won 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Total wars lost 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Total wars 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Win/Loss Streak Data 
               
               
                 Current winning streak 
                 0 
                 0 
                 1 
                 2 
                 0 
                 1 
                 0 
               
               
                 Current losing streak 
                 0 
                 1 
                 0 
                 0 
                 1 
                 0 
                 1 
               
               
                 Current Bet 
                 5 
                 20 
                 30 
                 40 
                 50 
                 50 
                 10 
               
               
                 Maximum winning streak 
                 0 
                 0 
                 1 
                 2 
                 2 
                 2 
                 2 
               
               
                 Maximum losing streak 
                 0 
                 1 
                 1 
                 1 
                 1 
                 1 
                 1 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE XI 
               
             
            
               
                   
               
               
                 Examples of War Game Play With Various Strategies 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Example 3 
                 Example 4 
                 Example 5 
                 Example 6 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 Bankroll data 
                   
                   
                   
                   
               
               
                 Current bankroll 
                 10,000 
                 9,972.50 
                 10,000 
                 10,005 
               
               
                 Maximum bankroll 
                 10,005 
                 10,032.50 
                 10,104 
                 10,185 
               
               
                 Minimum bankroll 
                 9,930 
                 9,920 
                 9,900 
                 9,932 
               
               
                 Total Won on War 
                 10 
                 0 
                 150 
                 0 
               
               
                 Total Loss on war 
                 20 
                 52.56 
                 80 
                 45 
               
               
                 Total Hand Data 
               
               
                 Total hands won 
                 25 
                 21 
                 26 
                 25 
               
               
                 Total hands lost 
                 25 
                 21 
                 24 
                 22 
               
               
                 Total wars won 
                 1 
                 0 
                 5 
                 0 
               
               
                 Total wars lost 
                 1 
                 8 
                 3 
                 3 
               
               
                 Total wars 
                 2 
                 0 
                 8 
                 0 
               
               
                 Win/Loss Streak Data 
               
               
                 Current winning streak 
                 1 
                 1 
                 1 
                 2 
               
               
                 Current losing streak 
                 0 
                 0 
                 0 
                 0 
               
               
                 Current Bet 
                 5 
                 5 
                 20 
                 50 
               
               
                 Maximum winning streak 
                 5 
                 4 
                 4 
                 6 
               
               
                 Maximum losing streak 
                 5 
                 6 
                 5 
                 3 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE XII 
               
             
            
               
                   
               
               
                 Example 7: War Game Session Simulation 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Maximum Winning 
                 Maximum Losing 
                   
                   
                   
                   
                   
               
               
                 Play 
                 Amount 
                 Amount 
                 Hands Played 
                 Time (Min.) 
                 Total 
                 Won/Lost 
                 Total Won/Lost 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 1 
                 5.00 
                 −5.00 
                 5 
                 00:02 
                 10,000.00 
                 0.00 
                 0.00 
               
               
                 2 
                 15.00 
                 −10.00 
                 5 
                 00:02 
                 10,015.00 
                 15.00 
                 15.00 
               
               
                 3 
                 0.00 
                 −50.00 
                 5 
                 00:02 
                 9,965.00 
                 −50.00 
                 −35.00 
               
               
                 4 
                 5.00 
                 −5.00 
                 5 
                 00:02 
                 9,960.00 
                 −5.00 
                 −40.00 
               
               
                 5 
                 5.00 
                 −15.00 
                 5 
                 00:02 
                 9,965.00 
                 5.00 
                 −35.00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE XIII 
               
             
            
               
                   
               
               
                 Example 7: War Game Hourly Statistics 
               
            
           
           
               
               
               
            
               
                 Play 
                 Time (Min.) 
                 Hourly Avg. (Per Session) 
               
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 00:02 
                 0.00 
               
               
                 2 
                 00:02 
                 450.00 
               
               
                 3 
                 00:02 
                 −1,500.00 
               
               
                 4 
                 00:02 
                 −150.00 
               
               
                 5 
                 00:02 
                 150.00 
               
            
           
           
               
               
            
               
                   
                 Total Won/Lost Per Hour—$262.50 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE XIV 
               
             
            
               
                   
               
               
                  Examples of Blackjack Games Play With Various Strategies 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Example 8 
                 Example 9 
                 Example 10 
                 Example 11 
                 Example 12 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Bankroll data 
                   
                   
                   
                   
                   
               
               
                 Current bankroll 
                 10,125 
                 9,835 
                 10,400 
                 10,140 
                 9667.50 
               
               
                 Maximum bankroll 
                 10,340 
                 10,085 
                 10,425 
                 10,265 
                 10,067.50 
               
               
                 Minimum bankroll 
                 9,905 
                 9602.50 
                 9,815 
                 4,947.50 
                 9,597.50 
               
               
                 Amount won/lost on hand 
                 −5 
                 tie 
                 5 
                 −5 
                 0 
               
               
                 Amount won on even money 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Total Hand Data 
               
               
                 Total hands won 
                 429 
                 437 
                 446 
                 436 
                 427 
               
               
                 Total hands lost 
                 474 
                 487 
                 464 
                 478 
                 479 
               
               
                 Total blackjack won 
                 50 
                 45 
                 45 
                 52 
                 49 
               
               
                 Amount won on Blackjack 
                 690 
                 660 
                 615 
                 690 
                 667.50 
               
               
                 Win/Loss Streak Data 
               
               
                 Current winning streak 
                 0 
                 1 
                 2 
                 0 
                 1 
               
               
                 Current losing streak 
                 2 
                 0 
                 0 
                 1 
                 0 
               
               
                 Current push streak 
                 0 
                 1 
                 0 
                 0 
                 0 
               
               
                 Current Bet 
                 10 
                 5 
                 10 
                 5 
                 5 
               
               
                 Maximum winning streak 
                 10 
                 7 
                 8 
                 8 
                 8 
               
               
                 Maximum losing Streak 
                 10 
                 9 
                 7 
                 8 
                 9 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE XV 
               
             
            
               
                   
               
               
                 Examples of Blackjack Games Play With Various Strategies 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Example 13 
                 Example 14 
                 Example 15 
                 Example 16 
                 Example 17 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                 Bankroll data 
                   
                   
                   
                   
                   
               
               
                 Current bankroll 
                 8,427.50 
                 8,952.50 
                 9,277.50 
                 9,020 
                 9,282.50 
               
               
                 Maximum bankroll 
                 10,050 
                 10,740 
                 10,490 
                 11,455 
                 11,257.50 
               
               
                 Minimum bankroll 
                 8,335 
                 8,947.50 
                 8,662.50 
                 8,945 
                 9,282.50 
               
               
                 Amount won/lost on hand 
                 −40 
                 5 
                 15 
                 25 
                 −10 
               
               
                 Amount won on even money 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Total Hand Data 
               
               
                 Total hands won 
                 433 
                 436 
                 420 
                 424 
                 429 
               
               
                 Total hands lost 
                 475 
                 490 
                 498 
                 499 
                 468 
               
               
                 Total blackjack won 
                 35 
                 58 
                 43 
                 42 
                 36 
               
               
                 Amount won on Blackjack 
                 1,597.50 
                 2,947.50 
                 2,467.50 
                 1,845 
                 2,392.50 
               
               
                 Win/Loss Streak Data 
               
               
                 Current winning streak 
                 0 
                 1 
                 2 
                 2 
                 0 
               
               
                 Current losing streak 
                 2 
                 0 
                 0 
                 0 
                 1 
               
               
                 Current push streak 
                 0 
                 0 
                 0 
                 0 
                 0 
               
               
                 Current Bet 
                 35 
                 10 
                 20 
                 30 
                 5 
               
               
                 Maximum winning streak 
                 9 
                 9 
                 8 
                 6 
                 7 
               
               
                 Maximum losing Streak 
                 9 
                 9 
                 9 
                 11 
                 9 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE XVI 
               
             
            
               
                   
               
               
                 Example 18: Blackjack - Session Simulation 
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                   
                 Maximum Winning 
                 Maximum Losing 
                   
                   
                   
                   
                   
               
               
                 Play 
                 Amount 
                 Amount 
                 Hands Played 
                 Time (Min.) 
                 Total 
                 Won/Lost 
                 Total Won/Lost 
               
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 1 
                 0.00 
                 −20.00 
                 5 
                 00:02 
                 9,995.00 
                 −5.00 
                 −5.00 
               
               
                 2 
                 40.00 
                 −5.00 
                 5 
                 00:02 
                 10,005.00 
                 40.00 
                 35.00 
               
               
                 3 
                 10.00 
                 0.00 
                 5 
                 00:02 
                 10,400.00 
                 5.00 
                 40.00 
               
               
                 4 
                 0.00 
                 −20.00 
                 5 
                 00:02 
                 10,020.00 
                 −20.00 
                 20.00 
               
               
                 5 
                 10.00 
                 −10.00 
                 5 
                 00:02 
                 10,025.00 
                 50.00 
                 23.00 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE XVII 
               
             
            
               
                   
               
               
                 Example 18: Blackjack Game—Hourly Statistics 
               
            
           
           
               
               
               
            
               
                 Play 
                 Time (Min.) 
                 Hourly Avg. (Per Session) 
               
               
                   
               
            
           
           
               
               
               
            
               
                 1 
                 00:02 
                 −150.00 
               
               
                 2 
                 00:02 
                 1,200.00 
               
               
                 3 
                 00:02 
                 150.00 
               
               
                 4 
                 00:02 
                 −600.00 
               
               
                 5 
                 00:02 
                 150.00 
               
            
           
           
               
               
            
               
                   
                 Total Won/Lost Per Hour—$187.50