Abstract:
A dice simulator for simulating dice rolling or the like utilizes operator selectable probability weighting to cause quasi-random rolling results to be biased in accordance with the selected probability weighing.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention pertains to random/pseudo-random number generators and particularly to electronic dice simulators to provide displays of numbers in specified ranges. 
     2. Description of the Related Art 
     Prior art electronic dice simulators include those disclosed in U.S. Pat. No. 4,819,818 granted Apr. 11, 1989 to Simkus et al, and U.S. Pat. No. 4,432,189 granted Feb. 14, 1984 to Wiencek et al. 
     Simkus et al provides a micro-computer driven random data selection system wherein a processor is arranged to read a matrix of switches to determine a range of numbers and to establish a software controlled sequencing routine corresponding to that range. The interrupt terminal of the micro-computer is used to sense the activation of the system and cause the number selection. The software of the Simkus device presents the internal counters to the requisite range in response to the status of the switch matrix and displays that range in one of the two LED displays. Following sensing of the range, the computer starts the sequencing or counting and continuously sequences until deactivated. When the &#34;roll&#34; switch is operated, the computer samples and displays the last number in the sequence. Data for controlling the displays and loading the counter is stored in memory locations and the address for this data is developed from an index generated from the switch matrix inputs. 
     Wiencek et al provide a circuit in a device for electronically determining a simulated roll of a six-sided die (or two-sided dice). The circuit consists of a multi-position switch and related circuitry which allows the device to also simulate a roll of a die other than six-sided, namely four-sided, eight-sided, twelve-sided, twenty-sided or one hundred-sided. 
     The above mentioned prior art devices have the drawback of allowing only one or two dice to be thrown at one time. Moreover, prior art dice simulators have generally not provided one or more random or pseudo-random numbers from an unlisted range. Nor have they allowed for operators to weight the probability of &#34;rolling&#34; either a high number or a low number. 
     SUMMARY OF THE INVENTION 
     The present invention provides apparatus for simulating dice rolling or the like, comprising: first data entry means for entering numerical selection data; microprocessor means for processing said numerical selection data and computing, in a predetermined, quasi-random manner, results corresponding to the selected numerical data; and second data entry means for entering probability weighting criteria to bias said computing in a predetermined quasi-random manner and cause the processing of the numerical selector data to yield simulation results in accord with said probability weighting criteria. 
     In a narrower aspect of the invention further provides duplicated display means to permit simulation results to be viewed by other users, as well as the operator. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The preferred embodiment of the invention will now be described with reference to the annexed drawings, in which: 
     FIG. 1 is a perspective view of a dice simulator according to the present invention; 
     FIG. 2 is a block schematic diagram of the circuit of the dice simulator of FIG. 1; 
     FIGS. 3a and 3b are the flowchart of the software for operating the circuit shown in FIG. 1; and 
     FIGS. 4a, 4b and 4c are the flowchart of the subroutine &#34;ANSWER&#34; in the flowchart of FIGS. 3a and 3b. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     Referring to FIG. 1, a dice simulator 10 comprises an on/off button 11, numerical key pad buttons 12a-12j corresponding to the digits 0 to 9, an operator&#39;s display 13, a display 14 for other users, a probability weighting dial 15, non-numeric key pad buttons 16 and 17, and four pre-set &#34;dice type&#34; buttons 18a to 18d. 
     Referring now to FIG. 2, circuit of the dice simulator 10 comprises a microprocessor 19 (preferably a Motorola MC68HC705) which is connected via its PORT A to a probability weighting selector 20. The microprocessor 19 includes an internal clock, at least one memory, at least one register, and at least one arithmetic-logic unit. The at least one register includes an accumulator as well as variables or storage spaces, which may be included in the at least one memory. The at least one register may serve as counters and as variables in operation. The microprocessor 19 is more fully described in the 1989 Motorola Inc. Semiconductor publication BR594/D, which is incorporated herein by reference. The selector 20 is a seven position switch, each of which is connected to the first seven pins while the wiper of which is connected to the eighth pin of the PORT A and to circuit ground. The position of the switch 20 determining the probability weighting implemented using the dial 15 (FIG. 1). For each position a corresponding line is connected to a corresponding pin in the PORT A. The terminals of the switch 20 are each connected to a logic &#34;high&#34; through respective 1 kOhm resistors referred to generally by the number 21 in FIG. 2. This configuration results in the seven first pins of PORT A being logically high, unless grounded by the wiper of the switch 20. The system software interrogates the pins of PORT A to determine which switch 20 position is selected and to apply the predetermined probability weighting, assigned to the selected position. 
     A key pad 22 is connected to the pins of PORT B of the microprocessor 19 by eight lines. Four of those lines are for input to the microprocessor 19 and four are for output from it. The four input lines are connected to ground through respective 10 kOhm resistors referred to generally by the number 23 in FIG. 2. As a result of that configuration the output lines are kept high. Depressing a key on key pad 22 causes a corresponding input line to go &#34;high&#34;. The input lines between the key pad 22 and microprocessor 19 are also connected to the IRQ pin of the microprocessor 19 through a four input NAND gate 24. The IRQ pin provides two different choices of interrupting triggering sensitivity. As a result, pressing a key on the key pad 22 causes the microprocessor 19 to search the input lines and identify the pressed key. 
     PORT C of the microprocessor 19 is connected to an L.C.D. driver 25 by eight lines designated generally by reference number 26 in the figure. Four of the lines 26 transmit the number that is to be displayed. The other four lines indicate which digit of the L.C.D. receives the incoming number and signals the L.C.D. to display. Either of the Intersil 7211 or 7211M devices may be used in accordance with manufacturer&#39;s specifications. 
     The L.C.D. driver 25 drives two conventional LCD displays in parallel, one LCD display 27, corresponding to display 13 in FIG. 1, for the operator, and the other LCD display 28, corresponding to display 14 in FIG. 1 for viewers on the other side. 
     Referring to FIGS. 3a and 3b once the on/off button 11 (FIG. 1) is used to close the main switch 31 to the buttons 30 the software &#34;starts&#34; by initializing the dice simulator 10 and displays the word &#34;dICE&#34; on the displays 13 and 14. After initialization, the software proceeds according to the flowchart of FIGS. 3a and 3b. For example, the next step is &#34;search keypad&#34;, where the lines from PORT B of the microprocessor 19 to the key pad 22 are searched until the operator pushes a key on the key pad 22. 
     The main system software shown in FIGS. 3a and 3b is written in Motorola Assembly Language, and, in machine code form, operates on the at least one memory, the at least one register, and the at least one arithmetic-logic unit of the microprocessor 19. The program corresponding to FIGS. 3a and 3b is given below in segments preceded and annotated by the customary explanatory commentary in English. 
     
         __________________________________________________________________________ ORG $1FFE          The Reset vector is located at $1FFE and FCB #$01 $1FFF. This sets the Reset vector to $0100 FCB #$00 which is where the program starts.PORTA EQU $00  All inputs - captures LUCK factorPORTB EQU $01  Keypad interfacePORTC EQU $02  All outputs - to the LCDDDRA  EQU $04  Data direction PORTADDRB  EQU $05  Data direction PORTBDDRC  EQU $06  Data direction PORTCFDATA EQU $60  Flag to proceed to ANSWERDFLAG EQU $61  Flag when a D is pressedPNUM1 EQU $62  Storage words forPNUM2 EQU $63  what is printedPNUM3 EQU $64  to the LCDPNUM4 EQU $65  4 in allNUMD1 EQU $66  One&#39;s digit for number of dice rolledNUMD2 EQU $67  Ten&#39;s digit for number of dice rolledDSIDE1 EQU $68  One&#39;s digit for the sides on the diceDSIDE2 EQU $69  Ten&#39;s digit for the sides on the diceDSIDE3 EQU $6A  Hundred&#39;s digit for the dice sidesDIESID EQU $6B  Binary equivalent of DSIDES 1,2,3PRSKEY EQU $6C  Value received from the keypadLUCK  EQU $6D  Luck factorTOTALL EQU $6E  Lower word of total rolled on diceTOTALH EQU $6F  Higher word of total rolled on diceTIMEH EQU $70  Higher word of time read from clockTIMEL EQU $71  Lower word of time read from clockFOUND EQU $72  Flag that&#39;s true when answer is foundROLL  EQU $73  Roll of the individual dieROLL1 EQU $74  Test variable in LUCK4ROLL2 EQU $75  Test variable in LUCK4NUMDIE EQU $76  Binary form of number of diceNUMDIC EQU $77  Storage form for NUMDIEDICSID EQU $78  Storage form for DIESIDTSTEQ EQU $79  Test for an equal sign for repeating__________________________________________________________________________ 
    
     The main system program clears and initializes the necessary variables before starting the subroutine calls. Once a key is found and identified, a check is made to ensure that the needed data is available. It the needed data is not available, the keypad is scanned again, until the needed info is obtained. With the info and more data that is obtained in further subroutines, the answer is returned, converted to decimal and then printed out. The flags are then set back to false and the keypad scanned for the next question. 
     
         __________________________________________________________________________ORG $100  Program starts at $0100CLRASTA DDRA  Set up PORTA as all inputs (LUCK factor)LDA #$99  PORTB is set up as half inputs and halfSTA DDRB  outputsLDA #$FFSTA PORTC PORTC is all outputs (LCD) and thisSTA DDRC  turns them on.JSR PDICE Print dice in the displayJSR INIT1 Clear flags, initialize variablesFALSEJSR SRCHKY          Get a key from the keypadLDA TST   Is this the first pass through?CMP #$00  If no, skip the next partBNE USUAL If yes then test for an equal signLDA PRSKEY          If not, continue as usualCMP #$0F  If yes, then prepare to repeat theBNE USUAL past roll of the diceLDA NUMDIC          First put the number of dice rolledSTA NUMDIE          into NUMDIELDA DICSID          Then put the sides of the dice intoSTA DIESID          DIESIDBRA GTLK  Now skip to the calculation partUSUALINC TST   Inc TST to show we&#39;ve been throughJSR SRTKEY          Identify key and act accordinglyLDA #$01  Test to see if Found is true (if weCMP FDATA the needed data). If not go back andBNE FALSE get more. If yes, continue onJSR CONVRT          Convert DSIDEs to DIESIDGTLK JSR GTLUCK          Get luck factor for answer to useJSR ANSWER          Get the answerJSR TODEC Convert the answer to decimal formJSR PRNT4 Print the answerJSR INIT1 Clear the flags and reset to zeroJSR TMFRDC          This displays the answer for 10 secondsJSR PDICE then prints dice.BRA FALSE Scan for the next question__________________________________________________________________________ 
    
     The following subroutine clears FDATA, DFLAG, NUMD1 and NUMD2. 
     
         ______________________________________INIT1           CLRA           STA         FDATA           STA         DFLAG           STA         NUMD1           STA         NUMD2           STA         TST           RTS______________________________________ 
    
     The following subroutine scans the keyboard until a key is depressed. It then identifies the key and sends it to the main program as PRSKEY. 
     
         __________________________________________________________________________SRCHKY  LDA  #$99   STA  PORTB   STA  DDRB   Turn on all columnsANYKEY  LDA  PORTB   AND  #$66   Mask away columns   BEQ  ANYKEY   LDA  #$20OUTLP   CLRXINRLP   DECX   BNE  INRLP   DECA   BNE  OUTLP   CLRXKEYLP   LDA  KYTBL,X   STA  PORTB   CMP  PORTB   BEQ  KEYFND   INCX   TXA   CMP  #$10   BEQ  SRCHKY   BRA  KEYLPKEYFND  TXA   STA  PRSKEYTILRLS  LDA  PORTB  This part ensures against people   AND  #$66   who leave their finger on the   BNE  TILRLS button. It delays until released   LDA  #$99   STA  PORTB   RTSKYTBL   FCB  #$21   D8   FCB  #$28   D10   FCB  #$30   D20   FCB  #$A0   D100   FCB  #$05   0   FCB  #$0C   1   FCB  #$14   2   FCB  #$84   3   FCB  #$03   4   FCB  #$0A   5   FCB  #$12   6   FCB  #$82   7   FCB  #$41   8   FCB  #$48   9   FCB  #$50   D   FCB  #$C0   =__________________________________________________________________________ 
    
     The following subroutine tests the key pressed. If the key was in the row (D8, D10, D20 or D100), it calls TOPROW. If it was a D it calls YESD. Otherwise it tests if we already have a D. If so, it calls DCSIDE. Otherwise NUMDC. It then returns. 
     
         __________________________________________________________________________SRTKEY LDA  PRSKEY CMP  #$04   If key pressed was in the toprow BHS  PAD    call TOPROW then go to end JSR  TOPROW else go on to next test BRA  ENDSRTPAD   CMP  #$0E   If it&#39;s a D call YESD then goto end BNE  NOTD   else go on to next test JSR  YESD BRA  ENDSRTNOTD  LDA  DFLAG  If we already have a D, this must CMP  #$01   be for the sides of the dice, so BEQ  HAVED  call DCSIDE. If we don&#39;t, it must be JSR  NUMDC  for the number of dice, call NUMDC BRA  ENDSRTHAVED JSR  DCSIDEENDSRT RTS__________________________________________________________________________ 
    
     The following subroutine is called when a D8, D10, D20 or D100 is pressed. It calls YESD (to print a D and ensure a NUMDI exists). It then puts the correct numbers in DSIDEs 1, 2, 3 and prints them. It flags FDATA as true and returns. 
     
         ______________________________________TOPROW   JSR     YESD      Call YESD to print a D, etc.    LDA     PRSKEY    Was a D8 pressed?    CMP     #$00    BNE     NOTZER    LDA     #$08      If not, put 8 into DSIDE1    STA     DSIDE1    BRA     WRITE     Was a D100 pressed?NOTZER   CMP     #$03      If yes, put a 1 in DSIDE3    BNE     NOT3    LDA     #$01    STA     DSIDE3    STA     PNUM3    BRA     WRITENOT3     STA     DSIDE2    Put a 1 Or 2 in DSIDE2WRITE    LDA     DSIDE1    STA     PNUM1    LDA     DSIDE2    STA     PNUM2    LDA     DSIDE3    STA     PNUM3    JSR     PRNT3    INC     FDATA     Set data flag true    RTS______________________________________ 
    
     The following subroutine is called when a D is pressed on the keypad. It prints a D and sets the die sides to 0. It then checks for a positive NUMD1 and defaults to 1 if not found. Finally it sets the DFLAG positive and returns. 
     
         __________________________________________________________________________YESD  LDA  #S0D STA  PNUM4 Put a D in PNUM4 CLRA STA  PNUM3 and clear the other PNUMs. STA  PNUM2 This causes d000 to be printed. STA  PNUM1 STA  DSIDE1            Initialize DSIDES to zero. This ensures STA  DSIDE2            no unwanted numbers for DIESID. STA  DSIDE3 JSR  PRNT4 LDA  #$01  Make sure we have a NUMDIE CMP  NUMD1 by seeing if NUMD1 or NUMD2 has a BLS  HNUMD number in it. CMP  NUMD2 BLS  HNUMD If no number is found for NUMDIE STA  NUMD1 put a 1 into NUMD1.HNUMD STA  DFLAG Set Dflag positive. RTS__________________________________________________________________________ 
    
     The following subroutine is called when the number of dice hasn&#39;t been determined yet. It checked for an equal sign and returns to PRTKEY if it finds one. Otherwise it moves NUMD1 to NUMD2 and puts PRSKEY into NUMD1. It then prints out the number. 
     
         ______________________________________NUMDC    LDA     PRSKEY    If PRSKEY is =, go to end    CMP     #$0F    BEQ     NUMEND    LDA     NUMD1     Put NUMD1 into NUMD2    STA     NUMD2    STA     PNUM2    JSR     MAKNUM    Get the number    LDA     PNUM1     Put PRSKEY into NUMD1    STA     NUMD1    CLRA    STA     PNUM3    STA     PNUM4    JSR     PRNT4     Print out new numberNUMEND   RTS______________________________________ 
    
     The following subroutine is called when the sides of the dice are being determined. It checks for an equal sign and if it finds one, it checks to make sure that DSIDES do exist. If not, it returns to the keypad, if yes it makes FDATA true and returns if it is not an equal sign. DSIDE1 is moved to DSIDE2, and the new number is put into DSIDE1. Both are printed. 
     
         __________________________________________________________________________DCSIDE LDA  PRSKEY CMP  #$0F   If PRSKEY was an equal sign BEQ  EQSGN  go to EQSGN JSR  MAKNUM Get decimal equivalent of PRSKEY LDA  DSIDE1 Move DSIDE1 to DSIDE2 STA  DSIDE2 STA  PNUM2  Ready to be printed LDA  PNUM1  Put new number into DSIDE1 STA  DSIDE1 JSR  PRNT2  Print out the number BRA  ENDDCSEQSGN CLRA CMP  DSIDE1 Test to see if we have a BNE  HAVDAT valid number of die sides CMP  DSIDE2 If yes FDATA is true, otherwise BNE  HAVDAT return to get more info BRA  ENDDCSHAVDAT INC  FDATAENDDCS RTS__________________________________________________________________________ 
    
     The following subroutine converts PRSKEY to the correct number and puts the result in PNUM1. 
     
         ______________________________________MAKNUM         LDA         PRSKEY          SUB         #$04          STA         PNUM1          RTS______________________________________ 
    
     The following subroutine converts the sides of the dice contained in DSIDEs 1, 2, 3 to single binary equivalent in DIESID. It first checks DSIDE3 for a one. If it finds one, the D100 was called for. If not, CONVRT then adds ten for each value in DSIDE2 to the number in DSIDE1 and stores the result in DIESID. It then converts the numbers in NUMD1 and NUMD2 to a single variable called NUMDIE. Finally, CONVRT stores NUMDIE and DIESID in additional storage spaces called NUMDIC and DICSID. 
     
         __________________________________________________________________________CONVRT CLRA STA  DIESID Test to see if we have a D100 CMP  DSIDE3 If so branch to DIE100 BNE  DIE100DC10  CMP  DSIDE2 Test to see if more then 9 sides BEQ  SMDIE  remain on the die. LDA  DIESID Add ten to DIESID ADD  #$0A STA  DIESID DEC  DSIDE2 Subtract one from DSIDE2 CLRA BRA  DC10   Check another time for sidesSMDIE LDA  DIESID ADD  DSIDE1 Add DSIDE1 to DIESID STA  DIESID BRA  ENDCONDIE100 LDA  #$64   Put 100 into DIESID STA  DIESID CLR  DSIDE3ENDCON CLR  DSIDE2 CLR  DSIDE1 LDA  #$00   This part of the subroutine STA  NUMDIE converts the numbers in the NUMDsNM2   CMP  NUMD2  to a single number called NUMDIE BEQ  NM1    First loop through NUMD2, adding LDA  NUMDIE 0A (10) to NUMDIE and subtracting ADD  #$0A   one from NUMD2 each time until STA  NUMDIE NUMD2 is zero. Then add NUMD1 to DEC  NUMD2  NUMDIE LDA  #$00 BRA  NM2NM1   LDA  NUMDIE ADD  NUMD1 STA  NUMDIE STA  NUMDIC Store NUMDIE in NUMDIC LDA  DIESID Store DIESID in DICSID STA  DICSID RTS__________________________________________________________________________ 
    
     The following subroutine checks with PORTA (which is wired to the luck selector) until it finds a match. When a match is found, the corresponding luck factor is returned. From the hard wiring all the choices are wires high. The return is wired low and is bit 0 in PORTA. The selected luck factor will also be low but all others will be high. Thus the accumulataor is loaded with PORTA and comparisons are made until the zero is found. That will give us the luck factor. 
     
         __________________________________________________________________________GTLUCK  LDA  #$01   Initialize LUCK to one   STA  LUCK   LDA  PORTA  Load the luck selector reading   LSRA        Get rid of the zero bitSTRTLK  LSRA        Move the next bit into carry   BCC  ENDLCK See if the carry bit is clear   INC  LUCK   If no, try the next bit in PORTA   BRA  STRTLK If the carry was clear, theENDLCK  RTS         selector was pointing there.__________________________________________________________________________ 
    
     A major subroutine of the program is &#34;GET ANSWER&#34; which is invoked once the last block in FIG. 3a is reached. The subroutine &#34;GET ANSWER&#34; is shown in flowchart form in FIGS. 4a, 4b and 4c. The subroutine returns the answer that is the total of all the dice rolled, it gets the time, selects the correct luck program to call (receiving ROLL back) then adds ROLL to its previous total until all the dice have been counted. The sum is returned as TOTAL. 
     
         __________________________________________________________________________ANSWER  CLRA   STA  TOTALL Set totals (high and low)   STA  TOTALH to zeroSTARTA  JSR  GTTIME Get the time   CLR  FOUND  Set FOUND false   LDA  LUCK   CMP  #$04   BEQ  L4     In this section the LUCK factor   CMP  #$01   is used to select the appropriate   BEQ  L1     subroutine to find the ROLL.   CMP  #$07   BEQ  L7   CMP  #$02   BEQ  L   CMP  #$03   BEQ  L3   CMP  #$05   BEQ  L5   JSR  LUCK6   BRA  ENDA   After ROLL is returned, theL1      JSR  LUCK1  subroutine jumps to ENDA.   BRA  ENDAL2      JSR  LUCK2   BRA  ENDAL3      JSR  LUCK3   BRA  ENDAL4      JSR  LUCK4   BRA  ENDAL5      JSR  LUCK5   BRA  ENDAL7      JSR  LUCK7   BRA  ENDAENDA    LDA  TOTALL   ADD  ROLL   Add ROLL to the lower byte   STA  TOTALL of total   LDA  TOTALH Add carry bit to Totalh - this   ADC  #$00   allows numbers higher than 255   STA  TOTALH   DEC  NUMDIE After each die is rolled, the   CLRA        number of dice remaining is   CMP  NUMDIE checked. When that number is   BEQ  ENDANS zero, all the dice have been   JMP  STARTAENDANS  RTS__________________________________________________________________________ 
    
     The following subroutine collects, in the accumulator, the time from the internal clock and stores it in a high byte and low byte, in variables TIMEH and TIMEL, respectively. The variables TIMEH and TIMEL serve as a counter. It then masks part of the higher byte, depending on the die&#39;s number of sides. This is to ensure fast response time without sacrificing randomness. 
     
         ______________________________________GTTIME  LDA     $1A   STA     TIMEH     Get the time and store it   LDA     $1B   STA     TIMEL   LDA     DIESID    Test the die sides   CMP     #$14      Is it more than 20?   BHI     M3        If yes, branch to M3   CMP     #$0A      Is it more than 10?   BHI     M2        If yes go to M2   LDA     TIMEH   AND     #$03   STA     TIMEH     For 10 or less sides TIMERH   BRA     ENDTIM    uses only its 2 right-most bitsM2      LDA     TIMEH     For 11-20 sides, use four bits   AND     #$0F      from TIMEH   STA     TIMEH   BRA     ENDTIMM3      LDA     TIMEH     For more than 20 sides, use   AND     #$3F      six bits of TIMEH   STA     TIMEHENDTIM  RTS______________________________________ 
    
     The following subroutine scans the list of numbers between 1 and DIESID, from the top down and bottom up simultaneously. When TESTIM returns FOUND as true, the number currently being searched is the ROLL and is returned to ANSWER. 
     
         ______________________________________LUCK4  NOPSTART4 LDA     DIESID   Initialize top down search  STA     ROLL2  CLR     ROLL1    Initialize bottom up searchBEGIN4 INC     ROLL1    ROLL1 gets next number on list  JSR     TESTIM   Is the time up?  CMP     FOUND    TESTIM always returns zero in  BNE     A4       the accumulator. If Found is true  JSR     TESTIM   the ROLL is decided, else try  CMP     FOUND    the next number.  BNE     B4  DEC     ROLL2    ROLL2 goes to next number on its  CMP     ROLL2    list. Does it = 0? (accumulator)  BNE     BEGIN4   If no, go to BEGIN4  BRA     START4   Else branch to START4A4     LDA     ROLL1  BRA     END4B4     LDA     ROLL2END4   STA     ROLL  RTS______________________________________ 
    
     The following subroutine is heavily favoured to ROLL low numbers. It 
     
         ______________________________________creates a pattern      1 1 1 1 1 1 . . .                  and searches through itfrom top down.      2 2 2 2 2 . . .                  When TESTIM returns apositive FOUND      3 3 3 3 . . .                  the number currentlyunder examination      4 4 4 . . . is the ROLL which LUCK1returns to 5 5 etc,.   ANSWER.LUCK1  NOPSTART1 CLR     ROLL     Initialize ROLL  CLR     ROLL1    ROLL1 is a dummy variableBEGIN1 INC     ROLL  INC     ROLL1  JSR     TESTIM   See if number is FOUND  CMP     FOUND    (accumulator = 0 from TESTIM)  BNE     END1     When Found go to end  LDA     ROLL1    This section creates the pattern  CMP     DIESID   Row one has DIESID 1&#39;s in it  BEQ     NEXT1    Row 2 has (DIESID-1) 2&#39;s in it  DEC     ROLL     This puts the correct number of  BRA     BEGIN1   entries in each rowNEXT1  LDA     ROLL     This part prepares to start  STA     ROLL1    the next row (which will have  CMP     DIESID   one less entry than the previous  BEQ     START1   one)  BRA     BEGIN1END1   RTS______________________________________ 
    
     The following subroutine is heavily favoured to ROLL high numbers. It 
     
         ______________________________________creates a pattern       1         and searches from bottomup. When TESTIM       2 2       returns FOUND as true, thenumber being       3 3 3     examined is returned toANSWER as the       4 4 4 4 etc,.                 ROLL.LUCK7   NOPSTART7  LDA     DIESID   Initialze bottom up search   STA     ROLL   STA     ROLL1    Dummy variableBEGIN7  CLRA   CMP     ROLL1    This subroutine operates the same   BEQ     NEXT7    as LUCK1 except that it runs   JSR     TESTIM   through the large numbers first   CMP     FOUND   BNE     END7   DEC     ROLL1   BRA     BEGIN7NEXT7   DEC     ROLL   LDA     ROLL   STA     ROLL1   CMP     #$00   BEQ     START7   BRA     BEGIN7END7    RTS______________________________________ 
    
     The following subroutine tests the value in the lower time byte. If the value is in the upper third, the value of ROLL returned to ANSWER will be from LUCK4, otherwise from LUCK1. 
     
         ______________________________________LUCK   LDA     TIMEL  CMP     #$AA      AA = 170 which is two thirds of  BHI     PRT2B     255  JSR     LUCK1  BRA     END2PRT2B  JSR     LUCK4END2   RTS______________________________________ 
    
     The following is the same as LUCK2 except that two thirds of the time ROLL will be from LUCK4 and one third from LUCK1. 
     
         ______________________________________LUCK3           LDA         TIMEL           CMP         #$AA           BHI         PRT3B           JSR         LUCK4           BRA         END3PRT3B           JSR         LUCK1END3            RTS______________________________________ 
    
     The following subroutine is the same as LUCK2 except that two thirds of the time the ROLL will be from LUCK4 and one third LUCK7. 
     
         ______________________________________LUCK5           LDA         TIMEL           CMP         #$AA           BHI         PRT5B           JSR         LUCK4           BRA         END5PRT5B           JSR         LUCK7END5            RTS______________________________________ 
    
     The following subroutine is the same as LUCK2 except that two thirds of the time the ROLL will be from LUCK7 and one third LUCK4. 
     
         ______________________________________LUCK6           LDA         TIMEL           CMP         #$AA           BHI         PRT6B           JSR         LUCK7           BRA         END6PRT6B           JSR         LUCK4END6            RTS______________________________________ 
    
     The following subroutine&#39;s purpose is to test if time=0 and to flag FOUND as true when it is. If time doesn&#39;t equal zero, time is decreased by 1 and the subroutine returns to the calling program. Time is stored in TIMEL and TIMEH. 
     
         ______________________________________TESTIM  CLRA               Test lower time byte   CMP      TIMEL     If it&#39;s not zero, goto continue   BNE      CONT1   CMP      TIMEH     If it is, test higher byte   BNE      CONT2     If it&#39;s not zero, go to cont2   INC      FOUND     If it is, set FOUND as true   BRA      ENDTTCONT2   DEC      TIMEHCONTl   DEC      TIMELENDTT   LDA      #$00   RTS______________________________________ 
    
     Now the &#34;GET ANSWER&#34; subroutine is finished and the program returns to the block &#34;CONVERT ANSWER TO DECIMAL FORM&#34; at the top of FIG. 3b. Thus, the following subroutine converts TOTALH and TOTALL to decimal form and readies it for printing. It does the lower byte by itself and calls BIGNUM if there is a value in TOTALH. 
     
         __________________________________________________________________________TODEC   CLR  PNUM4   CLR  PNUM3  Set all the outputs to zero   CLR  PNUM2   CLR  PNUM1   LDA  TOTALL Sort out the hundreds firstDG100   CMP  #$64   When TOTALL is less than 100   BLO  DG10   move on to the tens column   SUB  #$64   INC  PNUM3  PNUM3 has the 100&#39;s value   BRA  DG100DG10    CMP  #$0A   Is TOTALL now less than 10?   BLO  DG1    When it is, move on to the ones   SUB  #$0A   INC  PNUM2  PNUM2 has the 10&#39;s value   BRA  DG10DG1     STA  PNUM1  The remainder is the ones value   LDA  TOTALH Test to see if TOTALH exists   CMP  #$00   If it does then the total is   BEQ  ENDTOD above 255 and we call BIGNUM   JSR  BIGNUMENDTOD__________________________________________________________________________ 
    
     The following subroutine is called when the answer in total exceeds 255. It converts the number in TOTALH to decimal form and adds it to the numbers obtained from TOTALL. The result is stored in PNUM and is ready to be printed. 
     
         __________________________________________________________________________BIGNUM  NOPSTRTBG  LDA  PNUM3   ADD  #$02   STA  PNUM3   LDA  PNUM2  This adds 256 to the PNUMs for   ADD  #$05   each value in TOTALH.   STA  PNUM2   LDA  PNUM1   ADD  #$06   STA  PNUM1   DEC  TOTALH   CLRA   CMP  TOTALH   BNE  STRTBG   LDA  PNUM1  This section makes sure thatBABNUM  CMP  #$09   PNUM1 contains nine or less   BLS  TENSOR with the excess converted to   SUB  #$0A   PNUM2   INC  PNUM2   STA  PNUM1   BRA  BABNUMTENSOR  LDA  PNUM2  This section ensures that PNUM2TENNUM  CMP  #$09   contains nine or less with the   BLS  HUNOR  excess converted to PNUM3   SUB  #$0A   INC  PNUM3   STA  PNUM2   BRA  TENNUMHUNOR   LDA  PNUM3  This section ensures that PNUM3SENNUM  CMP  #$09   contains nine or less with the   BLS  DONER  excess converted to PNUM4   SUB  #$0A   INC  PNUM4   STA  PNUM3   BRA  SENNUMDONER   RTS__________________________________________________________________________ 
    
     The following subroutine is called to initialize the PNUMs so that the word diCE is printed on the display. 
     
         ______________________________________PDICE   LDA      #$0D   STA      PNUM4     This subroutine simply   LDA      #$01      loads the PNUMs from the   STA      PNUM3     accumulator, one at a time   LDA      #$0C   STA      PNUM2   LDA      #$0E   STA      PNUM1   JSR      PRNT4   RTS______________________________________ 
    
     The following subroutine displays the answer for 10 seconds, then changes the display to dice. If a key is pressed before the ten seconds expires, the loop is ended and the regular program is resumed at SRCHKY. 
     
         __________________________________________________________________________TMFRDC LDA  #$0F  STA  PNUM3LOOP3  LDA  #$80  STA  PNUM1  This subroutine creates a loop.  DEC  PNUM3LOOP2  LDA  #$FF   Every time through its inner loop,  STA  PNUM2  it checks to see if anything has  DEC  PNUM1LOOP1  LDA  PORTB  been hit on the keypad. If it has  CMP  #$99   the subroutine kicks out.  BNE  DICEND  DEC  PNUM2  CLRA  CMP  PNUM2  BNE  LOOP1  CMP  PNUM1  BNE  LOOP2  CMP  PNUM3  BNE  LOOP3DICEND RTS__________________________________________________________________________ 
    
     The following is the subroutine that prints out at the LCD. Calling a PRNT program also calls those beneath it. 
     
         __________________________________________________________________________PRINT4 LDA  PNUM4 Load the accumulator with PNUM4 and STA  PORTC send to the output file LDA  #$10  This is the switch that causes the STA  PORTC output file to be printed JSR  PRNT3 Now call PRNT3 RTS        Return to calling programPRNT3 LDA  PNUM3 This is the same as PRNT4 except ADD  #$40  that PNUM3 is printed STA  PORTC The #$40 must be added to PNUM3 so LDA  #$10  the LCD will know the digit that STA  PORTC PNUM3 gets printed in. JSR  PRNT2 RTSPRNT2 LDA  PNUM2 ADD  #$80 STA  PORTC LDA  #$10 STA  PORTC JSR  PRNT1 RTSPRNT1 LDA  PNUM1 ADD  #$C0 STA  PORTC LDA  #$10 STA  PORTC RTS__________________________________________________________________________ 
    
     In operation, the program begins by searching the keypad to detect the number of dice selected (from 1 to 99); the number of sides on each die (from 1 to 100); and the probability weighting factor. 
     For example, by setting the dial 15 at &#34;4&#34; and pressing from among the &#34;dice-type&#34; buttons the button 18a (D8) the operator selects a single, eight sided, evenly weighted die having &#34;sides&#34; numbered &#34;1&#34; to &#34;8&#34;. 
     In general, to determine the number of dice the operator presses numerical buttons 12a to 12j corresponding to the desired number of dice (1 to 99); the default is one die. For die other than those provided by pressing the buttons 18 for the pre-selected types (8 sided. 10 sided. 20 sided and 100 sided) the operator then presses the &#34;D&#34; button 16 and then presses numerical buttons 12a to 12j corresponding to the desired number of sides (1 to 100); otherwise the operator does not press the &#34;D&#34; button 16 and just presses the desired &#34;dice-type&#34; button 18. Subsequently pressing the &#34;=&#34; button 17 would start the simulation. Therefore, before pressing the &#34;=&#34; button 17 the desired probability weighting should be selected using the dial 15. 
     Pressing the &#34;=&#34; button 17 indicates to the device that the operator is ready to &#34;roll&#34;, provided the device has received sufficient information. If it has received enough information, pressing the &#34;=&#34; button 17 causes the device to convert the numerical input from base 10 form to binary form. The position of the dial 15 of the probability weighting selector 20 then determines the weighting of the die or dice, and that weighting is recorded. 
     Due to the fact that the microprocessor 19 is running at high clock rate, say, 2 MHz, it is difficult for human operators to determine, without the aid of electronics, what clock value will be recorded by pressing the &#34;=&#34; button 17 on the key pad 22. Therefore, it is in this sense that the disc simulator 10 is a random/pseudo-random device. 
     The count on the internal clock of the microprocessor 19 is recorded by pushing the &#34;=&#34; key 17 of key pad 22. The microprocessor 19 clock has an 8 bit higher time register and an 8 bit lower time register. It is preferred to mask some of the higher bits in the clock count, to decrease the response time of the device 10. The number of higher bits masked is masked is proportional to the number of sides on each die. Thus if a 20 sided die were rolled, there would be 1024 different numbers that would actually be used to determine the number rolled. 
     The number 1024 is obtained because the six left-most bits of the higher time register are masked away. This leaves the entire lower time register which has eight bits and the two remaining bits from the higher time register, for a total of ten bits. Each bit may be zero or one. Therefore, there are 1024 different combinations possible (2 to the exponent ten). 
     If a 100 sided die were to be rolled, then there are 0.096 possible readings since only the four left-most bits of the higher time register are masked away. 
     If the probability weighting dial 15 is set to position 4, i.e. the middle position, there is for an ordinary unaided operator an even chance of any number between 1 and the number of sides of the die being &#34;rolled&#34;. A number is &#34;rolled &#34; in that instance by the device 10 iteratively comparing the recorded clock count to a lower value and to that upper value. First, if the recorded clock count is &#34;zero&#34; then the value &#34;1&#34; has been &#34;rolled&#34;. If that clock count is not &#34;zero&#34; then the clock count is compared to the upper value (at this stage, the number of sides of the die). If the clock count is that upper value then that upper value is &#34;rolled&#34;. If the clock count is not that upper value then the lower value is increased by one and the upper value is decreased by one. The new upper and lower values are once again compared to the recorded clock count. The comparisons and iterations continue until (i) the lower value and the recorded clock count equal or (ii) the &#34;upper value&#34; has been iterated down to zero. Once that &#34;upper value&#34; has been iterated to zero (i) it is reassigned the value of the number of sides of the die and (ii) the lower value is reassigned the value &#34;1&#34;. 
     The possibility of repeated comparisons and resettings, ad infinitum, is precluded as follows. After each comparison the recorded clock count is compared to zero. If the clock count is zero then the device indicates the value is &#34;rolled&#34;. If the recorded clock count is not zero that count is decreased by one and the next iteration and comparison begin. 
     The probability weighting dial 15 may alternatively be set to any one of positions 1, 2 or 3, position 1 being the most weighted towards producing low number &#34;rolls&#34;, position 3 being the least weighted towards producing low number &#34;rolls&#34; and position 2 being intermediately weighted between positions 1 and 3. 
     In position 1 the &#34;upper value&#34; is used as a counter rather than as a possible &#34;roll&#34;. That is done by the &#34;upper value&#34; and &#34;lower value&#34; initially being given the value &#34;1&#34;. The recorded clock count is then compared to the upper and lower value. If the recorded clock count does not match that value then the upper value is increased by one. Such comparisons and increases continue until the upper value equals the selected number of sides on the die. Once that equality occurs the lower value is increased by one and the upper value becomes the same as that new lower value. The comparisons and increases continue as in the initial round on the setting, until the lower value equals the selected number of sides on the die. Once that equality occurs the upper and lower values are again set at &#34;1&#34; and the process continues until the recorded clock count matches either the upper value or the lower value. 
     The &#34;rolls&#34; at settings &#34;2&#34; and &#34;3&#34; are obtained by examining the lower time register of the internal clock of the microprocessor 19. The lower time register of the microprocessor 19 has 8 bits in it and so can have 256 (i.e. 2 to the exponent 8) different values, from 1 to 256. The number 170 is approximately 2/3 of 256. If the value on the lower time register is greater than 170 then the simulated roll is arrived at by the procedure used at setting 4. Therefore if the device 10 is set to position 2 of the probability weighting dial 15 then two thirds of the generated numbers will be arrived at by the procedure used at setting 1 (&#34;Luck 1&#34; in FIG. 4a) and one third of the generated numbers will be arrived at by the procedure used at setting 4 (&#34;Luck 4&#34; in FIG. 4a). Conversely if the device is set to position 3 then the respective splits are 1/3 and 2/3 rather than 2/3 and 1/3. 
     Settings 5 to 7 of the probability weighting dial 15 weight the device towards producing high &#34;rolls&#34;. They do so in a manner analogous to the weighting provided by settings 1, 2 and 3 i.e. by using the upper value as a counter. However, at setting 7 of the dial 15 the upper and lower values are not initially set at 1  but rather at the value that is the number of sides of the die. The iterations result in the upper value being decreased by one each time, until it equals zero; the lower value is then reduced by one and the lower value becomes the new upper value. Such iterations occur until the lower value equals zero. Upon that event the upper and lower values are reset to the value that is the number of sides on the die and the comparisons and iterations start over. 
     The &#34;rolls&#34; at settings &#34;5&#34; and &#34;6&#34; are obtained by examining the lower time register of the internal clock of the microprocessor 19. When the value in the lower time register is less than or equal to 170 the roll will be simulated in accordance with the procedure at setting &#34;4&#34;. When the value in the lower time register is greater than 170 the roll will be simulated in accordance with the procedure at setting &#34;7&#34;. Therefore, if the device 10 is set to position 5 of the probability weighting dial 15 then two thirds of the generated numbers will be arrived at by the procedure used at setting 4 and one third of the generated numbers will be arrived at by the procedure used at setting 7. Conversely, if the device is set to position 6 then the respective splits are 1/3 and 2/3 rather than 2/3 and 1/3. 
     As the &#34;rolls&#34; for each die are produced they are summed. The device then converts the sum to the base 10 system and displays on screens 13 and 14 the final sum of the individual die rolls comprising that simulation. 
     After 10 seconds of display of the simulation result the device is re-initialized and enters a low power mode to conserve the power supply 30. It remains in that mode until a key on the key pad 22 is pressed. If the key is the &#34;=&#34; button 17, the device generates and displays a simulation, using the same variables (i.e. number of die, number of sides per die and probability weighting) as in the previous roll as many times as that button is pressed, until the device is turned off. If before pressing the &#34;=&#34; button 17 the position of the dial 15 is changed no other variables, by that act alone, are changed. If before pressing the &#34;=&#34; button 17 one or more of the numerical key pad buttons 12a-12j are pressed the device generates and displays a simulation based on the previously set number of sides per die and probability weighting and on the newly set number of die. 
     It will be apparent to those skilled in the art that various modifications can be made to the apparatus and method for simulating dice rolling and the like of the instant invention without departing from the scope or spirit of the invention, and it is intended that the present invention cover modifications and variations of the apparatus and method for simulating dice rolling and the like provided they come within the scope of the appended claims and their equivalents. Further, it is intended that the present invention cover present and new applications of the apparatus and method of the present invention.