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EP0061052A2 - Elektronische Spieleinrichtung und Verfahren zur Auswahl von Ereigniskombinationen - Google Patents

Elektronische Spieleinrichtung und Verfahren zur Auswahl von Ereigniskombinationen Download PDF

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Publication number
EP0061052A2
EP0061052A2 EP82101801A EP82101801A EP0061052A2 EP 0061052 A2 EP0061052 A2 EP 0061052A2 EP 82101801 A EP82101801 A EP 82101801A EP 82101801 A EP82101801 A EP 82101801A EP 0061052 A2 EP0061052 A2 EP 0061052A2
Authority
EP
European Patent Office
Prior art keywords
outcomes
combinations
predetermined probabilities
events
selecting
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Withdrawn
Application number
EP82101801A
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English (en)
French (fr)
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EP0061052A3 (en
Inventor
Yoel Gat
Eliezer Pasternak
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Individual
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Individual
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Priority claimed from IL8265048A external-priority patent/IL65048A0/xx
Application filed by Individual filed Critical Individual
Publication of EP0061052A2 publication Critical patent/EP0061052A2/de
Publication of EP0061052A3 publication Critical patent/EP0061052A3/en
Withdrawn legal-status Critical Current

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    • G—PHYSICS
    • G07—CHECKING-DEVICES
    • G07C—TIME OR ATTENDANCE REGISTERS; REGISTERING OR INDICATING THE WORKING OF MACHINES; GENERATING RANDOM NUMBERS; VOTING OR LOTTERY APPARATUS; ARRANGEMENTS, SYSTEMS OR APPARATUS FOR CHECKING NOT PROVIDED FOR ELSEWHERE
    • G07C15/00—Generating random numbers; Lottery apparatus
    • G07C15/006—Generating random numbers; Lottery apparatus electronically
    • A—HUMAN NECESSITIES
    • A63—SPORTS; GAMES; AMUSEMENTS
    • A63F—CARD, BOARD, OR ROULETTE GAMES; INDOOR GAMES USING SMALL MOVING PLAYING BODIES; VIDEO GAMES; GAMES NOT OTHERWISE PROVIDED FOR
    • A63F3/00—Board games; Raffle games
    • A63F3/08—Raffle games that can be played by a fairly large number of people
    • A63F3/081—Raffle games that can be played by a fairly large number of people electric

Definitions

  • This invention relates generally to gaming devices, and more particularly the invention relates to the selection of possible combinations of outcomes of a plurality of events based on probability and on a random selection.
  • an object of the present invention is means for assisting in determining combinations of outcomes of such events based on probability and on random selection.
  • Another object of the invention is means for rapidly determining outcome selections of such events in a descending order of probability.
  • Still another object of the invention is means for providing random selections of outcomes with a predetermined bias.
  • Yet another object of the invention is a method for automatically computing selections of events based upon probability data.
  • apparatus selects combinations of outcomes of events such as games based on predetermined probability of outcome of each events.
  • predetermined probabilities are stored in memory means, and computation means receives the predetermined probabilities and first selects the most likely combination of outcomes. The computation means then sequentially selects the next most likely combinations based on the predetermined probabilities.
  • Display means displays each combination of outcomes.
  • the computation means comprises a programmed microprocessor which can sequentially select the most likely combinations ("best" mode) and also can randomly select combinations of outcomes based on predetermined probabilities ("luck” mode).
  • the random selection in a preferred embodiment is achieved by a pseudorandom sequence formed by a Linear feedback shift register (LFSR).
  • LFSR Linear feedback shift register
  • the reading is compared with the stored probabilities to determine the selected outcome.
  • a mode switch is provided for selecting a data Insertion mode of operation, a "best" mode of operation, and a random or “luck” mode of operation.
  • a keyboard is provided for inserting data, and a columned display provides the selected combinations.
  • Doubles meaning 2 outcomes of a single game
  • triples meaning all 3 outcomes of a single game
  • the invention will be described with reference to 2 embodiments: first, for selecting combinations of outcomes of 13 soccer games in which the home team can win (designated 1), the visiting team can win (designated 2), or the game can end in na tie or a draw (designated by X).
  • the user first formulates his guess as to the likelihood of the three possible outcomes for each game, and he inputs three numbers representing the likelihood of a home team victory (1), a visiting team victory (2), or a tie (X).
  • Each of the numbers ranges from 0 to 99 with a 0 representing the least likelihood and 99 representing maximum likelihood for the event to occur.
  • the three numbers will be normalized whereby the sum equals to 100 (representing unity), as will be described below.
  • the most likely combination of selections can be identified by selecting the outcome associated with the highest probability of each game.
  • the selection of the next likely probability is identified by the product of probabilities for all games and sequentially selecting several combinations in a descending probability order. Several combinations may have the same probability, and each is identified.
  • a "Luck" mode is provided whereby the outcome of each game is individually selected with the aid of a random number generation. The reading is compared with the stored probabilities to determine the selected outcome. Doubles and triples can be generated from “luck” and from "best” modes, by keying "2" or "3" key in the keyboard.
  • the second embodiment relates to selecting combinations of outcome of 55 soccer games in which 8 games that would end in scored draw (2:2, 1:1 etc.) need to be selected.
  • the user may formulate his guess as to the likelihood of all or several of the possible 4 outcomes: 1- home team victory, 2- visiting team victory, X- unscored draw (0:0) and XX---scored draw for every game. This is done as in the first embodiment. Whenever the user does not formulate his guess, best statistical results (regarding to the last few years for example) are entered automatically. After all numbers are inserted and normalized, the most likely combination can be identified by selecting the outcome associated with the highest probabilities of scored draws. In a similar matter next likely combination could be chosen. Alternatively in a "luck" mode, game numbers are individually selected with the aid of the random number generator, in such a way that the probability for each possible game number (to appear on the display) is proportional to the chance estimate entered for score draw for that game.
  • the apparatus includes a four position switch 12 for power off, data insert, "luck” mode operation, and "best” mode operation.
  • a sixteen digit keyboard 13 is used for inserting data, for registering combinations of outcomes in the "best” mode, and for requesting game outcome selections during the "luck” mode of operation.
  • An optical display 14 consisting of two seven segment light emitting diodes provides a readout of the input data, and an optical display 15 provides a readout of a combination for 13 games.
  • each game Associated with each game are three light emitting diodes which are selectively illuminated (as indicated by an I) to indicate a home team victory (1), a tie (X), or a visiting team victory (2).
  • I a home team victory
  • X a tie
  • visiting team victory (2) a visiting team victory
  • the apparatus In the insert mode of operation, the apparatus is energized and the system is ready to receive and store input data.
  • the user enters numbers representing the chances for the three possible outcomes of each game, i.e. the numbers are proportional to the user's estimate of the probabilities of the outcomes.
  • the numbers are entered by pressing the keyboard 13, and are displayed on the numeric display 14.
  • the various combinations are illustrated on the display 15 as a function of the numbers which have been inserted and stored during the insert mode of operation.
  • the generation of.output combinations is based on an electronic lottery in which the probability for each possible outcome is proportional to the chance estimate entered for that outcome.
  • Each stroke of the key marked "c" in the keyboard 13 causes a lottery of a new outcome combination on the display. Therefore, after each stroke, a complete column is displayed.
  • all of the 3 13 possible combinations may be successively displayed one after another by depressing the " ⁇ " key, and the combinations, in a descending order of probability, are provided on display 15 in response to each depression of the down key.
  • Doubles and triples can be generated by a stroke on keys "2" or “3” accordingly.
  • Each stroke of "2" key adds a second outcome to one of the games.
  • Each stroke on "3" key selects all three outcomes of one of the games.
  • the user may enter his chances estimates for each possible outcome of each game. Whenever probability assigments are not entered by the user, predetermined probabilities based on statistical knowledge are entered automatically.
  • the game numbers are individually displayed on the display 14 in a descending probability order. Each time "c" key is stroked, a new game number is entered to the display.
  • the generation of game numbers is based on an electronic lottery in which the probability for each possible game number is proportional to the chance estimate entered for scored-draw for that game.
  • the apparatus includes a 6 volt power supply 16 which is interconnected to a microprocessor 17 along with the keyboard 13, the alpha numeric display 14, and the display 15 comprising three columns of light emitting diodes.
  • the microprocessor 17 is an R 6500/1 microcomputer, manufactured by Rockwell International of Anahaim California. This family of microcomputers contains several I.C.s that differ in the size of the program ROM, DATA RAM, I/O lines and on chip peripherals.
  • the R 6500/1-10 microcomputer contains 2048 bytes of Program ROM, 64 bytes of DATA RAM and 32 I/O lines.
  • the R 6500/1-11 microcomputer contains 3072 bytes of Program ROM, 192 bytes of DATA RAM and 32 I/O lines.
  • the R 6500/1-10 microcomputer suits the first embodiment and the R 6500/1-11 suits the second embodiment (as well as the first).
  • the keyboard 13 is a 4 by 4 matrix with 4 input lines I 1 -I4 and 4 output lines 0 1 -0 4 interconnecting the matrix with the microprocessor 17.
  • the input lines are connected to pins 35-38 of the microprocessor, and the keyboard outputs are connected to the microprocessor pins 31-34.
  • the keyboard output lines are read after each "high” setting of one of the four keyboard input lines. After all output lines have been successively set high a unique identification of any single key depression is accomplished.
  • Resistors 18 are pull- down resistors to ensure "low" state in the non- activated line.
  • the two digit display 14 is provided to display the numbers entered in the "insert” mode and to display the serial number (modulo 100) of each combination displayed in the "best chance” mode.
  • the two digit display may comprise a seven segment LED display such as the HP 5082-7740 of Hewlett Packard.
  • the display is driven by a BCD to seven segment latch-decoder-drivers 8 such as an RCA CD 4511B.
  • Pins 4-9 of the microprocessor 17 control the drivers 8 with the digits being separately set by the setting of a BCD code at pins 6-9 and then temporarily setting pins 4 and 5 low according to the digit selected to be updated.
  • the light emitting diode array 15 consists of 39 LED's arranged in 13 rows with 3'LED's per row, assuming 13 games in each column with each game having three possible outcomes. Each LED displays one possible outcome for each game.
  • the LED's are driven by an array of low power logic inverters 20 such as the Texas Instruments SN74LS05, which is a hex inverter, open collector LS-TTL device. Each inverter output pin is connected to one row of LED's ⁇ via a resistor 21 for limiting the current.
  • the anodes of the LEDs are each connected to a collector of one of PNP transistors 22, 23 or 24.
  • the transistors are 2N2904 devices.
  • the microprocessor 17 controls the three transistors 22-24 whereby only one transistor can conduct at a time and a combination of "high” and “low” levels appears on the microcomputer output pins 13-29 and one column with any combination of LED states is displayed at one time.
  • the three columns are successively selected through transistors 22-24 at a high rate whereby the combinations can be visually observed.
  • the three operational modes of the apparatus are selected via the switch 12.
  • Two microprocessor input lines are connected to the switch and to the pull-up resistors 26.
  • the switch can connect one of the lines to ground thus providing the distinguishable combinations necessary to define the three operational modes: insert, best chance, and luck.
  • a crystal oscillator 27 provides a clock frequency of four megahertz to the microprocessor 17. Power is turned on and off by the switch 28, and a silicon diode 29 such -as a 1N4001 connects the V BB line to the V cc line to provide a voltage drop of about 0.8 volt at 100 milliamps and thus provides V cc in the allowable range for the microcomputer and the logic devices.
  • the reset pin 39 of the microprocessor is connected to the V cc line through resistor 30 and diode 31.
  • the reset line is held “low” by the charge on capacitor 32. This forces the reset procedure in the microprocessor.
  • Resistor 30 charges the capacitor to release the reset condition.
  • Diode 31 provides a fast discharge pass for the capacitor, once the switch 28 has been turned off, and thus ensures a new reset condition even after a short off period.
  • Capacitor 33 is provided to reduce noise in the V cc line.
  • FIG. 3 is a general flow diagram'of the apparatus operation
  • switch 12 When switch 12 is turned on (from off to insert) the apparatus goes through a reset and initialization procedure and then enters a "Cold Insert" mode. In this mode all of the 39 chance values (3 values for each one of the 13 games) can be entered by the user.
  • the probability of each combination can be calculated by multiplying all 13 outcome probabilities associated with it. Since the microprocessor inherently performs add and subtract operations it is more efficient to convert all possible probabilities in the range of 0 to 99 to logarithmic numbers of 16 bits and perform summation rather than multiplication. The range of numbers in the table will allow summation of the 13 logarithmic probabilities without overflow.
  • a counter format is defined as shown in Fig. 4.
  • Each 2 bit combination in Fig. 4 represents the outcome of a specific game in the following manner:
  • the counter Since the microprocessor cannot count modulo 3 the counter is advanced through a ROM table.
  • the entry to the ROM table is one of the 4 x 2 bit cells (C 1 - C 4 ), and the output of the table is the binary difference needed to increment the counter modulo 3. This difference is added to the current cell content.
  • the status of the carry bit determines whether the next significant byte of the counter should be advanced.
  • This algorithm is based on the fact that many combinations will be defined for any given probability.
  • the total number of possible combinations is 1 , 594 ,323 (3 13 ) while only 65,536 different probabilities may exist since the logarithmic sum is arbitrarily limited to 16 bits. Thus, there are 2 16 possible values. If the probabilities are distributed uniformly then about 24 combinations will have the same probability.
  • the combinations counter is manipulated the microprocessor searches another combination with the same probability and displays it next. While running through the counter possibilities, the microprocessor also searches for the next (lower) probability that would be the virtual probability of the next counter cycle (LN). It will be appreciated that there is a trade-off between the time required for a complete cycle and the accuracy of the comb. probabilities.
  • a 13 bit accuracy per logarithmic probability for each game and 16 bit accuracy for the combination probabilities
  • the mode search flowchart is shown in Fig. 6 and is provided in two separate locations. After “COLD INSERT” the mode search determines the mode requested by the user. If the main panel switch 12 has not been moved to the "BEST CHANCE” or “LUCK” modes a "WARM INSERT" (modifications of input data) is assumed. The interrupt subroutine, after displaying the present buffer, checks if a change has been made in one of the main panel keys.
  • the user can input the chances of the three outcomes for each game by means of 2 digit decimal numbers.
  • the relative chance for each outcome is determined by the ratio between the chance numbers associated with the appropriate outcomes.
  • the numbers have to be normalized so that the sum of the three probabilities is 100 (when the probabilities are represented in percentage form).
  • S X + Y + Z
  • S is represented in memory by a 16 bit word (4 BCD digits).
  • the 8 leftmost bits are defined as SUM high and the 8 rightmost bits are defined as SUM low.
  • Fig. 7 is a flow chart for normalizing outcome probabilities. Prior to the. actual normalization a rough normalization is performed. This step reduces the value of X, Y and Z by a factor of 2 until their sum does not exceed 100.
  • Fig. 8 is a flow diagram of the Insert Mode Program. This mode deals with the initial insertion of data or chances for the 13 games (COLD INSERT), or changes to the data which were already input (WARM INSERT).
  • COLD INSERT COLD INSERT
  • WARM INSERT changes to the data which were already input
  • LINK is a flag used to indicate whether the digit just inserted is the first or second in order to determine whether the game number pointer should be advanced.
  • WARM/COLD Insert is a flag indicating which part of the software should be used. This flag is erased after the INSERT routine is completed. When the "?" key is pressed, some fixed preset probabilities are entered to the active game indicated by the pointer.
  • the pointer state is not affected by a transfer to another software section to allow convenient return through "WARM INSERT".
  • a random number generator is implemented in the preferred embodiment.
  • the RNG comprises of 32 bits "Linear feedback shift register” (LFSR).
  • LFSR Linear feedback shift register
  • the series generated by LFSR are called M-series or pseudo random series.
  • the feedback is formed by XORing the 1,2,22,32 bits, entering the results in the LSB of the LFSR after rotating the whole LFSR 1 bit left.
  • Generation of random number is done by parallel sampling n ⁇ 32 bits from the LFSR forming a number with the range 0+(2 n- 1 ). The randomness of such a process is discussed in mathematical and technical books.
  • Fig. 9 illustrates the initialization of the LFSR.
  • 21 random bits are placed in the LFSR in order to distinguish between up to 3 13 simultaneous users.
  • Those random bits can be generated in many ways. One example is by letting the ⁇ P timer free-run, and each time a probability is entered (in the INSERT mode), the LSB of the timer is being sampled and entered to the LFSR.
  • Fig. 10 illustrates the method of moving the LFSR. Bits 1,2,22,32 are being XORed and the result is stored in the carry bit. The 4 bytes are successively rotated left through the carry bit. A check of all zero is made (illegal state) and if by mistake such a situation arises, 1 is entered to the LSB (least significant bit).
  • Fig. 11 illustrates the process of a random number generation.
  • the LFSR is moved 32 times. n bits are sampled. The number is normalized to the appropriate value.
  • FIG. 12 An example of such normalization is shown on Fig. 12. Whenever a number in the range of 0 to 99 need to be generated, 8 bits are sampled (forming a number in the range 0 to 255). This number is 16 bits added to itself 99 times (forming a multiplication by 99), and the upper byte (most significant) of the 16 bit number contains the normalized result.
  • Fig. 13 is a flow diagram of the Luck mode.
  • the value (R) is compared to the probabilities of row I, i.e. P(1) is the probability of outcome 1, P(X) is the probability of outcome X, and P(2) is the probability of outcome 2. If R ⁇ P(1) then "1" is the lottery outcome, else If R ⁇ P(1)+P(X) then "X” is the lottery outcome, otherwise "2" is the lottery outcome.
  • the display buffer is being updated each time an outcome is selected.
  • Double - means two possible outcomes of a single game.
  • Triple - means three possible outcomes of a single game. Doubles and Triples can be entered from within Luck and Best modes, by stroking keys 2 and 3 respectively. After an output combination is being selected the user can add as many doubles and triples as he wishes, until the display is full.
  • Fig..14 illustrates the generation of a double from Best mode.
  • LP is the maximal double probability at a certain stage, and L is a temporary probability.
  • I is the game number and J is the double number (there are 3 in a game: 1,X; X,2; 1,2).
  • the double probability is being calculated as a multiplication between the two probability assignments.
  • Fig. 16 illustrates the generation of a double from Luck mode.
  • SD is calculated as the sum of all 26 available doubles.
  • P IM is the probability of the outcome that has been selected for the I th game in this current outcome combination.
  • P IJ represents, one of the two probabilities of an outcome that has not been selected: (one of the two available doubles).
  • SD is calculated as the sum of the two available doubles in each game summed for all games.
  • a random number R is generated in the range O ⁇ SD.
  • the number K 2 represents the double number (1 or 2), and K 2 represents the game number.
  • the display is updated so as to light the appropriate LED.
  • ST is-calculated as the sum of all available triples.
  • a triple probability is the multiplication of all three normalized probabilities of a single game.
  • a random number R is generated in the range O+ST.
  • a summing procedure takes place until the sum equals or is greater than R for the first time.
  • K represents the game number in which the triple is generated.
  • More than 110 bytes of RAM are required, so a microcomputer with at least 128 bytes of internal RAM need to be chosen.
  • a good example as in the preferred embodiment is Rockwell's R 6500/1-11 which contains 192 bytes of internal RAM.
  • INSERT mode cold and warm
  • P(1),P(2),P(X),P(XX) predetermined probabilities obtained by best statistical result (of the last several years) are entered automatically to P(1),P(2),P(X),P(XX).
  • the user may enter his chance estimates to all, part of, one or none of the available outcomes. For each possibility the value of P(XX) is calculated. If for example, the user has changed only P(1), then the new P(XX) I is P'(XX) is inserted to the appropriate place of the P ( XX ) I array (the I th place). After the user finishes entering his chance estimates, he can activate Best or Luck mode.
  • Best mode game numbers are successively displayed in a descending probability order (of P(XX)).With each stroke of "C" key a new game number appears on the display.
  • Luck mode is shown on Fig. 19.
  • SE is calculated as the sum of all P(XX) I .
  • R is generated (each time "c" key is stroked) in the range 0 to SE.
  • a summing procedure takes place until for the first time the sum is equal or greater than R, K is the generated game number for that stroke.
  • Fig. 20 is an electrical schematic of another embodiment of the invention in which electronic means randomly selects outcomes of each game based on predetermined probabilities.
  • the probabilities for each game are set by means of three potentiometers. Consecutive lotteries for each game can then be effected by pressing a button. Each buttom depression results in a lottery based on the potentiometers setting, and one of three LED's is turned on to indicate the selected outcome.
  • the potentiometers are then modified to represent the probabilities for the next game.
  • CMOS NOR gates 80, 82, 84 have interactive feedback which create a ring counter.
  • Each gate in the ring counter goes high in its turn for a period proportional to the resistance of the associated potentiometer 81, 83, and 85 while the two remaining gates are in the "low" state.
  • the three gates comprise a recycling ring counter.
  • the total rate of oscillations is designed to be higher than human response to ensure a random lottery.
  • Selection apparatus in accordance with the invention is useful in quickly determining combinations of outcomes of sporting events such as soccer games.
  • the description is illustrative of the invention and not limiting of the invention.
  • low power consumption can be realized through use of a CMOS processor and LCD display, and the visual display can be replaced by or used with a printer or sound output.
  • Improved accuracy can be realized with a 16 bit microprocessor or by increasing computation time.

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • Multimedia (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
EP82101801A 1981-03-18 1982-03-08 Electronic game apparatus and methods of selecting combinations of events Withdrawn EP0061052A3 (en)

Applications Claiming Priority (4)

Application Number Priority Date Filing Date Title
US24509081A 1981-03-18 1981-03-18
IL65048 1982-02-18
IL8265048A IL65048A0 (en) 1981-03-18 1982-02-18 Electronic game apparatus and methods of selecting combinations of events
US245090 1988-09-16

Publications (2)

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EP0061052A2 true EP0061052A2 (de) 1982-09-29
EP0061052A3 EP0061052A3 (en) 1983-05-25

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EP82101801A Withdrawn EP0061052A3 (en) 1981-03-18 1982-03-08 Electronic game apparatus and methods of selecting combinations of events

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AU (1) AU8101782A (de)

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2555065A1 (fr) * 1983-11-22 1985-05-24 Rinaldi Massimo Ordinateur pour la compilation automatique de systemes reduits pour jeux de pronostic
US4858932A (en) * 1988-04-21 1989-08-22 Bally Manufacturing Corporation Nonuniform probability reel stop mechanism for gaming machines
US5238249A (en) * 1991-02-11 1993-08-24 Elias Stephen L Dice simulator
US5356144A (en) * 1992-07-21 1994-10-18 Fitzpatrick James R Hand-held lottery number generating device
GB2296116A (en) * 1994-12-15 1996-06-19 Colin Barnes Calculator for winning combinations and points totals

Family Cites Families (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
GB696737A (en) * 1951-11-03 1953-09-09 Pasquale La Fauci Electric device for the random formation of a large number of combinations of forecasts regarding sporting events
GB958975A (en) * 1959-11-24 1964-05-27 Ernest William Hugh White A game, particularly for use in the forecasting of results of football or other pools
GB2092342A (en) * 1981-02-03 1982-08-11 Dutchford Ltd A computing device for giving an indication of the probable result of a football match
GB2093237A (en) * 1981-02-14 1982-08-25 Dutchford Ltd A computing device for giving an indication of the probable result of a horse race

Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2555065A1 (fr) * 1983-11-22 1985-05-24 Rinaldi Massimo Ordinateur pour la compilation automatique de systemes reduits pour jeux de pronostic
US4858932A (en) * 1988-04-21 1989-08-22 Bally Manufacturing Corporation Nonuniform probability reel stop mechanism for gaming machines
EP0338743A3 (de) * 1988-04-21 1991-04-17 Bally Gaming International, Inc. Rollensperrvorrichtung durch ungleichförmige Wahrscheinlichkeit für Spielautomaten
US5238249A (en) * 1991-02-11 1993-08-24 Elias Stephen L Dice simulator
US5356144A (en) * 1992-07-21 1994-10-18 Fitzpatrick James R Hand-held lottery number generating device
GB2296116A (en) * 1994-12-15 1996-06-19 Colin Barnes Calculator for winning combinations and points totals

Also Published As

Publication number Publication date
EP0061052A3 (en) 1983-05-25
AU8101782A (en) 1982-09-23

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