WO2017214158A1

WO2017214158A1 - Systems, devices, and methods for gaming

Info

Publication number: WO2017214158A1
Application number: PCT/US2017/036167
Authority: WO
Inventors: Stewart N. ETHIER; Jiyeon Lee
Original assignee: University Of Utah Research Foundation
Priority date: 2016-06-06
Filing date: 2017-06-06
Publication date: 2017-12-14

Abstract

Described herein are systems, devices, and methods for wagering games. Two-Table Baccarat, a modern casino version of the 19th-century French parlor game Baccara ô Deux Tableaux is described. Two-Table Baccarat comprises two simultaneous games of Baccarat, Player 1 vs. Banker, and Player 2 vs. Banker, but with only one Banker hand and with a reduced commission on Banker wins. Two-Table Baccarat includes mandatory card-drawing strategies for Players and a mandatory card-drawing strategy for Banker that is a compromise between a Baccarat strategy against Player 1 and a Baccarat strategy against Player 2. Two-Table Baccarat has several advantages for gamblers and therefore will attract them to casinos that offer the game.

Description

SYSTEMS, DEVICES, AND METHODS FOR GAMING

CROSS REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority to and the benefit of United States Provisional Application No. 62/346,266, filed June 6, 2016, and entitled "Two-Table Baccarat," which application is incorporated by reference herein in its entirety.

Background

[0002] The French parlor game Baccara Chemin de Fer, dating back to the nineteenth century, evolved over more than a century into the present-day casino game Baccarat. Present-day Baccarat is a game preferred by premium or VIP players (high-stakes gamblers) at casinos around the world. One can think of Baccarat as a modernization of Baccara Chemin de Fer. Another nineteenth-century French parlor game, Baccara ^λ a Deux Tableaux or Baccara Banque, reached its height of popularity in the 1920s and 1930s but is today largely extinct.

[0003] Baccara Chemin de Fer

[0004] Baccara Chemin de Fer is a simple game. The rules are as follows. The role of Banker rotates among the players (counter-clockwise), changing hands after a Banker loss or when Banker chooses to relinquish his role. Banker announces the amount he is willing to risk, and the total amount bet on Player's hand cannot exceed that amount. Denominations Ace, 2-9, 10, Jack, Queen, and King have values 1, 2-9, 0, 0, 0, and 0, respectively. Suits (hearts, clubs, etc.) are irrelevant. The total of a hand, comprising two or three cards, is the sum of the values of the cards, modulo 10. In other words, only the final digit of the sum is used to evaluate a hand. Two cards are dealt face down to Player and two face down to Banker. The object of the game is to have the higher total (closer to 9) at the end of play. Winning bets on Player's hand are paid by Banker at even odds. Losing bets on Player's hand are collected by Banker. Equal totals result in a push (i.e., a tie) and no money changes hands. A two- card total of 8 or 9 is a "natural." If either hand is a natural, play ends. If neither hand is a natural, Player then has the option of drawing a third card (but this option is heavily constrained; see below). If the player exercises this option, his third card is dealt face up. Next, Banker, observing Player's third card, if any, has the option of drawing a third card. This completes the game. Since several players (sometimes called participants) can bet on Player's hand, Player's strategy is restricted. The player must draw on a two-card total of 4 or less and must stand on a two-card total of 6 or 7. When his two-card total is 5, he is free to draw or stand as he chooses. Banker, on whose hand no one can bet, has no constraints.

[0005] Baccara a Deux Tableaux

[0006] Even older than baccara chemin de fer is Baccara a Deux Tableaux (or baccara banque). Baccara a Deux Tableaux is a relatively simple game in which two Player hands compete against one Banker hand. Baccara a Deux Tableaux became a popular banking game in the 1920s, owing to Nicolas Zographos of the Greek Syndicate. It is still played in Monte Carlo but know to be played in few other places.

[0007] The rules for Baccara a Deux Tableaux are as follows. There are three hands, Player 1, Player 2, and Banker. Two bets are available to participants, a bet on the hand of Player 1 and a bet on the hand of Player 2. Denominations Ace, 2-9, 10, Jack, Queen, and King have values 1, 2-9, 0, 0, 0, and 0, respectively. Suits are irrelevant. The total of a hand, comprising two or three cards, is the sum of the values of the cards, modulo 10. In other words, only the final digit of the sum is used to evaluate a hand. Two cards are dealt face down to each of Player 1, Player 2, and Banker. The object of the game is to have the higher total (closer to 9) at the end of play. Winning bets on Player l's hand or Player 2's hand are paid by Banker at even odds. Losing bets are collected by Banker. Equal totals result in a push (no money changes hands). A two-card total of 8 or 9 is a natural. First, if either Banker or both Players have naturals, play ends. If only one Player has a natural and Banker does not, that Player wins the amount bet from Banker, while play continues between the other Player and Banker. Next, if neither Player 1 nor Banker has a natural, Player 1 has the option of drawing a third card. Then, if neither Player 2 nor Banker has a natural, Player 2 has the option of drawing a third card. In either case, the Player must draw on a two-card total of 4 or less and stand on a two-card total of 6 or 7. When his two-card total is 5, he is free to draw or stand as he chooses. Any third card is dealt face up. Finally, if at least one Player and Banker fail to have naturals, Banker has the option of drawing a third card and his strategy is unconstrained. Bets are then settled, both Player 1 vs. Banker and Player 2 vs. Banker. In both competitions, the higher total wins.

[0008] Baccarat

[0009] The more modern and common form of Baccarat is a modernized variation of Baccara Chemin de Fer. First, it is a house-banked game, that is, bets of all participants are banked by the house. This avoids the need for offsetting bets. Second, there are no strategy options - whether to draw a third card or to stand is complete constrained by pre-set criteria. Player draws on two-card totals of 5 or less and stands on two-card totals of 6 or 7. If Player's third card has value i (i = 0, 1, 9), Banker draws on two-card totals of h(i) or less and otherwise stands. The rules specify that (h(0), h(l), h(9)) = (3, 3, 4, 4, 5, 5, 6, 6, 2, 3). If Player stands, Banker draws on two-card totals of 5 or less. Finally, bets are allowed both on Player's hand, paying 1 to 1, and on Banker's hand, paying 19 to 20. The latter is equivalent to a 1 to 1 payoff with a 5% commission on winning Banker bets.

Summary

[0010] Embodiments described herein pertain to systems, devices, and methods for conducting and/or providing card games and providing and/or conducting wagering games. Embodiments include systems, devices, and methods for conducting and/or providing a card game of Two-Table Baccarat.

[0011] One embodiment described herein is a new wagering game referred to as Two-Table Baccarat. Such a game may be played in casinos, for instance.

[0012] Two-Table Baccarat can be thought of as a modernization of the 19th-century French parlor game Baccara a Deux Tableaux. Two-Table Baccarat is a house-banked game, that is, bets of all participants are banked by the house. In Two-Table Baccarat, there are no strategy options, drawing or standing on two initially dealt cards is fixed by pre-determined rules and criteria. Players 1 and 2 draw on two-card totals of 5 or less and stand on two-card totals of 6 or 7. Banker's maximum drawing total depends on Player l's third-card value (or stand or natural) and Player 2's third-card value (or stand or natural). Finally, bets are allowed on Player l's hand (vs. Banker), paying 1 to 1, on Player 2's hand (vs. Banker), paying 1 to 1, on Banker's hand (vs. Player 1), paying 24 to 25, and on Banker's hand (vs. Player 2), paying 24 to 25. The latter is equivalent to a 1 to 1 payoff with a 4% commission on winning Banker bet. In some embodiments, additional bets of tie (Player vs. Banker) and three-way tie are also allowed.

[0013] A benefit of Two-Table Baccarat is to give players, especially those referred to as VTP players, an alternative to previously existing games (such as common present-day Baccarat). Unlike other proprietary casino games, Two-Table Baccarat is not contrived. Two-Table Baccarat may be considered novel variation and improvement of Baccara a Deux Tableaux, much in the same way that Baccarat was derived from Baccara Chemin de Fer. Advantages of Two-Table Baccarat include the following:

[0014] (a) The game has a historical connection with Baccarat.

[0015] (b) The rules are clear at a glance— there is little or no learning curve. [0016] (c) The house edge is lower than at Baccarat. For the bets on Player hands, this is clear without calculation. For the bets on Banker's hand, this is suggested by the fact that the commission on wins is 4%, not 5%.

[0017] (d) The game will attract VIP players.

[0018] (e) Even with the lower house edge (about 20% lower than at Baccarat), the game will earn substantial revenue.

[0019] (f) A commission-free variation is possible.

[0020] Two-Table Baccarat may be described as comprising two simultaneous games of Baccarat - Player 1 vs. Banker, and Player 2 vs. Banker - but with only one Banker hand and with a reduction in the commission when Banker wins (from 5% to 4%).

[0021] Player 1 and Player 2 play similarly as done in Baccarat, but Banker, having to defend simultaneously against two Player hands instead of one, has a mandated compromise strategy, which does not depend on the amounts bet on the hands of Player 1 and Player 2; nevertheless, it maximizes Banker's expected gain when those two amounts are equal.

[0022] Participants in Two-Table Baccarat have four basic betting opportunities instead of just two. The four available betting options include bets on:

1) Player 1 (vs. Banker),

2) Player 2 (vs. Banker),

3) Banker (vs. Player 1), and

4) Banker (vs. Player 2).

In some embodiments, bets may also be allowed on three different ties - a tie between Player 1 and Banker, a tie between Player 2 and Banker, and a three-way tie between both players and Banker.

BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Fig. 1 illustrates one possible embodiment of a playing table and betting layout.

[0024] Fig. 2 illustrates Banker's mandated third-card drawing strategy.

[0025] Fig. 3 displays a schematic diagram of an exemplary system configured for implementing embodiments described herein.

[0026] Fig. 4 is a process flowchart depicting an embodiment described herein.

[0027] Fig. 5 displays a Mathematica™ program which can be used to simulate one billion coups of Two-Table Baccarat. DETAILED DESCRIPTION

[0028] Embodiments described herein relate to systems, devices, and methods pertaining to wagering games. Such wagering games may be variants of Baccarat or variants and modifications thereof in which wagers for such games may be placed by players and received by the house or casino, or a person or entity acting as a banker of the game. A method for conducting a wagering game may be conducted on an electronic device (or, in some embodiments, at a live table). A game may be conducted for at least one participant (i.e., gambler) using a set of playing cards to form two Players' hands and a banker hand.

[0029] Embodiments described herein may be partially or wholly implemented in a variety of ways using a variety of devices or systems. These may include, but are not limited to, an electronic gaming machine (EGM) for use by one or more players, a multiplayer platform which may include a player interface such as a touchscreen or touch-enabled display and involve physical or virtual playing cards, dealer, and wagering chips, a home computer or portable computing device, such as a tablet computer or mobile phone capable of communicating with a network, over the Internet, global telecommunication network or world wide web.

[0030] Embodiments may include an electronic device, such as a computer or electronic gaming machine, which can accept or receive value or credit, accept or receive bets or wagers, conduct games including the below-described Two-Table Baccarat, determine outcomes of the conducted games, resolve bets and wagers, pay, output, or record values according to the resolved bets and wagers, and increment or debit credit values according to the resolved bets and wagers. The electronic devices may comprise stand-alone systems as well as distributed systems including servers, hand-held devices, personal computers, tablet computers, smart phones, etc.

[0031] It should further be understood that embodiments of the methods and systems of the invention are described herein in connection with a Two-Table Baccarat game as particularly defined below. The methods and systems of the invention may be employed, combined or integrated with other modified, variant or otherwise non-conventional Baccarat games, including variants with modified rules, additional wagers, including no-commission or commission-free versions of baccarat.

[0032] It should be noted that references made in this description to "cards", "decks", "dealing", "hands" or other such expressions that are ordinarily used in describing wagering games played with physical playing cards are also meant to describe and capture all associated electronic and online representations of physical playing cards, including associated graphical and numeric symbols (for instance, suits such as hearts, spades, diamonds or clubs, face cards such as jacks, queens and kings, and the aces and other numbered cards of a typical playing deck). These expressions are also meant to include all forms of electronic dealing, distribution and allocation of the symbols, in accordance with the rules of the underlying wagering game.

[0033] Embodiments described herein include a modernization and novel variant of Baccara a Deux Tableaux, called Two-Table Baccarat.

[0034] Two-Table Baccarat

[0035] Embodiments described herein pertain to systems, devices, and methods for conducting and/or providing card games and providing and/or conducting wagering games. Embodiments include systems, devices, and methods for conducting and/or providing a card game of Two-Table Baccarat.

[0036] One embodiment described herein is a new wagering game referred to as Two-Table Baccarat. Such a game may be played in casinos, for instance.

[0037] Two-Table Baccarat can be thought of as a modernization of the 19th-century French parlor game Baccara a Deux Tableaux. Two-Table Baccarat is a house-banked game, that is, bets of all participants are banked by the house. In Two-Table Baccarat, there are no strategy options, drawing or standing on two initially dealt cards is fixed by pre-determined rules and criteria. Players 1 and 2 draw on two-card totals of 5 or less and stand on two-card totals of 6 or 7. Banker's maximum drawing total depends on Player l's third-card value (or stand or natural) and Player 2's third-card value (or stand or natural). Finally, bets are allowed on Player l's hand (vs. Banker), paying 1 to 1, on Player 2's hand (vs. Banker), paying 1 to 1, on Banker's hand (vs. Player 1), paying 24 to 25, and on Banker's hand (vs. Player 2), paying 24 to 25. The latter is equivalent to a 1 to 1 payoff with a 4% commission on winning Banker bet. In some embodiments, additional bets of tie (Player vs. Banker) and three-way tie are also allowed.

[0038] In one embodiment, Two-Table Baccarat may be played at a kidney-shaped table. (See Fig. 1.) One side of the table may be called Table 1 and the other side may be called Table 2. Three two-card hands can be dealt, one hand to Player 1 at Table 1, one hand to Player 2 at Table 2, and one hand to Banker representing the house. The hands of card may be randomly dealt, for instance, from an electronic card dealer which deals from an eight-deck virtual shoe. The playing table may be a virtual representation of a table which is generated by an electronic gaming machine and displayed upon an electronic video display. In a live-action embodiment, cards may be dealt by a dealer (electronic, mechanical, or otherwise) onto a physical table.

[0039] Four basic bets are available to each player (gambler or participant) in Two- Table Baccarat. (Note, "Player 1" and "Player 2" are simply designations that indicate the "Players" to whom the cards are dealt but are not the actual participants (i.e., gamblers or players) in the game who are betting or wagering on the possible outcomes of the game.) Four basic bets a participant (gambler) in the game may make may include a bet on the hand of Player 1 vs. Banker, a bet on the hand of Player 2 vs. Banker, a bet on the hand of Banker vs. Player 1, and a bet on the hand of Banker vs. Player 2. In one embodiment, eight 52-card decks may be randomly mixed together and dealt from a shoe. The eight- card shoe may be a virtual shoe generated within an electronic gaming machine. Card denominations Ace, 2-9, 10, Jack, Queen, and King have values 1, 2-9, 0, 0, 0, and 0, respectively. Suits (hearts, clubs, etc.) are irrelevant. The total of a hand, comprising either two or three cards, is the sum of the values of the cards, modulo 10. In other words, only the final digit of the sum of the cards is used to evaluate a hand.

[0040] Two cards are dealt to each of Player 1, Player 2, and Banker. The cards may be dealt face down. The cards dealt may be virtual cards generated and dealt by an electronic gaming machine and may be displayed upon an electronic display device. A two-card total of 8 or 9 is a "natural." First, if either the Banker or both Players have naturals, play ends (i.e., no further cards are drawn, outcomes are determined, and bets are settled). If only one Player has a natural and Banker does not, that Player wins, while play continues between the other Player and Banker. Next, if neither Player 1 nor Banker has a natural, Player 1 has the option of drawing a third card. Then, if neither Player 2 nor Banker has a natural, Player 2 has the option of drawing a third card. In either case, the Player must draw on a two-card total of 5 or less and stand on a two-card total of 6 or 7. Any third card is dealt face up. Finally, if at least one Player and Banker fail to have naturals, Banker has the option of drawing a third card, and his strategy is mandated by a table of play. Bets are then settled, Player 1 vs. Banker, Player 2 vs. Banker, Banker vs. Player 1, and Banker vs. Player 2. In both competitions, the higher total wins. Winning bets on Player 1 vs. Banker or Player 2 vs. Banker are paid at even odds. Winning bets on Banker vs. Player 1 or Banker vs. Player 2 are paid at 24 to 25, that is, they are paid at 1 to 1 and a 4% commission is levied on winning Banker bets. Losing bets are collected. Equal totals result in a push (no money changes hands). [0041] The table of play can be defined as follows: Banker observes Player l 's third card (values 0-9) or stand or natural. He also observes Player 2's third card (values 0-9) or stand or natural. There are 143 distinct situations that can occur. Corresponding to each is a number, namely Banker's maximum drawing total. (See Table 1 & Fig 2.) If his two-card total is less than or equal to this number, he draws, otherwise he stands. The table of play should not depend on the amounts bet on the hands of Players 1 and 2. Indeed, because we allow betting on both the Players' hands and on Banker's hand, all strategies must be mandated and independent of amounts bet. Therefore, the table of play was derived under the assumption that equal amounts are bet on the hands of Players 1 and 2 (and nothing is bet on the hand of Banker). Under this assumption, Banker's strategy is optimal, and uniquely so.

[0042] A list of Banker maximum drawing totals is given in Table 1, below. Player l's third-card value is listed in column 1. Player 2's third-card value is listed in row 1. ("S" and "N" indicate, respectively, a stand or a natural for each of Player 1 and Player 2.) Banker's maximum drawing total is listed in the intersection of Player l's and Player 2's third-card value (plus stand and natural). For another useful chart depicting the pre-determined Banker's strategy, see the Banker draw chart 200 of Fig 2.

[0043] Table 1 and item 200 in Fig. 2 depict the Banker's card-drawing strategy. Entries in the tables are maximum Banker drawing totals. Specifically, it is a table that displays Banker's maximum drawing total as a function of Player l's third card (or stand or natural) and Player 2's third card (or stand or natural). For example, if Player l 's third card is 7 and Player 2's third card is 8, then the table shows a 3 in the (7, 8) position (i.e., the Banker's maximum drawing total is 3) and so the Banker draws on 0-3 and stands on 4-7. It may be noted that the tables are symmetric in Player 1 and Player 2.

[0044] Another feature of the card-drawing rules (Table 1 and Fig. 2) is that, when one of the Players has a natural, Banker plays against the other Player in a way that departs slightly from the rules of common Baccarat. Specifically, when one Player has a natural and the other draws an ace, Banker draws on 4 in Two-Table Baccarat, whereas when Player draws an ace, Banker stands on 4 in common Baccarat. Similarly, when one Player has a natural and the other Player stands, Banker draws on 6 in Two-Table Baccarat (whereas when Player stands, Banker stands on 6 in common baccarat). Why the discrepancies? The answer is that Banker's strategy in baccarat is not a best response to Player's strategy. Some observers have regarded this as a mistake by the developers of baccarat {see Wilson, The Casino Gambler's Guide, Harper & Row, 1965, p. 204). Instead, for historical reasons, Banker's strategy in baccarat is a best response to Player's (1=2; 1=2) mixed strategy in baccara chemin de fer {see Ethier and Lee, The evolution of the game of baccarat, J. Gambling Bus. Econ., 2015).

[0045] To illustrate how the table of play was computed, consider the case in which Player l's third card is 7 and Player 2's third card is 8. If Banker were playing common Baccarat against Player 1, the difference between his drawing expectation and standing expectation would be (169, 105, 41, 9, 9, 9, 9, -41)/273 if his two-card total is (0, 1, 2, 3, 4, 5, 6, 7), respectively. Thus, he should draw with 0-6 and stand on 7. If Banker were playing Baccarat against Player 2, the difference between his drawing expectation and standing expectation would be (191, 127, 63, -1, -33, -33, -33, -33)/273 if his two-card total is (0, 1, 2, 3, 4, 5, 6, 7), respectively. Thus, he should draw with 0-2 and stand on 3-7. But Banker is playing Two-Table Baccarat against both Players, so he must compromise. The difference between his drawing expectation and standing expectation is the average of the two cases just considered, namely (180, 116, 52, 4, -12, -12, -12, -37)/273 if his two-card total is (0, 1, 2, 3, 4, 5, 6, 7), respectively. Thus, he should draw with 0-3 and stand on 4-7. Therefore, 3 is his maximum drawing total, as confirmed by the table of play. A similar analysis was done in all 143 combinations of Player 1 and Player 2 third cards (plus stand and natural).

[0046] One useful statistic for describing the performance of a casino game is the house edge. The house edge is a statistical value which indicates what proportion, over time, that the house (e.g., casino) will retain of the sum of the overall wagers placed on a wagering game. The house edge for Two-Table Baccarat is lower than it is for Baccarat. The house edge for Two-Table Baccarat will attract gamblers to the game (because, in the long run, the house will retain less of the total value wagered return more of the value wagered to the participants in the game). In more detail, and assuming an eight-deck shoe, the house edge on the two Player bets in Two-Table Baccarat is 0.9293%, compared to 1.2351% for the Player bet at Baccarat. The house edge for the two Banker bets in Two-Table Baccarat, with a 4%> commission on wins, is 0.9055%), compared to 1.0579%) for the Banker bet, with a 5% commission on wins, at Baccarat.

[0047] Other embodiments of Two-Table Baccarat may also allow and accept two tie bets (Player 1 ties Banker; Player 2 ties Banker) and a Three-Way Tie bet (Player 1, Player 2, and Banker tie). Embodiments may include a payoff of 9 to 1 for the Tie bet and 90 to 1 for the Three-Way Tie bet. In those cases, the house edges are 8.1057%> and 15.3524%), respectively, assuming an eight-deck shoe. In Baccarat the Tie bet pays only 8 to 1, for a house edge of 14.3596%). An 8 to 1 payoff in Two-Table Baccarat would result in a 17.2952%) house edge, which is too high.

[0048] In some implementations, the 4% commission on winning Banker bets may be considered a nuisance or difficult to calculate and collect and/or an inefficient use of time. In that case an alternate commission-free version of the game is available. A commission-free version of Two-Table Baccarat may, in some ways, be similar to that of EZ Baccarat™, in which a 5%) commission is eliminated and, instead, winning Banker bets may be paid 1 to 1 unless Banker wins with a three-card 7, in which case the bet is considered pushed. In one embodiment of Two-Table Baccarat the 4% commission may be eliminated and, instead, winning Banker bets may be paid 1 to 1 unless Banker wins with a three-card 7 against a three- card Player hand, in which case the bet (vs. that Player) is considered pushed. The effective commission for this commission-free version of Two-Table Baccarat is approximately 4.203%), so the house edge on Banker bets becomes 0.9987%> (instead of 0.9055%), assuming an eight-deck shoe. [0049] In some embodiments, the initial two-card hands are dealt face down, subsequent draw cards are dealt face up, and face down cards are revealed after all draws have been completed. This staged revealing of the face-down cards may enhance the entertainment value of game play. In other embodiments, cards may be dealt face up. (As the card-draw rules in Two-Table Baccarat are fixed by pre-determined criteria, dealing cards face up will not affect the outcome of the game.)

[0050] Ramifications

[0051] Two-Table Baccarat is a casino wagering game that provides a novel and modernized variation of Baccara a Deux Tableaux and provides and maintains certain advantages of common Baccarat. Two-Table Baccarat is a house-banked game with mandated strategies and allows betting on all three hands.

[0052] Two-Table Baccarat would be a fair game if all 143 entries in Banker's card-drawing table of play were equal to 5. In fact, 99 of them differ from 5 (see Table 1 & Fig. 2), and it is these departures from symmetry that give the house its advantage.

[0053] The basic bets at Two-Table Baccarat, namely the Player bets and the Banker bets, have house edges of 0.9293% and 0.9055% (0.9987% in the commission-free version of the game), assuming an eight-deck shoe. These figures have been calculated by exact computation and confirmed by Monte Carlo simulation.

[0054] We can be more precise about the house edges. The probabilities that Player 1 wins, ties, and loses, as suming an ei ght-deck shoe, are, respectively,

37521264124371517571 / 83490726069877110075,

7672319140927383773 / 83490726069877110075, and

38297142804578208731 / 83490726069877110075.

The sam e figures apply to Pl ayer 2. The only other needed probability is that of a three-way tie, which is

776625027254404781 / 83490726069877110075.

From these figures all house edge statistics (as well as variances) can be easily calculated.

[0055] Embodiments of the invention may include an electronic gaming device or system. Fig. 3 illustrates an exemplary system configured for implementing embodiments described herein. The electronic gaming device or system may include one or more computer processors 310. The electronic gaming device may include durable data storage 320. Computer executable instructions may be stored in the storage 320. When executed on one or more processors, the executable instructions may cause the gaming device to perform a wagering game such as Two-Table Baccarat.

[0056] The electronic gaming device may include one or more electronic displays 330. The displays 330 may display wagering games such as Two-Table Baccarat. The displays may also display the bets and wagers of participants in wagering games.

[0057] The electronic gaming device may include one or more input devices 340. Input devices 340 may accept indications of bets and wagers from participants in a wagering game such as Two-Table Baccarat. Input devices 340 may also accept information associated with credit or value used by participants to establish a credit balance for playing a wagering game. Input devices 340 may also accept any other information associated with participating in, playing, betting on, or wagering on a wagering game.

[0058] The electronic gaming device may include one or more output devices 350 (which may include the electronic displays 330).

[0059] The electronic gaming device may include one or more credit or value devices 360. Credit or value devices 360 may include credit card input devices, coin slots, paper currency readers, etc., which can accept currency or other information to establish credit that a participant may use to participate, bet on, wager on, etc. a wagering game. The electronic gaming device may include one or more network interfaces 370 which are configured to communicate with a network 380.

[0060] The network interfaces 370 may be communicatively coupled with a network and enable communication with various local or remote devices for facilitating a wagering game. Such networks may include local area networks, global networks, the Internet, etc. Local or remote devices for facilitating a wagering game may include application and or game servers, personal computers and devices such as smart tablets and smart phones which enable a local user-client for facilitating participation in a wagering game. Local or remote devices may also include financial interfaces for establishing credit and transferring money to enable a user's participation in a wagering game.

[0061] Fig. 1 illustrates one possible embodiment of a playing table and betting layout. The playing table or betting layout may be displayed by the display device 330 of system 300. The betting layout of Two-Table Baccarat may include two ends of the same table. The betting layout may include the Banker card-draw rules 120 (which are similar to those illustrated in the chart 200 of Fig. 2). The betting layout may include a position for a dealer 110. (Note that all the depictions on the betting layout, including the dealer 110, may be virtual depictions generated on system 300 and displayed on display 330.)

[0062] The betting layout 100 may include positions and options for bets or wagers allowed in a wagering game such as Two-Table Baccarat. Such bets or wagers may include four basic bets including a bet PI 150 on Player 1 (vs. Banker), a bet P2 140 on Player 2 (vs. Banker), a bet Bl 160 on Banker (vs. Player 1), and a bet B2 170 on Banker (vs. Player 2). In some embodiments, the bets and wagers included in layout 100 may also include bets for ties including a tie Tl 180 for a tie between Player 1 vs. Banker and a tie T2 190 for a tie between Player 2 vs. Banker. A three way tie may be indicated by simultaneous indications in both Tl 180 and T2 190 being indicated.

[0063] The betting layout may include multiple positions for a plurality of participants to play the game simultaneously. Fig. 1 displays positions 130 for simultaneous play and wagering. Fig. 1 illustrates 12 positions for participants but there is no inherent limit on the number of participants or players who may simultaneously play and/or place wagers on the game. Each participant position 130 has indications for each possible bet and/or wager on the game (as described above). (Note, each participant may place bets on Player 1, Player 2, Banker, etc. Further, each participant may make multiple simultaneous bets (such as Player 1 vs. Banker and also Banker against Player 2).

[0064] The betting layout may be displayed on display device 330 and be updated to reflect and display the bets placed by each participant to the same. Bets and wagers from each participant may be received by one or more input devices such as input device 340. In some embodiments, display device 330 may be an input/output device such as a touch-sensitive LCD display which can both display progress and outcomes of a game and also receive input from participants as to bets and wagers. Such an input/output device may be incorporated into an electronic gaming device configured as a table at which participants may sit or be positioned so as to interact with the table and participate in the game.

[0065] For display of cards used during the progress of a game, Fig. 1 includes card positions 195, 197, and 199. These cards positions may include card position 195 for display of Banker's hand, card position 197 for display of Player l 's hand, and card position 199 for display of Player 2's hand. (Note, each hand in Two-Table Baccarat will include at least 2 cards but may, or may not, depending on the first two cards, also include a third card.)

[0066] Embodiments of the invention may include methods for conducting a wagering game. Fig. 4 illustrates and exemplary method 400 for conducting a wagering game. The method 400 may be performed on a system such as system 300 or other electronic gaming device. The wagering game may be Two-Table Baccarat as described herein. The method 400 may include receiving a wager 410 from a game participant. A participant may place a bet (wager) on any of a number of possible outcomes. The wager or bet may be constrained by some pre-determined criteria. Such pre-determined criteria may include a minimum bet, a maximum bet, a bet required to be a multiple of a certain amount, or other criteria which may be configured. The bet or wager may be received through input device 340 or possibly an output device 350 configured to be both input and output such as a touch sensitive display device.

[0067] The method may further include receiving credit or value from each participant in the game. The credit or value may be used by participants in placing bets or wagers on a wagering game. Such credit or value may be received electronically, such as through a bank transfer, may be received by credit card via an appropriate credit card device, or may be deposited directly into the gaming device such as through a coin slot or paper money accepting device. Such received credit may be recorded and stored in the storage 320 of system 300, associated with a participant and for use by the participant in the game. Credit which is recorded and stored in the storage 320 may be adjusted during play of a game as appropriate to reflect the winning and/or losing bets of a participant in the game. Credit may be received through input device 340 or other suitable device. In other embodiments, a wager or bet may be received directly prior to the bet such as through a credit card device, a coin slot or paper money accepting device and applied to the bet or wager.

[0068] The method 400 may include selecting cards 420. Selecting cards 420 may include selecting or generating three 2-card hands - one for Player 1, one for Player 2, and one for Banker. For example, three two-card hands may be randomly generated from an eight-deck virtual shoe of cards generated by gaming system 300. The three two-cards hands may be displayed for each participant on the display device 330 of system 300. The selected or generated cards may be displayed at positions 195, 197, and 199 of the gaming table 100. A display 330 may also be used to display entertainment content to enhance the visual interest of the game, the selection of cards, subsequent selection and display of card draws, and the outcome of the game and the bets and wagers.

[0069] The method 400 may include determining card draws 430. The card draws may be determined according to pre-set or pre-determined criteria. The predetermined criteria may be the criteria determined in accordance with the rules for Two-Table Baccarat as discussed herein. In one embodiment, Player 1 and Player 2 may draw when their two-card value is 5 or less and stand on two-card totals of 6 or 7. In this embodiment, Banker's card draw may depend on Player l's third-card value (or stand or natural) and Player 2's third-card value (or stand or natural) as illustrated in Table 1 and the chart in Fig. 2. The cards drawn for each of the three hands may be displayed on an electronic display. Drawn cards, if any, may be displayed at positions 195, 197, and 199 of the gaming table 100 adjacent to the originally selected two cards of each of Player l 's, Player 2's and Banker's hands, as appropriate. Drawn cards may be randomly selected or generated by system 300 and may be drawn from a previously generated eight-deck shoe.

[0070] The method 400 may include determining the outcomes 440 of the game. Outcomes of the game may be determined in accordance with the rules for Two-Table Baccarat as discussed herein. Outcome may be determined for each of Player 1 vs. Banker and Player 2 vs. Banker by determining which final hand's final value is closest to 9 (or tied). An outcome for Player 1 vs. Banker (e.g., win, lose, tie) may be determined. An outcome for Player 2 vs. Banker (e.g., win, lose, tie) may be determined.

[0071] The method 400 may include resolving 450 the wagers (which had been placed, for instance, in step 410). Each bet or wager which had been placed 410 by one or more participants in the game may be determined and resolved. The wagers may be determined and resolved in accordance with the rules for Two-Table Baccarat as discussed herein. For example, a winning bet on Player 1 in Player 1 vs. Banker may be resolved by paying one-to-one to the participant having placed the bet. In another example, a winning bet on Banker in Player 1 vs. Banker may be resolved by paying 24-to-25 (i.e., 4% commission) to the participant having placed the bet. (Note, a bet on Banker in Player 1 vs. Banker (e.g., Bl 160 in Fig. 1) is equivalent to a "lose" for Player 1 in Player 1 vs. Banker, that is, Banker wins against Player 1.) "Paying" may comprise an immediate disbursement of funds or may comprise incrementing a recorded credit balance.

[0072] The method 400 may also include incrementing or decrementing a credit balance for each participant who placed a wager in accordance with the appropriate resolution of the wagers 450. A credit balance stored in Storage 320 for a participant may be adjusted in accordance with the appropriate resolution of the outcome of a wager placed by the participant. In an alternate embodiment, the wager as resolved, when appropriate, may be paid out or disbursed directly to a participant in the form of money or casino chips from an appropriate dispensing device connected to the gaming system 300. Such direct payouts may be similar to the coin or casino chip payouts from common slot machines.

[0073] A Mathematica™ program which can be used to simulate one billion coups of Two-Table Baccarat is illustrated in Fig. 5. This simulation was run and produced experimental results are consistent with theoretical expectations. A computer simulation of one billion coups of Two-Table Baccarat was run, with one unit bet on each of the four basic bets. The house edges after the computer simulation are given in Table 2.

[0074] Mathematics of Two-Table Baccarat

The necessary calculations are relatively easy when we^' assume infinitely .many decks (or sampling with replacement), so let us make that assumption first, recognizing thai results are slightly inaccurate. The distribution of the total of a two-card hand is

where is the Kronecker delta and the distribution

of the value of a card is

[0075] Those skilled in the art will appreciate that the methods described herein may be incorporated in a system in accordance with the invention using virtual representations of Two-Table Baccarat table layouts. The system of the invention may include various computer and network related software and hardware, such as programs, operating systems, memory storage devices, data input/output devices, data processors, servers with links to data communication systems, wireless or otherwise, and data terminals. Those skilled in the art will further appreciate that the precise types of software and hardware used are not vital to the full implementation of the methods described herein so long as players and operators are provided with useful access to the systems and methods.

[0076] Accordingly, presented herein are systems, devices, and methods for enabling, facilitating wagering games. While exemplary systems and methods, and applications of methods of the invention, have been described herein, it should be understood that the foregoing is only illustrative of a few particular embodiments with exemplary and/or preferred features, as well as principles of the invention, and that various modifications can be made by those skilled in the art without departing from the scope and spirit of the invention. Therefore, the described embodiments should not be considered as limiting of the scope of the invention in any way. Accordingly, the invention embraces alternatives, modifications and variations which fall within the spirit and scope of the invention as set forth in the claims and equivalents thereto.

Claims

CLAIMS We claim:

1. A system for conducting a wagering game, the system comprising:

one or more computer processors;

one or more input devices;

one or more display devices;

a wager accepting device;

and a data storage device, the data storage device having stored therein executable instructions which, when executed on the one or more processors, cause the system to perform a wagering game including:

receiving a wager;

randomly selecting three two-card hands of cards

displaying the three two-card hands of cards;

determining card draws for each of the three two-card hands of cards;

determining outcomes for the wagering game based on the resulting hands of cards; and

resolving the wager based upon the outcome for the wagering game.

2. The system of claim 1, wherein the three two-card hands of cards include a Player 1 hand, a Player 2 hand, and a Banker hand.

3. The system of claim 1, wherein the card draws for each of the three two-card hands of cards is determined according to a pre-determined criteria.

4. The system of claim 1, wherein determining outcomes for the wagering game based on the resulting hands of cards comprises determining an outcome for Player 1 vs. Banker and determining an outcome for Player 2 vs. Banker.

5. The system of claim 1, wherein resolving the wager based upon the outcome for the wagering game includes withholding a commission.

6 The system of claim 1, wherein determining outcomes for the wagering game based on the resulting hands of cards includes determining if there is at least one of a tie between Player 1 and Banker, a tie between Player 2 and Banker, and a three-way tie.

7. The system of claim 1, wherein resolving the wager based upon the outcome for the wagering game is commission free.

8. A computer program product for conducting a wagering game, the computer program product comprising one or more data storage devices having stored thereon executable instructions which, when executed on one or more computer processors, cause the processors to perform a wagering game including:

receiving a wager;

randomly selecting three two-card hands of cards

displaying the three two-card hands of cards;

determining card draws for each of the three two-card hands of cards;

resolving the wager based upon the outcome for the wagering game.

9. The computer program product of claim 8, wherein the three two-card hands of cards include a Player 1 hand, a Player 2 hand, and a Banker hand.

10. The computer program product of claim 8, wherein the card draws for each of the three two-card hands of cards is determined according to a pre-determined criteria.

11. The computer program product of claim 8, wherein determining outcomes for the wagering game based on the resulting hands of cards comprises determining an outcome for Player 1 vs. Banker and determining an outcome for Player 2 vs. Banker.

12. The computer program product of claim 8, wherein resolving the wager based upon the outcome for the wagering game includes withholding a commission.

13 The computer program product of claim 8, wherein determining outcomes for the wagering game based on the resulting hands of cards includes determining if there is at least one of a tie between Player 1 and Banker, a tie between Player 2 and Banker, and a three-way tie.

14. The computer program product of claim 8, wherein resolving the wager based upon the outcome for the wagering game is commission free.

15. A method for conducting a wagering game, the method performed within a system comprising one or more computer processors, one or more input devices, one or more display devices, a wager accepting device, and a data storage device, the method performed by executing executable instructions on the one or more processors, thereby causing the system to perform the wagering game including: receiving a wager;

randomly selecting three two-card hands of cards

displaying the three two-card hands of cards;

determining card draws for each of the three two-card hands of cards;

resolving the wager based upon the outcome for the wagering game.

16. The method of claim 15, wherein the three two-card hands of cards include a Player 1 hand, a Player 2 hand, and a Banker hand.

17. The method of claim 15, wherein the card draws for each of the three two-card hands of cards is determined according to a pre-determined criteria.

18. The method of claim 15, wherein determining outcomes for the wagering game based on the resulting hands of cards comprises determining an outcome for Player 1 vs. Banker and determining an outcome for Player 2 vs. Banker.

19. The method of claim 15, wherein resolving the wager based upon the outcome for the wagering game includes withholding a commission.

20 The method of claim 15, wherein determining outcomes for the wagering game based on the resulting hands of cards includes determining if there is at least one of a tie between Player 1 and Banker, a tie between Player 2 and Banker, and a three-way tie.