Disclosed herein are methods, systems, and apparatus, including computer programs encoded on computer storage media, for performing counterfactual regret minimization (CFR) for strategy searching in strategic interaction between two or more parties. One of the methods includes: storing multiple regret samples in a first data store, wherein the multiple regret samples are obtained in two or more iterations of a CFR algorithm in strategy searching in strategic interaction between two or more parties; storing multiple strategy samples in a second data store; updating parameters of a first neural network for predicting a regret value of a possible action in a state of a party based on the multiple regret samples in the first data store; and updating parameters of a second neural network for predicting a strategy value of a possible action in a state of the party based on the multiple strategy samples in the second data store.

A player chooses a predetermined number of unique identifiers representing tokens from a set of tokens, forms a player hand from the token values randomly assigned to the chosen identifiers, and compares the player hand to an opponent hand or a pay table. A game can have one or more game segments. Each segment has a different number of cards, a different deck of cards, and/or plays by different rules. A player may play one or more segments in a game. A player may choose the number of consecutive games to play using the same identifier choices and/or the values randomly selected for those choices. In one form, as identifiers are selected or chosen, they are no longer available to be selected or chosen later in the game. Alternatively, identifiers are not removed as they are chosen or selected.

A flush-mountable playing card randomization system having a shuffling zone with a playing card insertion area comprising a playing card support surface at a first elevation with respect to a highest level within the randomization system. Associated with the playing card support surface is a playing card mover moving individual playing into a first side of the shuffling zone. There is a randomized playing card collection surface at a second elevation with respect to the randomization system. The collection surface at the second elevation is at least 5 centimeters lower than the playing card support surface, with an exposed or exposable playing card collection area. The system may be retracted to enable manual access.

Some embodiments may relate to a game in which a house takes a rake as a fee for playing a game. A game may include a multiplayer baccarat game that may add a skill element. For example, a baccarat game may add the ability for player's to bluff, choose whether to request cards, raise, fold, and so on. Other example methods and apparatus are described. Some embodiments may include a rake version of Chinese poker. Some embodiments include an open face version of a card game. Some embodiments include a card game with a virtual player position that allows users to play in the virtual player position.

Disclosed herein is a gaming table with detectors for tracking a game.

Methods of playing commission-free pai gow poker games are disclosed. The commission-free pai gow poker games have multiple features, including a novel push mechanism and a novel copy-fostering mechanism, that provide a gaming establishment with an adequate house edge without the need to charge a commission on player wins. The features of the commission-free pai gow poker games may be incorporated in one or more instruction sets or software configured in one or more mechanical devices and/or electronic devices. Furthermore, the features may be configured in one or more displays in communication with one or more servers as desired. Furthermore, the commission-free pai gow poker games may be offered in a non-gaming media environment as desired.

Some embodiments may relate to a game in which a house takes a rake as a fee for playing a game. A game may include a multiplayer baccarat game that may add a skill element. For example, a baccarat game may add the ability for player's to bluff, choose whether to request cards, raise, fold, and so on. Other example methods and apparatus are described. Some embodiments may include a rake version of Chinese poker. Some embodiments include an open face version of a card game. Some embodiments include a card game with a virtual player position that allows users to play in the virtual player position.

A system and method for conducting a card game including a player v. dealer arrangement involving a comparison of HI and LO hand values. Players declare a three-card hand as either HI or LO and a dealer forms three-card LO and HI hands using five cards with a shared card being used in both the LO and HI hand. Aces have a value of 1 point when used in a LO hand and 11 when used in a HI hand, face cards have a value of 0 points and cards 2 through 10 have values matching their rank. Match and poker bonus features may also be incorporated.

An electronic gaming table for hosting live table games involving wagers can include a physical surface, a dealer station, a plurality of player terminals, and a table controller. The physical surface permits the play of live table games with a live dealer and physical game components. The dealer station is situated proximate the physical surface and allows the presence of a live dealer who facilitates game play. Player terminals allow live players to play the games and include player terminal processors coupled to player interfaces having input and output devices. A table controller coupled to the player terminals controls various table functions and administers a live table game pitting a first hand against a second hand. Each of multiple live players can make different live game decisions independently based upon the same second hand, wherein resolution of the game varies by player depending upon the different live game decisions.

Automatic card shufflers may include a card input mechanism for inputting cards into the card shuffler, a card storage device for receiving cards from the card input mechanism and temporarily storing cards within the card shuffler, and a card output mechanism for outputting cards from the card shuffler. The automatic card shufflers may randomly select an internal compartment to be an overflow compartment for inserting cards when a failure of insertion of a card to a selected primary card position occurs.