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Game Shrink Interactive and Rhode Island Hold 'Em

GSI (Game Shrink Interactive) plays Rhode Island Hold 'Em optimally. Rhode Island Hold 'Em is a three card poker game invented by Jiefu Shi and Michael Littman. The main difference between Rhode Island Hold 'Em and Texas Hold 'Em is the number of cards in play. Here is how the game of Rhode Island Hold 'Em is played:

Each player pays an ante of 5 chips.
Each player is dealt a single card, placed face down. This is the player's hole card.
After receiving the hole cards, the players take part in one betting round. Each player may check, or bet if no bets have been placed. If a bet has been placed, then the player may fold (thus forfeiting the game), call (adding chips to the pot equal to the last player's bet), or raise (calling the current bet and making an additional bet). In Rhode Island Hold 'Em, the players are limited to 3 raises per betting round. In this betting round, the bets are 10 chips.
After the betting round, a community card is dealt face up. This is called the flop. Another betting round take places at this point, with bets equal to 20 chips.
Another community card is dealt face up. This is called the turn card. Another (and final) betting round takes place at this point, with bets equal to 20 chips.
If neither player folds, then the showdown takes place. Both players turn over their cards. The player who has the best 3-card poker hand takes the pot. In the event of a draw, the pot is split evenly. The ranking of hands is given below.

Hand rankings for 3-card poker

Hands in 3-card poker games are ranked slightly differently than 5-card poker hands. The main differences are that the order of flushes and straights are reversed, and a three of a kind is better than straights or flushes.

Rank Hand Probability Description Example

1 Straight flush 0.00217 Three cards with consecutive rank and the same suit. Ties are broken by highest card. King spades, Queen spades, Jack spades

2 Three of a kind 0.00235 Three cards of the same rank. Ties are broken by the card's rank. Queen spades, Queen hearts, Queen clubs

3 Straight 0.03258 Three cards with consecutive rank. Ties are broken by the highest card rank. 3 clubs, 4 spades, 5 hearts

4 Flush 0.04959 Three cards of the same suit. Ties are broken by the highest card rank, then second highest card rank, then third highest card rank. 2 diamonds, 5 diamonds, 8 diamonds

5 Pair 0.16941 Two cards of the same rank. Ties are broken by the rank of the pair, then by the rank of the third card. 2 diamonds, 2 spades, 3 hearts

6 High card 0.74389 The hand is ranked according to the highest ranked card in the hand. Ties are broken by comparing the highest ranked card, then the second highest ranked card, and then the third highest ranked card. Jack clubs, 9 hearts, 2 spades

Rank	Hand	Probability	Description	Example
1	Straight flush	0.00217	Three cards with consecutive rank and the same suit. Ties are broken by highest card.	King spades, Queen spades, Jack spades
2	Three of a kind	0.00235	Three cards of the same rank. Ties are broken by the card's rank.	Queen spades, Queen hearts, Queen clubs
3	Straight	0.03258	Three cards with consecutive rank. Ties are broken by the highest card rank.	3 clubs, 4 spades, 5 hearts
4	Flush	0.04959	Three cards of the same suit. Ties are broken by the highest card rank, then second highest card rank, then third highest card rank.	2 diamonds, 5 diamonds, 8 diamonds
5	Pair	0.16941	Two cards of the same rank. Ties are broken by the rank of the pair, then by the rank of the third card.	2 diamonds, 2 spades, 3 hearts
6	High card	0.74389	The hand is ranked according to the highest ranked card in the hand. Ties are broken by comparing the highest ranked card, then the second highest ranked card, and then the third highest ranked card.	Jack clubs, 9 hearts, 2 spades

An Ace may be used in a straight as either Ace-two-three or Queen-King-Ace. In the case of the former, the highest ranked card of the straight is the three.

Note that within a single game of Rhode Island Hold 'Em, the same player is first to act in each betting round. The player who is first to act changes after each game.

This program requires the Java Run-time Environment (JRE) to be installed on your computer. Visit Sun's Java website for information on downloading and installing the JRE if you don't already have it installed. Send questions, comments, and bugs to Andrew Gilpin.

Andrew Gilpin and Tuomas Sandholm have computed Nash equilibrium strategies for Rhode Island Hold 'em. Click here to play Rhode Island Hold 'Em against the optimal opponent.

Last updated: August 24, 2005