Probabilities are calculated for a simplified version of poker. Additional rules of the game will be added over time.
- Players are dealt two cards each
- Five community cards are dealt
- A hand is the single best card, not the five best cards.
- Community cards are not in play.
- The player with the highest card (from their hole cards) wins.
E: Known, set of cards in your hand and on the table.
D: Unknown, set of all other cards.
Rank(c): Rank of a card.
- Rank(A) = 14, Rank(K) = 13, ... , Rank(J) = 11, Rank(10) = 10, ... , Rank(2) = 2.
Count(c): The count of a given card in E.
- If there is a Jack in your hand and one on the table, Count(J) = 2.
Low(c): The count of cards of lower rank than a given card in E.
High(c): The count of cards of a higher rank than a given card in E.
With the current rules, a draw is when two or more players share the high card. This formula calculates the probability that at least one other player has at least one card of the same rank (the high card).