Dice Poker is more or less what you think it is; you roll 5 dice and then have the option of re-rolling some or all of the dice to improve your hand. Apparently, there could be gambling involved and the person with the better hand wins the stakes for a given hand. I guess if you have enough dice, you could have more than 2 players. Dice Poker, I have been informed, is one aspect of the Witcher action role-paying game.
Here’s how to calculate the probabilities in Dice Poker, in order of pay-off. In other words, even though the probability of a High Straight and a Low Straight are the same the High Straight beats the Low Straight the probability of a bust or losing hand is much lower than getting one pair, the pair beats the bust.
Five of a kind: there are 6 combinations one for each face on the dice.
High Straight: all the possible arrangements of 23456.
Low Straight: all possible arrangements of 12345.
Four of a kind: 6 face for the 4 of a kind; 5 possible singletons; 5 possible positions for the singleton.
Full House: 6 faces for the 3 of-a-kind; 5 left for the pair; 5c2 = 10 possible positions for the pair.
Three of a kind: 6 faces for the 3 of a kind; 5c2 singletons; 5c3 positions for the 3 of a kind.
Two pair: 6c2 ways to combine faces; 4 possible faces for the singleton; 5c2 positions for the first pair; 3c2 positions for the second pair.
One Pair: 6 faces for the pair; 5!/2! possible combinations for the singletons, 5c2 arrangements for the pair
Loser: The total permutations (65) minus all the preceding values; all the possible combinations of singletons (6!) minus the High Straight and Low Straight combinations
