#Poker dice full#

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So in poker dice, Bupkiss should actually beat Three of a Kind.Show off your work with this easy-to-customize and full-featured WordPress Theme. Interestingly, the chances of a nothing roll is pretty small! In fact, there are really only four nothing rolls: 12346, 12356, 12456, and 13456. The unofficial word for a nothing roll is Bupkiss. There are (5 2) ways to arrange the pair in 5 slots, (3 1) places to put B, (2 1) places to put C, and then the position of D is determined. This one has 6 choices for A, and (5 3) ways to assign values to B, C, and D. There are also (5 2) ways to arrange the A’s, and (3 2) ways to arrange the B’s in the remaining spots, and then the position of C is determined. But since the pairs are themselves indistinguishable, it’s not really 6 * 5, it’s actually (6 2) possibilities for assignments to A and B, with 4 choices for C. The pattern for two pair is AABBC, and you might think there are 6 choices for A, 5 choices for B, and 4 choices for C. There are (5 3) ways to arrange the A’s, and (2 1) ways to arrange B in the remaining slots and then the position of C is determined. But since B and C are indistinguishable, there are 6 choices for A and (5 2) choices for assignments to B and C. The pattern for three of a kind is AAABC, and you might think there are 6 choices for A, 5 choices for B, and 4 choices for C. (Or you can say there are (5 2) different ways to arrange the B’s and the A’s are determined you get the same answer.) The probability is 6 * 5 * (5 3) / 7776 = 300 / 7776 = 3.86%. The A’s can be arranged in (5 3) different ways and then the B’s are determined.

#Poker dice full#

The pattern for a full house is AAABB with 6 choices for A and 5 remaining choices for B. Since all dice are distinguishable, there are (5 1) places the first die can go, (4 1) for the second, (3 1) for the third, (2 1) for the fourth, and the last is determined. There’s a trick – in poker dice there are only two straights: 1236. The pattern here is ABCDE where all die are distinct numbers. In a departure from standard poker hands, the next hand in poker dice is a straight. But since A and B are distinguishable, we count all combinations, and B can be in (5 1) = 5 possible places, so the probability is 6 * 5 * 5 / 7776 = 150 / 7776 = 1.93%. There are 6 choices for A, and once A is chosen there are 5 choices left for B.

There are only 6 choices for A, so the probability is 6 / 7776 = 0.08%. In the following, to find the odds of plain old poker dice hands, I will simply count the number of ways each can happen and then divide by 7776. Some differences are inevitable since the number of possible 5 card poker hands is (52 5) = 52! / (5! (52-5)! ) = 2,598,960 and the number of possible 5-die rolls is only 6 to the power of 5 = 7776. Ranking poker dice hands by odds mostly follow the same order as poker hands dealt from a standard 52 card deck (except for 5 of a kind which doesn’t exist in a standard poker hand of course). But in any case, a good starting point is to calculate the relative probabilities of getting one of the basic poker hands on one roll. Often there is an opportunity to improve the hand by selectively re-rolling the dice, and sometimes there are constraints added to what hands can be scored. Many dice games like Yahtzee or Yamslam are based on making the best poker hand out of a roll of 5 dice.