1/13/2024 0 Comments Probability poker dice two pairThe multinomial coefficient is 6!/1!3!2! = 60. The number of ways in which this can be done is given by the multinomial coefficient n!/n 1! n 2! … n k!įor example a 1 pair hand partitions the population into k=3 subpopulations – a pair subpopulation of size n 1 = 1, a singleton subpopulation of size n 2 = 3 and a non-displayed face subpopulation of size n 3 = 2 satisfying the condition n 1 + n 2 + n 3 = 6. Hands are constructed from a face population of size n (in this case 6) and each hand partitions the population into k subpopulations of sizes n 1, n 2 etc. The number of outcomes for a Poker dice hand can be calculated as the product of a combinatorial expression relating to groups of faces and the permutation of those faces among five dice. But there is an alternative method of calculation which does make the difference clear. Then there are 4C 1 ways to choose the last dieĬonventional calculation gives no obvious indication of why there are twice as many outcomes for a 1 pair hand than a 2 pair hand. But when outcomes are calculated in the conventional way, it is not obvious why this is so.Ĭonventional calculation runs as follows:ġ pair – There are 6C 1 ways to choose which number will be a pair and 5C 2 ways to choose which of five dice will be a pair, then there are 5C 3 × 3! ways to choose the remaining three diceĢ pair – There are 6C 2 ways to choose which two numbers will be pairs, 5C 2 ways to choose which of five dice will be the first pair and 3C 2 ways to choose which of three dice will be the second pair. The percentage share of 5 of a kind (0.08%) is omitted due to its small sizeĪ noticeable feature of the data is that the number of outcomes for a 1 pair hand is exactly twice that of a 2 pair hand.
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