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#Poker dice probability Pc

Note that the numbers in bold are used in the second multinomial coefficient above. The second multinomial coefficient is 12 and is the number of ways to group 4 committees into three subgroups, one consisting of one committee (receiving one candidate), one consisting of two committees (receiving four candidates each) and one consisting of one committee (receiving two candidates). This is the second question indicated above. Another application is for calculating the probabilities of the hands in the game of poker dice (see Example 2 below). For example, this technique can be applied in the occupancy problem (see chapter 2 section 5 in p. This technique of the double applications of the multinomial coefficients is a useful one in probability and combinatorics. In other words, the first application of the multinomial coefficients is on the 11 objects to be distributed into four subgroups and the second instance is on the grouping the four subgroups.

But in the second question, the subgroups can rotate among the four committees, requiring a double use of the multinomial coefficients, once on the 11 candidates and a second time on the four committees. The second question is also about assigning 11 candidates into four subgroups. Note that the first question is a specific example of the second. Note that the numbers in bold are used in the denominator of the multinomial coefficient below. The first question is a straight application of the combinatorial technique of multinomial coefficients, namely, the number of ways to assign 11 candidates into four subgroups, one group consisting of one candidate (Committee M), one group consisting of four candidates (Committee I), one group consisting of four candidates (Committee S) and one group consisting of two candidates (Committee P).

How many ways can we randomly assign 11 candidates to these 4 committees such that one committee consists of one member, one committee consists of four members, another committee consists of four members and another committee consists of two members?.

How many ways can we randomly assign 11 candidates to these 4 committees such that Committee M consists of one member, Committee I consists of four members, Committee S consists of four members and Committee P consists of two members?.

Assume that each candidate can only be assigned to one committee. Eleven candidates are randomly assigned to these four committees. That is your mission, should you choose to accept it.Suppose there are four committees that are labeled M, I, S and P. What are the odds of getting making each of these hands with skill levels going from 1-5?

#Poker dice probability Pc

A PC with 'Shooting 1', can reroll 1 die one with 'Shooting 2' can reroll 2, and so forth up to 5, which can reroll all. The higher the character's skill level, the more rerolls he can make (like Draw Poker). What are the odds of making each of these hands?īut that isn't the really hard question.

The game relies on making (sorta) poker hands, with better hands beating worse hand in the following order: You have 5 poker dice, which go from 9-A (functionally the same as 1-6). So, I now challenge the math boffins with what I think is a hard one.

Alright, every time I ask a dice probability question, I'm stunned at how quickly and thoroughly folks here can answer these questions.