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216 permute 312/29/2023 If the combination is 1,1,2 there are three ways to roll that: 1,1,2 1,2,1 and 2,1,1. For example if the three dice are 1,1,1 there is only one way to roll that a 1 each time. With a three of a kind there is only one way permutation. ![]() A combination is a set without regard to order and a permutation is a set with regard to order. Next we have to determine the number of permutations of each combination. The whole list would look like the following. The third die must be greater or equal to the second die so the next combination in full would be 1,2,2. Obviously you can’t roll a 7 with one dice so next we increment the second die. In the interests of not listing the same number twice always order each combination from lowest to highest, not forgetting combinations with a pair or three of a kind. To avoid the list being 6 3=216 items long do not repeat the same combinations in different orders. What I recommend is list every combination of 3 dice. If you don’t know how to program you’re going to have to do this the hard way. The total would be 6 -3 * =ġ/218 * =Īlternatively, if you can program a computer that would probably be the fastest way to get the results.Ĭout << "Total\tCombinations\tProbability\n" Ĭout << i << "\t" << tot_array << "\t" << (float)tot_array/216 << "\n" Epstein, formula 5-14.įor example, let's look at the number of ways to get 11 spots over 3 dice. Following is a formula for s spots over n dice, taken from The Theory of Gambling and Statistical Logic by Richard A. The critical step in calculating the odds in Sic Bo is to find the probability of any given total in the throw of three dice. If chosen number appears 1 time bet pays 1 to 1, if it appears 2 times bet pays 2 to 1, and if it appears 3 times it pays 3 to 1.
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