Thread: Dice game formula

There is a game in wich you roll a number of ten sided dice and look for matches, a match is when two or more dice turn up the same number, well I have this table:

Dice pool

Chance of getting one or more matches

1

0,00%

2

10,00%

3

28,00%

4

50,00%

5

70,00%

6

85,00%

7

93,00%

8

98,00%

9

99,60%

10

99'9%

But I'm looking for the general formula that shows the chance of getting matches with n dice.

P(some matches) = 1 - P(no matches)



P(some matches) =

with the understanding that the probability is 1 if n>10.


The above formula seems to match your figures fairly closely (i checked 3 of them), hopefully differences are due to rounding and not a mistake