# Math Help - Dice game formula

1. ## 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.

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

$P(\text{no matches from n rolls}) = \frac{10!}{(10-n)!10^n}$

P(some matches) = $1 - \frac{10!}{(10-n)!10^n}$

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