grafzahl: The odds of a number coming up are as so...

First time... well... 100%
2 times: 16.66% - 1/6
3 times: 2.78% - 1/36
4 times: .46% - 1/216
5 times: .08% - 1/1296
6 times: .013% - 1/7776

Here is another example of such a game...