I am looking for a way to calculate the possibility of a die rolling 6, at least N rolls more than any other number.
Here is an example:
Let's say I throw a die 100 times and I want to calculate the possibilty that the number 6 appears 20 rolls more than any other number. So for example these could be the roll results:
6: 40x
5: 20x
4: 10x
3: 15x
2: 10x
1: 5x
So the 6 was rolled 20 rolls more than the 5.
Here is another example:
6: 50x
5: 10x
4: 30x
3: 10x
2: 0x
1: 0x
Here the 6 was rolled 20 rolls more than the 4. And so on. There must be an enormous number of cases in which this condition is satisfied.
I am looking for help on how to calculate the prbability, that the given condition is satisfied.
Thanks in advance!