Question

Challenge: How many 6-sided dice does it take to make rolling any 6 more likely than not?

Answer 1

dont they all have the same chances?

Answer 2

If you roll two dice, the chances for getting a six at all is greater than 1/6

Answer 3

It's easier to consider the chances of NOT having even one six.
For one die, P(1)=5/6
For two, P(2)=(5/6)^2
and for n dice, P(n)=(5/6)^n
We want P(n)=(5/6)^n <=0.5
Take log and solve for n to get
n=log(0.5)/log(5/6)=3.8
So with 4 dice, the probability of getting at least one 6 is more than half.

Answer 4

Which is why Risk only gives you three. It all makes sense.

Answer 5

:)