Let's take a coin flip as an example.
Let's assume we perform 10 flips.
I need to determine a formula to calculate the odds that somewhere within the 10 flips, there will be a point where heads has occurred at least 2 times more than tails.
So the final outcome could be 8 tails and 2 heads, but if the 2 heads came up in the first two events, then that outcome would still meet the criteria.
The standard binomial theorem wont work for my purposes, because if I set it to calculate the odds that I get at least 2 more heads results than tails (say 6 out of 10 heads at least), then it wont count the examples I specified above.
Mapping it out manually wont work for my purposes.
Can any clever person think of a solution?