No matter how many times you roll a dice, the chance is always 1:2 or 50% without house edge. A sample question would be this. If you toss a coin 9 times and the result is H, T, T, T, T, T, T, T, what is the chance that the coin will land in H on the 9th toss? (H=head, T=tail) . Please realize that the result in gambling depends entirely on its internal system.
Okay, so let's consider an heads tail bet between you and your friend.
First thing, chances of you winning a bet is 50%
Second thing, you both have $1000 initially in your pockets.
Third, you and your friend bet $1 in each bet. Winner takes $2.
Fourth, you'll leave as soon as your pocket has $1001
So the match starts,
If you win first bet, your pocket has $1001 , you leave . Chances of winning fist my was 50%.
Now chances of losing first match was 50% . In case first match is a loss, you'll continue to play till your pocket has more than 1000 dollar.
Okay, I think I get what you're describing here. You seem interested in the math behind this stuff so you might appreciate this. The danger with your permutation analysis lies within what is termed the "random walk." You can easily end up in a situation where it comes highly improbable that you'll ever come back toward the break even mark, let alone a positive profit. And, because your strategy dictates a "quit" on a win of one unit, the risk outweighs the reward significantly. You might find it enlightening to study the math behind the "random walk." Start here:
https://en.wikipedia.org/wiki/Random_walk
