I have the perfect strategy to win any sort of game of chance. Just when I lose, I say , "2 out of 3?" and my opponent always accepts due to my infinite persuasiveness. If I lose again, I propose 3 out of 5, then 4 out of 7, etc.

Essentially, the effect of this strategy is that if the number of games I have won ever exceeds the number of games won by my opponent, then I win overall.

If I have a 50% chance to win any one game, what is the probability that I will eventually win overall (or rather, what does the probability approach)?

What if we play a game that involves a little strategy, and I only win 1/3 of the games?

I took into account two possiblities: You lose the first game, or you win the next w. The problem is the possibility exists that you win the first x games (where 0<x<w) and lose a game after that, and that was not figured in. (For example, LWL, LLWWL, LWLWL, and so on)

 

Posted by Gamer on 2005-07-21 15:22:26