Cute Applicable Math Question

[emanon]

I'm quite sure the answer is right. I also wrote a quick excel program to make sure.

hmm, let me see if I can think of a better way of explaining why... its a bit of a mish-mash of stuff, maybe someone like brucez can give a clearer picture if this doesn't help.

1. There are only 2 events which matter:
i. A has 3 more wins than B
ii. B has 3 more wins than A

2. Regardless of the number of flips to reach event i or ii, the difference between Winner_victories and Loser_victories = 3. ie-->
Wins - Loses = 3.

3. In $2
(Wins -2) = Loses
So the only thing that mattered was reaching 2.
In $3
(Wins -3) = Loses
So the only thing that mattered is reaching 3.

4. Therefore, just as we did in the $2 case, we need only concern ourselves with calculating the probabilities of reaching the requisite number of wins. The steps taken to get there (ie, the path) is irrelevant. All that matters is reaching 3.
Thus we the prob (+3) and prob(-3) is the total prob space with which we are concerned.
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Now, to give an example of why this doesn't neccessarily work in a tournament:
Depending on relevant stack sizes, etc, a player may change his actions to adjust his EV/SD. This means that my probability changes depending on the results of the flips(cards), and we can now no longer ignore the path taken to acheive victory.