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Answer and comments

Posted By: Timothy Chow
Date: Wednesday, 28 April 2010, at 8:19 p.m.

In Response To: Answer and comments (Daniel Murphy)

Daniel Murphy wrote:

Say what? It's possible that a lower-equity play will come out ahead in the short run, but not with higher probability than the higher-equity play.

No, it's certainly possible for a lower-equity play to come out ahead in the short run with higher probability than a higher-equity play.

It's difficult to give explicit examples in backgammon because backgammon is such a complicated game. But for example, in the roulette puzzle, compare the roulette player to someone who is just flipping a fair coin 108 times in a row and winning $1 for each head and losing $1 for each tail. The coin-flipper is playing a higher-equity game, but the probability of either breaking even or coming out ahead after 108 games is about 54.3% for the roulette player whereas it's about 53.8% for the coin-flipper.

Of course if you increase the number of trials then the roulette player is going to fall badly behind, but I have been emphasizing the short run here.

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