Secrets of Poker #2

[2ndGoat]

>>Huh? How is an even money wager on a coin flip ever +EV?

Obviously it's a 0 EV play on its own. But consider the following game:
Opponent offers you an even money coin flip for some large amount. If you win, game's over (poker analog: he busts and leaves the table). If you lose, he will offer you the same proposition with a weighted coin- you'll be a 60/40 favorite, with varying wager sizes chosen randomly from a discrete uniform distribution on the integers in [0, total amount you've lost so far] (poker analog: you outplay him for the rest of the session). And you can make that wager as many times as you like until you've won all of the money he won on the first wager (poker analog: he plays til he busts).
Your other option is to decline the inital wager, and play the same series of 60/40 flips with the bests ranging from small to whatever the coin flip waer size would have been.

Clearly, the optimal strategy is to accept the wager, because by taking a 0 EV play, becausw half the timeyou have the opportunity to make a series of +EV plays for a longer period, and the other half of the time you've given up no expectation. Even if your opponent leaves after some number X favorable wagers, with X an unknown number chosen unformally from 0 to 100, (poker analog: he may even leave without going bust) it's still a +EV decision to take the initial wager.

Now, if this guy will leave after doubling through, it doesn't make sense to take the bet- you can only win what he has in front of him at the start of the game, so taking the coin flip denies you the chance to outplay your opponent half of the time, while giving him a free bet the other half of the time... I hadn't considered that when I first posted, so if you were to use this criterion, you would have to have some assumption about wheter he'll stay or go after doubling up, or going broke.

I made no assertion as to whether 66 was a coin flip. However, some hand *will* be a coin flip, and I advocate taking that race with whatever the break-even hand is, if the conditions are right, as detailed above.

2ndGoat