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

[Ed Miller]

While your logic is interesting, I believe it is fallacious.

As I understand it, your argument is that if you lose the 0 EV bet, then you get to make more +EV bets against your opponent than you would otherwise and hence make more money. But, by the same logic... if you win the 0 EV bet, then you get to make no +EV bets against your opponent at all. So.... you want to lose a 0 EV bet to make more money???

If your opponent is willing to make bets against you giving you the best of it until he loses a fixed amount of money... then your EV is the fixed amount of money he is risking. If he plays indefinitely, then you will make exactly that much basically every time... whether you make 0 EV bets with him or not. The only thing that varies is how long it takes... if you accept the huge 0 EV bet at the beginning, you will either get all his money immediately, or it will take twice as long to get his money as it would have had you not made the bet.

A 0 EV bet is a 0 EV bet. It gives you no value whatsoever. It only increases your variance. Furthermore, if you are on a limited bankroll, then it increases your risk of ruin without adding to your expectation.

[crazy canuck]

[2ndGoat]

I neglected to consider that you rob yourself positive EV plays when you win the coin flip... so it averages out, and remains 0 EV.

However, I still believe situations abound where taking the play of immediate EV 0 has a long-term positive EV. If you're on a unlimited or nearly-unlimited bankroll, I would play any starting hand with an EV of precisely 0 for that hand (not just that betting round. I mean to say any hand that has no expectation from the time I enter the pot to the time the winner rakes it in). (I make no claims as to *what* hands have precisely EV 0, just saying what I would do if I had that information). That way, when I have a +EV hand, I will be that much harder to put on a hand, which should be worth something in the long-run.

If it's correct to sometimes make an incorrect play on one round to gain bets on later rounds (slowplaying, for instance), it actually is the correct play if it maximizes your EV in the long run. If it can be correct to take immediately -EV plays, it has to be sometimes correct to take 0EV plays.

2ndGoat

[Boris]

I did exactly the same thing in the $1500 buy in no limit event at the Bellagio last weekend. 5 limpers and I pick up Ah-6h in the BB. I moved in and got busted by UTG limper with QQ. Boy did I feel like an idiot. That secret of poker sucks and is for suckers.

[Yerma]

I am not messing with you.

Paradise hand numbers: 247,899,723; 248,091,056