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The Chen Coin Flip

How You Make Money Playing - Poker Variance





Poker variance definition: The statistical measure of how your results will be dispersed; variance does not mean merely "bankroll swings".

Winning poker is all about the application and reapplication of advantages over a long period of time. If you play better than your opponents to a degree that overcomes the rake, you win. A problem with this that plagues many otherwise good players, especially those that play in very live games regularly, is that when they hit losing streaks or when bad luck hits them extra hard, they seemingly lose touch with the process of what is occurring when they win.

One specific example comes up a lot. Some "good" players insist games of a table full of maniacs can't be beaten. This "good" player complains that AA doesn't "stand up" in a ramming and jamming Holdem game where eight people commonly take the flop. He somehow seems to think that AA should be winning more than half the time, and needs to be winning more than half the time for him to be making money. Simple math should tell him that a hand that wins 40% (or 35% or 25%) of the time against seven players is enormously profitable. He should be welcoming those 60% (or 65% or 75%) of the times he does not win! You need to expect to lose most of the time to win in the long run.

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This carries over on an hourly and session basis too. You can't expect to win every hour or every day. Income in poker is not made in a linear, regular way. There is deviation. Sometimes you get unlucky.

Bad luck not only destroys some players because they play too high for their bankroll, it destroys their game mentally because they can't stand losing to weaker players. A lot of above average players simply need a more reasonable idea about how their edge makes them their money.

Poker VarianceOn the rec.gambling.poker newsgroup, two-time 2006 World Series of Poker bracelet winner William Chen posted the following excellent bit of advice (used by permission here):

"When we sit down at a table, every hour we're essentially doing a coin toss for a rack of chips. Now if you're a skilled player you may have an overlay of half a stack (assuming 100 chips in a rack and 20 in a stack). So if you're a skilled $3-6 player, it's like flipping a coin and getting $120 if you win and losing $100 if you lose or if you're a 15-30 player it's $600 if you win, $500 if you lose. Now this is a pretty huge edge when compared to blackjack on a per-hand basis but we shouldn't be too surprised at all if we get on a bad streak and lose $3000. How easy is it to flip tails 6 times a row? It's bound to happen if you flip coins all the time -- now 10 or 15 in a row is a little unlucky but nothing too phenomenal."

The way to win is to focus on playing your best to get that 6-to-5 edge, not on whether you win the flip this hour. If you do genuinely have an edge, and you simply go in and play your best all the time, what happens is you get something like this 600-500 or 120-100 coin flip every hour. Isn't that great?

But what a lot of players do is when as the 6-5 favorite they lose the toss three or four or ten times in a row, they start steaming and playing less optimally and tearing themselves up inside about their bad luck. Essentially what "tilt" is, for a winning player, is saying: okay, I've lost four of these coin flips in a row, so to get even for the day I'm going to take an additional couple of flips this hour, but in these additional flips I'm going to be the 5-6 underdog.

Sometimes you'll have a run of bad luck (be it an hour, a day, a month or a few months) when you are the coin flip favorite. Big deal. This is no excuse for trying to "get even" by transforming yourself from a favorite to an underdog just so you can get more flips that day!

Next time you are tilting and chasing, or playing an extra long session when you are stuck, ask yourself why instead of having the chance to flip a coin once an hour to win 600 while risking 500 you are insisting on all these extra flips where you can win 500 (or 465 or 275) while risking 600! "Getting even" is nothing in the grand scheme of things, applying and reapplying your advantage is.

Also: Poker Expected Value, Poker Math Skills vs. People Skills and Poker Odds and Gambler's Ruin

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