Variance

In July I had a lot of success pursuing the short stacking strategy I talked about in an earlier post. I made a solid hourly and collected a lot in bonuses. During one stretch I won 19 out of 22 days. Then in August, using the exact same strategy, I started to lose steadily. After losing a few days in a row I would start to get worried and go back over hands and statistics to make sure everything was okay. Once I had convinced myself that it was, I would start a new session feeling optimistic. Then I would lose again. At the end of the month I was way down at the tables and only slightly better than break even after factoring in bonuses.

There are a few explanations. One is simply luck. When you get all your money in you have a certain probability of winning the pot - poker players call this your equity. The size of the pot times your equity is your expected value in the hand, but you will not actually get that amount. You will either win or lose, and scoop the whole pot or none of it. For example, if you get all in pre-flop with pocket queens against ace-king your chance of winning is about 57%. So if there is $50 in the pot, you will on average win 50 x .57 = 28.50. But in any given hand, you will win either $50 or $0. If you win $50, you were $22.50 ahead of expectation for that hand. If you lose, you were $28.50 behind expectation. I have a program that does a similar calculation for every hand in which I get all-in. It turns out I was way ahead of expectation in July and way behind in August.

But that isn't the whole story. There is variance in poker that all-in equity doesn't account for. There is a lot of luck in how the cards are dealt out, but that's harder to measure. In any case, even accounting for the luck I could measure, my margin shrunk from July to August. I was "supposed" to win both months, but less in August. And the closer you get to break even, the more variance you will experience in your results. This is due to rake, the percentage of each pot that the house takes out. Poker players tend to focus on the bottom line, but a more accurate way of looking at results is to separate them into the amount you beat the game by minus the amount you pay in rake. So if you're making a small amount of money, you're actually beating the game by a significant margin, but paying most of it back in rake. If you're exactly break even, you're beating the game by exactly the amount you pay in rake. At that point any difference in how you do in the game will translate to a large difference in your bottom line. As my expectation crept very close to break even, I was more and more susceptible to variance and I happened to get very unlucky over that period.

Why did my edge get smaller? I think it was because I started playing enough volume that all the regulars in the game were forced to pay attention and figure out how to play against me. For example, a lot of the regulars in those games raise a wide range of hands from the button. I would shove a lot of hands from the blinds and win a lot when they folded. But eventually they adjusted by almost never folding to my shoves. They would snap-call with mediocre hands like queen-jack or weak aces, which they were probably always folding previously. I tried to adjust by pushing less hands from the blinds, but the new dynamic seemed to be less profitable than the old one.