Poker Variance

Variance in Poker

Poker Variance - There are two meanings to the word "variance" when used about poker: The technical term, and the colloquial term. The technical term, from statistics, is not what this article is about - but you can read about it here. No, when poker players talk about variance, they virtually always refer to bad luck.

The term gets thrown around because variance - in the technical sense - is an integral part of poker. Expected Value gives us a theoretical value of how profitable or unprofitable an action is, but in reality we sometimes are lucky and sometimes unlucky. Sometimes our pocket kings hold up versus aces thanks to a miracle turn card, and sometimes our flopped straight gets outdrawn on the river by a flush or a full house. Variance, practically speaking, is the element of luck in poker. A player can go on a hot streak and seemingly not be able to lose a single hand. Likewise, a solid pro can go on a sick run of cards where he can't seem to catch a hand to save his life, and when he finally does, someone else has him beat. The first player won't be talking much about "variance," but the second player will. Because when we run well, we like to think it's because we play well. But when we run bad, our psyche needs a scapegoat, so we call it "variance" and dismiss the money lost as a function of statistics, not of bad play. Poker variance is to be expected, but it's also expected to even out in the long run. Most of us get our fair share of hot streaks and cold streaks, and what's left in between them is the actual profit from our expected value.

For better or worse, PokerTracker 3 and Hold'em Manager now both come with "EV graphs" available. That is, they show you your graph of winnings, and then they add a second line to that showing how much you would have won if, every time you were all-in before the river, your hand would have produced its expected value. Someone who gets his aces cracked by kings when all the money goes in preflop, for instance, would have an EV graph that shows that they're unlucky - it's higher than their actual outcome. It's relatively common for people to post graphs showing how unlucky they are. On the flipside, you don't often see people posting graphs where they've been very lucky in all-in pots.

Wonder why.

-- Note the difference between the EV-line and the actual outcome. Note the wild swings.

An interesting psychological effect of bad luck is that we notice it a lot more than we do good luck. The most trivial example of this is a preflop all-in pot where you lose with AA. You will probably feel extremely unlucky - as you perhaps should, because you were around 80% to win. But do you feel a little lucky when you win with AA? Probably not. You feel entitled to the pot, so the fact that you escaped the 20% risk of losing it doesn't register as luck. But it is: You won more than your expected value. Of course, because of the discrete (in the mathematical sense) nature of all-in pots, you can't actually win your expected value. You either win it all, or you lose it all.

But the whole point is that you shouldn't worry about variance in poker. Not because it doesn't have a big impact on your bottom line - it most certainly will - but because there's absolutely zilch you can do about it. And, in the long run, you should expect to flop sets-over-sets as often as sets-under-sets. You should expect to be hit with an average amount of flush draws that hit and miss. When you've played a lot of poker, what will matter is the small things here and there - stealing blinds, making the occasional well-timed bluff, continuation betting and checking at the opportune moments - and the individual profit from each of them will be small, but you're playing for the long haul and the profit is cumulative.

When you go through a really rough stretch of hands, don't sit around bemoaning how unlucky you've been with aces or how your flush draws never hit. What you should do is go and look at the essentials: Are you playing a fundamentally solid poker game? This is what you can affect, and this is what you should focus on. If you've lost a big chunk of money over the last, say, 2,000 hands, don't fret about the big pots because the big pots were probably in the stars, so to speak. Instead, ask yourself if there were spots where you could have saved some money, or spots where you could have made a little extra.

-- Note that there were several downswings in this graph almost 20 buy-ins in size. The overall win-rate over this sample was a little over 3bb/100m, but swings are massive - in both directions. This is 150k hands from 6-max NLHE.

Downswings happen, and they are as close to a certainty as anything can be. Variance in poker is what keeps the fish from coming back, because it gives it its element of gamble, and in that sense it should be cherished. But as a player trying to play well and trying to win the maximum, they shouldn't matter to you because, again, there's nothing you can about them. Focus on the long term. Focus on making good decisions not just in big pots, but in small pots too - and the long run will look a lot better for you.

Article written by FPaulsson.

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