What is Variance in Poker?

written by: John

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Variance in poker is simply when you have short-term results that are significantly different then the results you should have in the long run. In other words, it's when you run well or worse then you should be. Everyone faces variance when playing poker, it's impossible not to. How much and the severity of variance you face will be dependent on many factors including mathematical probability, the games you play, the betting format of those games and your personal playing style.

Variance and Mathematical Probability

Variance and mathematical probability in poker go hand in hand because as we all know, poker hands will win a percentage of the time and the other percentage of the time it loses. You'll know when you are facing some variance when the mathematical probabilities of these hands swing heavily towards or against you in favor.

For example, a pocket pair will flop a set roughly 1 in 8 times. So, it would make sense to assume that if you were dealt a pocket pair 9 times in a row and saw a flop, one of those times you'd flop a set. While that makes sense, this math refers to the long-run. Over a shorter sample size, you might see that you had positive variance and flopped a set 1 in 4 attempts on average. Or, you could run bad and not flop a set once even though you were dealt over 20 pocket pairs. This is all variance.  

Another example would be pocket aces verses kings. You know if you're holding pocket aces, you are going to be an 80% favorite if you are all in preflop verses kings. This means that you should win 4 out of 5 all in situations. If you're facing bad variance, you might have your aces cracked by kings 3 out of 5 times on average over a short sample. You might even lose them all. At the same time, you could win the next 15 all in situations when, on average, you were only supposed to win 12.

The other thing I want to point out about variance and mathematical probability is that the bigger edge you have, the less variance you should expect to see. To explain what I mean, I'll use the aces versus kings example again.

If you have aces verses kings, you are an 80% favorite which is huge. You might face a spell where you lose 3 times in a row due to variance, but when you take your equity in the hand into consideration, the times you lose is minor in comparison to what you earn when you win. In a $100 pot, $80 on average is yours. So losing 3 times in a row is nothing ($60) when you could very well win the next 4 out of 5.

On the other hand, if you get AK suited all in preflop verses pocket 2s you'll be a coin flip. This situation will result in much bigger swings or higher variance. This is simply because the edge that one hand has over the other is minimal, if not non-existent. You'll win a pot, lose a pot, win a pot, lose a pot and repeat.

To better understand what I mean, take a few minutes and graph both situations on paper. With the aces verses kings hand, graph your first 4 pots won and then graph your 1 pot lost. Do this for a series of 100 hands. Now do it with the AK verses 22 hand. After you do both of them with their average win/loss, then start doing variations of win/losses. You should see what I mean immediately. The aces verses kings graph will have little dips (variance) in it while the AK verses 22 hand will resemble an EKG graph.

Games You Play and Variance

The games you choose to play will also have an impact as to how much variance you see. The reasons for this are pretty much the same as what I outlined in the last section. In a game like Texas Hold'em, players often get their money in as a coin flip or maybe a 55/45 - this will result in higher variance.

In games like Omaha or Stud, often times players are getting their money in when they are way ahead/behind or drawing dead. This will result in much lower variance.

Aside from specific games, how you play each game will also determine how much variance you see. If you choose to play in larger multi table tournaments, you'll see large amounts of variance because of how much you lose before you win. You'll lose many buy-ins before you win and get that big score. Sit n go's, on the other hand, will have less swings because the fields are much smaller so you could expect to cash far more often.  

Betting Formats and Variance

I'm sure this is self-explanatory, but I'll explain it anyway. The betting format of any game you play will play a huge roll in how much variance you see. This is simply because the more money you are allowed to wager, the more that can be won or loss at any given time.

With that said, the no limit betting format will yield much higher swings of all the betting formats. Next will be pot limit followed by fix limit.

Personal Playing Style and Variance

The reason why your playing style will affect the amount or severity of variance you see is similar to the reasons outlined in the betting format section.

If you are a really tight player you are not going to put yourself in as many marginal situations or put a ton of money in the pot when you aren't for sure ahead of your opponent. Think of this kind of like "fixed limit" poker. Very little money is being invested on your part which results in fewer and much smaller swings.

On the other hand, if you are loose and aggressive, you are going to be in marginal situations more frequently where you aren't such a huge favorite. This is kind of like the "no limit" format. You'll spend more, and as a result, see more swings.

Summary of Variance in Poker

Having an understanding of variance in poker is extremely important. Often times, players will confuse playing great/poorly with running great/poorly. This can affect your confidence for better or for worse. However, if you know you are playing well but the cards aren't going your way, you can chalk up your losses to simply running bad, or vice versa, and move on.

Also, once you realize that variance is more about the short-term, you will then also realize that the best way to get past stints of variance is to play more. Putting more volume in will get you past the variance and on your way to your well-deserved long-term results.