In this article I am going to talk about the basics of variance in poker and how it affects your game.
Ita€™s quite possibly the least technical definition for a term I have ever written, but the a€?ups and downsa€? of poker when it comes to winning and losing money sums it up rather well. Variance is the difference between how much money you expect to win on average over the long run and the results you are seeing in the short term. Leta€™s say that you are playing heads up against a total maniac that moves all-in on every hand.
However, you actually end up losing all 5 all-ins against your opponenta€™s 5 random hands.
On average you expected to win 4 out of these 5 all-ins, but thanks to variance you ended up winning 0 out of 5. As you can see from this graph the rate at which this player wins money is far from linear. Over a long enough period of time his actual results will meet up with his expected results, but in the short term the amount that he wins or loses in the hands of our good friend variance. As we know there is an element of skill involved in poker, but there is also a lot of luck.
There are definitely a lot more factors that can affect the variance that you come up against in your poker career, but these are the most obvious ones and the ones that will have the greatest influence on the size of your a€?ups and downsa€?. To get a really good idea of how much your winnings can vary over a set number of hands, try using this poker variance simulator. Just enter your winrate and standard deviation (which can be found in PokerTracker or Holdem Manager) and see how differently the outcomes can be. You may be surprised at the size of the possible swings and just how different your results can be over large sample sizes. More information on standard deviation and variance can be found in the Holdem Manager guide video starting at 6:16.
1) Thanks to variance, you can never truly rely on your short-term results as an indication of how well you are currently playing. You have to trust that you are making good plays and feel genuinely comfortable about how you are playing, regardless of what current results attempt to indicate.

3) On the other side of the coin, the fact that players (specifically bad ones) can win money even when they are playing terribly is actually a good thing. For further reading, you may find the articles on expected value and Sklansky bucks interesting too. When discussing the sample mean, we found that the sample mean for diastolic blood pressure was 71.3. The deviations from the mean reflect how far each individual's diastolic blood pressure is from the mean diastolic blood pressure. Here's what's happening here: first, we're finding out how much each individual number deviates from the mean. To get the standard deviation of this data set, all we need to do is take the square root of 2.17. However, this is largely going to be a non-mathsy article about variance, which Ia€™m sure will be very welcomed by a large number of you reading this.
So for example, if according to your win rate you expect to win $500 in a month on average but end up losing $1,000 instead, this is attributed to variance.
Furthermore, by a pure stroke of luck and through the magic of me being able to make examples up, you are dealt pocket aces 5 times in a row.
Therefore we expect to win roughly 4 out of these 5 all-ins, although we would ideally like to win them all.
It was amazingly unlikely (0.007% unlikely), but the fact is that it is possible (1 in 1,410,192 possible) and it did happen. As you can see, variance is the difference between the expected long term results and actual short term results, in this case it is 4 buy-ins worth of variance. If we plot this expected winrate on the graph, we get to see how much variance is taking place compared to what this player expects to be winning in a perfect world.
We have no control over the hands that we are dealt or the cards that are dealt on the board, so this uncertainty or a€?lucka€? is the cause of variance over the short term. Regardless of how good you are, those 5, 10 and even 20+ buy in downswings will hit us at various points in our poker careers. If you play a very loose-aggressive style of play then you will be involved in a lot more pots and will be consequently risking more money than your average tight player.

No limit has greater variance than limit poker, where the amount of money that players can put in to the pot is much smaller in relation to the blinds in limit games than it is in no limit games.
Large MTTs will have much more variance than SNGs because you expect to win far less often.
You might be playing out-of-your-skin poker but still lose money, which makes it frustratingly difficult to analyse what you might be doing right and what you might be doing wrong.
Confidence in your ability at the poker table is a very important quality to posses during a downswing. Sometimes it sends us on ridiculously good upswings, sometimes it sends on horrendously frustrating downswings.
The table below shows each of the observed values along with its respective deviation from the sample mean. We take the sum of all deviations and divide by the total number of scores minus 1 to get a variance of 2.17. However, when you do win an MTT you receive sudden large payouts, which obviously results in higher levels of variance. Playing well when youa€™re winning is easy; playing well when youa€™re losing is a different kettle of fish. Be thankful that bad beats exist so that these bad players can slowly but surely hand their money to you. Either way, at the end of the day you have to accept the fact that variance plays a big part in every poker playera€™s game. If you expect variance to kick the shit out of you once in a while, it will be much easier for you to deal with it.

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