You may have noticed a word cropping up in poker players’ vocabulary a bit more often lately. People have always talked about luck and bad beats in poker, but now you’re more likely to hear the term ‘variance’ to describe the ups and downs of our beloved game.
Most solid players have an idea of just how good they are..You’d know, for example, how much money you made or lost per hand at a certain level, or per tournament buy-in. That amount would be a kind of batting average – or the ‘norm’ for your level of play. This is also sometimes called your expectation – the amount you can expect to make or lose on average.
The problem with expectation in the short-term though comes when players hit either a good or bad spell of luck that can skew results one way or another. Taking this into account we can then use the highly talked about variance model as a measure of the amount your results deviate from your expectation.
Are you a luck-box?
For instance most people know that Aces versus Kings all-in preflop is about 80/20 in favour of the Aces. That means that if you ran enough trials, the Aces would win 80% of the showdowns on average. Now, imagine you only dealt that same match-up ten times. Obviously, on average the Aces would win eight times and the Kings would win two, but assuming you did hundreds of trials of ten showdowns, how often would it end up being 7-3 to the Aces? How many times would it actually end up 8-2 to the Kings?! In everyday terms, this is what measuring variance attempts to understand.
In order to measure variance properly you need to record your results for a great length of time and probably use a statistics package to get the final figure. Fortunately, you don’t need to get down to the nitty maths to understand the various principles that govern variance.
Bluffer's guide
Misunderstanding variance has probably caused more hardship and pain than anything else in the game. Yet detailed analysis is not necessary as long as you know the factors that affect variance, and select your games accordingly. So, in the absence of reams of data and sophisticated mathematical analysis, what should you know about variance? Here are the main factors to consider…
Edge: The more of an edge you have over your opponents, the less your long-term results will fluctuate. In other words, stick to games you know you can beat. For example, if there are players who will pay you off with their whole stack every time you have a set, the bad times will bite much less than in a game where in order to show a long-run profit, you need to make moves such as value-betting middle pair on the river.
Stack depth: Whether in a cash game or tournament, the relationship between the size of the blinds and the size of your stack will govern how you play your hand. If you are ‘deep’ (i.e. you have a big stack-to-blind ratio), you can wait for a big hand or a very favourable situation before committing a large amount of chips. The shallower you are, the more risks you will have to take.
Blind increases (tournaments): In cash games, you have much more control over how deep you are; not so in tournaments. The lower the stack-to-blind ratio, the more variance. Pay attention to: (a) starting stack; (b) length of levels; (c) blind structure (i.e. how much the blinds increase each level). Faster structures like turbos and super turbos will obviously yield higher variance.
Tournament opponents: You are likely to show greater variance in overall results when playing tournaments with larger fields. For example, if dumb luck accounts for, say, two of the final-table places in tournaments with fields of 1,000+ players, your results will deviate much further from the norm than in those with fields of only 30 players.
Playing more hands: Whenever you play more hands than advised by the ‘old school’ wisdom of waiting for a premium holding, you will attract greater variance in your results. The following factors will tend to increase the number of hands you play, and thus the variance in your results: (a) playing shorter handed; (b) going up the stakes (i.e. reducing your edge); (c) having a looser and more aggressive style. This is not to say you should be a rock, just be aware that the more creative and aggressive your style, the higher your variance is likely to be.
Sample size
Players are forever asking themselves how good they are. Egotistical delusions aside, the best measure of this is results. However, results can be a fickle friend. World class players can crash out of 25 WSOP tournaments in a row while watching complete novices take down major prizes. So how big a sample of hands or tournaments do you need to know that you are a winning player? And how does that inform your bankroll considerations?
The answer depends on the various factors listed above. Playing at a level where you have a big edge, at full-ring tables, and in deep cash games or tournaments with structures that give a generous stack-to-blind ratio, you will need to post a smaller sample of results to know how well you’re doing than if you are multi-tabling a bunch of turbo tournaments against good players.
The bad news is that even in the first scenario – where you stick to low-variance games – the required sample size is larger than you might expect. Your results should start showing defined long-term patterns (good or bad!) within about 500 tournaments or 50,000 hands at cash games. Depending on the aforementioned factors, it takes around two to eight times that amount before the fluctuations settle enough to show a convincing long-term picture. That’s a lot of hands! So in high-variance situations, you could be looking at anything up to 4,000 tournaments before you start posting your results on the forums with pride.
Bankroll and variance
Variance is what informs correct bankroll management. If even solid, profitable players have to wait thousands of hands for the luck factor to even out, it’s a sure bet a healthy bankroll is needed in order to stay afloat.
Indeed, the received wisdom is that you should not buy into a cash game or multi-table tournament for more than 2% of your bankroll. In other words, if you regularly play $20 multi-table tournaments, you should have a bankroll of around $1,000 set aside to cover the up and downs.Many players use different bankroll structures, however. For example, to take ‘shots’ at higher levels, they might set aside 20 times the buy-in at that level, and if they bust that bankroll drop down to the previous level.
Either way, be sure to take into account all the factors that affect variance. Remember, the more variance in the game you play, the bigger the bankroll you’ll need to overcome the swings, and the larger the sample of results you’ll need to know how well you’re doing.