Variance – Why variance in poker is a good thing

Variance

Variance, in terms of poker results, is how much the results differ from expected results if the same plays were done over a sufficiently large sample size.

Variance can be positive (in your favor), or negative.

An example of variance

Let us imagine you got 10,000 people to toss a fair coin 10 times each, and note down whether the coin came down heads or tails. You would have 100,000 results, and the combined results will likely be extremely close to 50% heads and 50% tails. However, if you looked at the data of each individual (each of which only made 10 tosses), whilst the most popular outcome in the results would be 50% tails and 50% heads, all sorts of other results will be found amongst the results (e.g. 20% heads/80% tails, or 100% heads/0% tails etc). In the massive combined sample, the effects of variance are so low as to have to no real effect. In the tiny individual samples, variance will cause all sorts of results.

Sample size

In the above example, you can see how the effects of variance can be massive in small sample sizes. It is important that when you have a small sample size of results you don’t get carried away. This means if you are winning a lot of money per hour in cash game poker, but this is not over a sufficient sample size you are not necessarily a winning player. Just because you are losing over a insufficient sample size does not mean you are playing incorrectly. Players often underestimate exactly how much of a sample size is needed, so that variance has little effect – this is especially true of live part time players who may be putting in a lot of their spare time into poker, but at 25-35 hands/hour, even over a year or two playing part time that’s not enough of a sample size to know if you are truly a winning player.

Minimizing the effects of (negative) variance

  • Managing your bankroll correctly
    You want to have a sufficient bankroll for the stakes you are playing, so as to minimize the chances of going broke due to negative variance.
  • Putting in sufficient volume
    The larger the sample size, the less the effects of any variance (including negative). You increase your poker sample size, by playing more hands – this can be by playing longer, and/or playing more tables simultaneously (the latter is only possible online).

Control volatility (when appropriate)

Variance is built into the rules of poker, and is not something you can decide to control during any individual hand. However, you can control your own volatility. The more the amount of chips you put on the line, and the less likely you are to win, the more volatile your play. For example regularly putting in a lot of chips in race (50%-50%) situations, is more volatile than only putting in a lot of chips in favorable situations (e.g. 65%-35% to you). Keeping pots small would be even less volatile.

Generally in a cash game you are not looking at controlling volatility. You should always be looking to maximizing your chip EV. In a tournament you will certainly be looking to control your volatility, when your tournament incentives dictate that you should. At UnfairPoker.com, we have a full article on volatility incentives in tournaments.

Variance keeps poker profitable for good players

Variance in poker is what makes the game profitable for good players. If there was less variance, results would better reflect the decisions the players make. Changes to the rules could reduce variance (e.g. if every time you are all in, instead of one player normally winning the whole pot and the other nothing, you each shared the pot according to your equity at the time of the all-in). However, if you are thinking that’s a great idea, we urge you to think again.

Reducing variance means the best players would defeat weaker players more often. Players would get better instant feedback on their play, in terms of whether they won or lost money. The weaker players would thus quit the game faster, and the players willing to play you for money will be more likely to be those of similar of better ability.