Poker Variance

It is a proven fact that poker is in fact a game of skill; however, it must not be denied that it is also a game of chance (or luck if you want to look at it that way). The chance factor in poker comes from the randomly shuffled and distributed deck of cards. In poker, variance describes the effect of chance, which can be applied to the short-term and the long-term of your game. The skilled poker player knows that variance can be his worst nemesis, while at the same time, he understands the concept and uses it to his advantage.

In poker, variance is the average of a player’s individual results over a prolonged series of hands or sessions, also the shifts of positive and negative cash flow. A player with high variance will have significant shifts, while a player with low variance will be more likely to produce hand or session results that are closer to his overall average results over time.

Consider that you play 1000 hours of poker over a period of time. During that span, you profited $20,000; therefore, you made $20 per hour. While you may have actually lost $30 one hour or won $50 another and lost some sessions and won some, the closer you came to the $20 per hour mark each hour, the lower your variance is. If your actual hourly intake was nowhere near $20 per hour, your variance was higher. In mathematical language, variance is the square of the standard deviation.

Tight players who seldom take risks may tend to be steady winners, and their play is likely to show low variance. Aggressive players, on the other hand, who take risks more frequently, may win more in the long run, but they show high variance in their play. Thus, if you are a high variance player, you’ll need a fatter bankroll.

Playing tight and by the book is an effective strategy for many players. These types of players play only the strongest hands, especially at the lower-limit levels. This strategy, which is characterized by very little deviation from the overall average result, or low variance, will in fact show consistent results, but at a lower hourly average. However, playing more aggressively on more hands, even the weak ones, while risky and less safe, may produce a greater win average. But this is all relative to the player. What works for one guy may not work for another.

A high variance player will raise on the last betting round on a pure bluff when he believes his opponent is betting on a weak hand. If this works in his favour, the opponent will fold. When things are going well, the bluffer will win more pots than the player who would never take such a risk. However, the high variance player will end up losing many pots, as well, on the same hands that a low variance player wouldn’t have even thought twice about before folding.

Another way of looking at it is to comprehend that you must lose in order to win in the long term. This will help you understand and cope with bad beats. Winning is about application and reapplication of advantages over time and learning to take the good with the bad, as one doesn’t exist without the other. If you expect to win at poker every hour or every session, you will be sadly disappointed. Poker income is not linear; it deviates between lucky and unlucky while you add the skill. If you let bad luck destroy you, it will. The best way to win is to focus on playing at your best level no matter what happens, so that you play good enough poker to win enough to cover your losses.

The Bottom Line
A good poker player must allow time for the element of skill to manifest itself. As long as your bankroll can withstand the natural variance of poker, once you get the right hand, let your chips do the talking. There will undoubtedly be room for debate when it comes to what percentage of the game can be attributed to skill and what percentage to luck. The best way to incorporate the concept of variance into your poker game is to look at in terms of time. Think about the following hypothesis as a rule of thumb until you learn better: chance will take prominence in one hand of poker; skill will begin to affect your game at 100 hands of poker; skill becomes the prominent factor in 1000 hands of poker; the probability of chance affecting your game at 10,000 hands of poker is low; and at 100,000 hands of poker, the likelihood of chance is pretty much absent in your game. If you can focus on the skill and understand poker variance, over time, your game will ultimately improve.