Saturday, 22nd September, 2018

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# Why is sample size important?

Poker is a game of skill with an element of luck. This element of luck is such a big influence on the results of a poker game that we must use statistics to estimate its influence. Three statistical terms that are found in every introduction to statistics book are standard deviation, variance, and sample size.

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The standard deviation is also known as the amount of luck involved in any coinflip. Each type of poker has a different standard deviation. In games with a higher standard deviation, like no limit hold ‘em, bad players get lucky and win more often. In games with a lower standard deviation, the better players are rewarded slowly and the poor players leak money without ever taking home a big win.

This works both ways, though. Games with a lower standard deviation don’t have the potential for large wins. You will consistently take home about the same amount, but in games with high standard deviations, you can potentially rake in huge scores. Some poker games with the lowest standard deviation are seven card stud and limit hold’em. Some poker games with the highest standard deviation are Omaha and >tournaments.

Variance is defined statistically simply as the square of the standard deviation, however, when people talk about variance, they are really talking about the swings that poker players undergo. Players often blame variance for running bad but forget to give it credit when they run good.

Sample size is the number of hands that you have played at a particular game and stake. Since poker does involve a lot of luck, the only way to be confident when estimating how much you win or lose at a particular game is by having a very large sample size. A good sample size is usually over ten thousand hands of poker, which is often fifty or a hundred hours. Only by reaching these sample sizes can one be confident that their win rate is accurate.

It’s when you get this large amount of data that you can start to pick up on things within your game that you need to work on. Maybe you bluff too much, maybe you chase draws harder than you should or maybe you really are just that darn good and you should go to the World Series of Poker as soon as possible. You just can’t know until you have the large sample size to properly judge your play.

Poker can be a very, very cruel game where every river card goes against you or it can be the greatest game on earth where every pocket pair hits a set and every flush gets made on the flop. That doesn’t make you a good or bad poker player, even though it can often feel that way. The sample size is the key to everything and when you analyze a large sample of 10,000 or more hands, only then can you truly know your skill level.

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