Small Sample Size

Several years ago a discussion about luck and probability broke out at the poker table and being the numbers guy that I am I fell on the side of probability and over time the luck factor evens out. People run good for a while and they run bad for a while but over the long term everyone runs the same and the results conform to the probabilities like the math says they must.

A couple of my friskier opponents who believed in luck, the tooth fairy, Santa Claus, leprechauns, chasing rainbows and Karma among other things were just unwilling to admit that the distribution of the cards is random. I got sucked into the discussion and pretty soon we had our own wager going and we did our own trial. We decided that every hand one Saturday night the three of us would put up $25 each and after the hand was over the person with the best hand took the $75. I was pretty sure I was right and I had some idea how this challenge was going to turn out.

My belief was that each persons stack would swing up and down with the ups being slightly sharper because you would win two bets instead of losing one bet. I really did not know the variance of this seven card exercise. We all agreed to run the experiment for 300 hands as that would be an average night of poker. In my mind I felt that 300 hands would be an adequate sample size to see our stacks show some ups and downs and each of us to remain near zero. Was imagining this sign wave looking graph with some highs and lows but each of us tending back toward zero by the time the three hundred hands were over.

I would learn a lesson about probability and mathematics that night. The variance was far greater than I perceived and I had not done the math prior to getting involved in this 300 hand trial. I expected each of us would win around 100 hands of the 300 dealt. I only won 71 hands out of 300. I won just over 23% when I should have won over 33% and at the $25 per hand stakes I lost $2175.

Yes 300 hands or one night of play in a brick and mortar casino is a very small sample size and luck can play a major factor in the outcome of a game.


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