Variance is Overrated
When you run bad in poker over long stretches the common cliche expression heard from poker players is “it’s just due to variance”. Their belief is that over the long haul or over a very large sample size their overall net results will eventually mirror the expected statistical probability of various situations and mask out those anomolies of running good or bad. In other words, there does not or should not exist the concept of being lucky or cursed, because everything can be attributed to variance in the game of poker.
In Jared Tendler’s book “The Mental Game of Poker” it defines a player to be a “mental game fish” if one believes that factors outside of one’s control influences the outcome and if one tries to make adjustments to their game when the actual results deviate from expected probabilities. This is a very broad summary of the book’s concept and you will have to read his book for more details. It can be purchased on Amazon:
The Mental Game of Poker: Proven Strategies For Improving Tilt Control, Confidence, Motivation, Coping with Variance, and More
The point that I would like to emphasize that is typically glossed over or neglected is that statistical probabilities are only guidelines for expectations over large sample sizes that never changes. But scenarios that deviate significantly from expectations, known as outliers, can and often due occur not just in poker but in all areas of life. What I personally find absurd is people who quickly point out that running bad in poker can only be attributed to variance and that luck has no involvement in such determination.
Let us run through a common example of the coin toss. The expected probability of a coin landing on either heads or tails is 50%. That probability never changes regardless if you toss the coin once, ten times, or ten million times. Intuitively we can observe that with small sample sizes or during short stretches there could be instances where it could land more times on one side of the coin and exceed the expected 50% probability by a significant margin skewing the overall net results. But over the long term and after many coin tosses one is correct in assuming the results should conform back to its expected 50% probability.
But let us look at the situation of poker pro Fred and the wannabe Joe. They both flip coins for one hundred tosses with Fred betting on heads and Joe betting on tails each time. Somehow the coin lands on heads one hundred consecutive times despite the fact that the expected probability of 50% should have delivered results closer to an even split of heads and tails. As expected due to human psychology, Joe believes he has bad luck or just unlucky to run so bad in a freak anomoly. Jared’s book would label Joe for such a thought process as a “mental game fish”. But is that fair and if so what could be said about this coin toss outlier having occurred and how should it be described or attributed to?
The bottom line when you investigate and dig deeper is that it has something more to do than with merely variance. Fred and Joe could double the betting stakes and compete over a larger one thousand coin tosses. This still does not dismiss the possibility that the coin could still land on heads one thousand consecutive times despite having just landed on it one hundred times already. Why did Fred have the fortune of receiving such a favourable but freakish outcome at the expense of poor Joe. There can be no other logical explanation other than Fred was simply lucky enough to be on such a positive deviation of expectations.
This phenomenon is also apparent when you buy a lottery ticket and select six numers. It is a random draw and any six numbers have equal chance of being selected. Yet why do most folks avoid picking the six numbers 1 – 2 – 3 – 4 -5 -6 and refuse to believe that such a situation would rarely occur? Or why would gamblers pay attention to recent number trends at the roulette table when the ball landing on any number is of the same probability? Yet many people do vary their selection to either play high range or low range or even or odd numbers depending on the trend.
I believe such experiences is how the phrase “gambler’s luck” has been derived from. It can be attributed to some folks and not others as observed in our hypothetical example of Fred and Joe. Variance and the expectation that everything eventually reverts back to the norm is thus a myth, because that is irrelevent if it does not occur within one’s lifetime.