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Variance is Overrated

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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.

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  • Guest

    Probability of 100 fair coin flips landing 100 times on heads.http://calculator.tutorvista.com/coin-toss-probability-calculator.html

    • Steve

      Yes, it is an unlikely event but the fact is that it is possible, an outlier. What if it happened to you? Most people would label you as lucky (or unlucky) depending on which side of the bet you took and that is the point of my article. Same thing that most folks never win a lottery in their lifetime, yet some individuals have even won it two or three times and there is a (true) saying that the chances of winning just one lottery is worse than being struck by lightning.

      • Alex

        This is interesting purely from an academic point of view, whereas as a poker player with a professional mindset, adequate bankroll and solid tilt-limited game, things should be OK in the long-run. 🙂

        • ohmesohrny

          Variance is overrated for sure, but still a major factor in the outcome of poker. The main issue is how players approach this concept. They use variance as an excuse for playing bad or losing.

          • Ivan Y

            I agree with (players) using “variance as an excuse for playing bad or losing.” I think good players separate themselves from the bad/recreational ones because they take time to identify a solution for a leak in their game.

      • keulniss

        I don’t see what you are trying to point out in your article. You seem to know and define variance correctly but then later say:“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.”This seems to imply to me that you think variance and luck are somehow two different things. They aren’t. Luck is just the lamen’s term for the mathematical concept of variance. Having good luck being the positive side of variance and bad luck being the opposite. Both being short run concepts.I do however get what you mean when people blame their bad runs on “bad luck” or “variance” when in fact they’ve been playing like horse shit and are just oblivious to the fact.

        • Steve T

          “This seems to imply to me that you think variance and luck are somehow two different things. They aren’t. Luck is just the la[y]men’s term for the mathematical concept of variance. Having good luck being the positive side of variance and bad luck being the opposite. Both being short run concepts.”Keulniss, you made some very intriguing and valid comments and it is obvious you are an astute observer who also thinks about things quite deeply.While what you say about luck and variance being intertwined is correct from one interpretation, I am implying that they are also different from another perspective. I should attempt to clarify by what I meant by my quote above. Players who continuously or frequently run bad in poker (and by this I do not mean play bad) and blame it on variance are under the belief that actual results may veer above or under expectations at varying times and that it eventually evens out to go back towards the mean. In other words, they are expecting to run bad at certain intervals to balance out the times they run good. From this interpretation, one would not be unlucky or have anything to do with luck because it is never a smooth straight line to the mean and that is the realistic expectation of variance.But what I imply about luck and variance being different is if a player is frequently residing on one extreme side of expectations AND the correction back towards the mean does not happen in the near future. As in your bankroll gets decimated and you do not survive until it happens, or you grow old and retire or die before it happens, or you become psychologically or emotionally scarred and retire or quit in frustration or disbelief before it happens.Luck or unluckiness from my perspective is thus more connected with variance when a deviation is overextended in both magnitude and duration which is a long run view.This is again a somewhat difficult concept to express in writing or verbally because it deals with intangible matters, such as my other article “The Power of Positive Thinking”. I am not saying that I am right but merely attempting to highlight an important point about luck and variance.

      • keulniss

        Also, as for the the secenario you pointed out:“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?”I haven’t read that book, but first off, Joe would be absolutely correct in thinking he had “bad luck” or was just “unlucky” (or equivalently, was on the shit side of variance). I have no idea what it means to call him a “mental game fish” but I’m going to guess that it is not fair since Joe is correct. What can be said about it occurring? Well, it will happen, with a probability of exactly (1/2)^100. This happened to be one of those times.

  • Shahdad Samimi

    I am currently reading this book. It I quite interesting and I will write my thoughts about it once I have finished it.