Understanding Poker Variance & the Long Run

Any person pursuing poker as a career, or recreationally will have at least come across the words poker variance. To the novice, it is simple to understand that when playing poker sometimes you win, and sometimes you lose. To turn a profit from our poker endeavours, we should aim to win more frequently than we lose. Variance plays a part in all of these factors and in turn how much we profit from poker. Within this article, I will outline what is meant by poker variance, why it is so important and how it can impact you as a player.

Poker Variance

Variance can be defined mathematically as ‘the average of the squared differences from the mean.’ Although this sounds technical, to us mere mortals, poker terminology can better explain the concept of variance in poker. Let us consider the scenario where we have a 20% ROI (return on investment) in the tournaments we play. In each tournament we do not make exactly a 20% profit, sometimes we make much more than 20% and other times we make far less than 20%. Although on average our result is 20% ROI, we do not consistently have this result. Thus, our results carry some variance to them.

Variance: Why is it so important?

When playing a game of chance, it is impossible to avoid variance regardless of whether or not you are a professional or recreational. The difference is that professionals have dealt with general and poker variance for a much longer period of time and become accustomed to it. However, there is a significant gap that every professional must take when transitioning from a recreational player. It is not common to hear of poker success stories from professionals whereby they ran badly from the outset managed to grind out of a hole to become a big winner. It is, however, common to hear of people running very well at the beginning of their career and this driving them to love and become good at the game.

The frequency at which professionals use ‘mental game’ coaches and suffer mental health problems underlines the impact variance has upon player’s lives. Having an uncertain income from day to day creates stress. Although it is great when the going is easy, it isn’t always that way. It is the ability to deal with variance and understand its role that separates the good from the great. Every professional player will have dealt with a ‘downswing’ at some point in their career. Even recreational players will experience variance, we’ve all had our pocket Aces cracked as an 80% favourite!.

Variance: Illustrated

Online, there are tools known as variance calculators, which can be used by both cash game and tournament players alike. They take what is believed to be a player’s true win rate or ROI and over a specified sample show the worst and best outcomes feasible within confidence intervals.

I have used a tournament variance calculator from to produce the below image. We have assumed a 20% ROI (a substantial level of profit) and a sample size of 10000 tournaments with an average buy-in of $10.

Tournament Poker Variance

The x-axis represents tournaments played, while the y-axis represents profits made. As you can see, the difference in potential profit made resulting from variance is astounding. In one run the same player could lose as much as $5,000 or gain as much as $60,000 while having the same theoretic profitability. The EV of a player with a 20% ROI over 10,000 games with a buy-in of $10 is $20,000. This clearly illustrates the impact of ‘luck’ or variance.

Handling Variance

Having explained both what variance is and its impact on profitability, we must now consider the effect it can have on a player. The first thing to note is that variance does not only affect our bank balance! Variance can have a direct impact both on our play on the felt and our lives off the felt:

At the table:

  • Variance causes stress and hence can manifest itself as ‘tilt’. Tilt is where a player ‘adopts a less than optimal strategy because of mental or emotional frustration’. There are many forms of tilt, but one of the most common is that of entitlement tilt. Entitlement tilt occurs because a player feels entitled to winning more than they are currently. An obvious example of which is if you lose AK vs. AQ all-in preflop in a cash game and your opponent collects the pot.
  • Variance can directly impact our decision making through confirmation bias. This form of bias occurs when we make a decision based upon some belief. If the result of our action reinforces that idea, we can have confirmation bias. This is a dangerous tool in poker and can result in players making poor decisions. A prime example is if you decide to bluff-catch a player who bets the river because you believe he has a busted draw. You call and win the pot because he does, in fact, have a busted draw. Experienced players realise that this does not necessarily make the call a good one. It could simply be variance that you ran into one of his only bluffs and versus his entire range the call was a losing play.

Off the table:

  • As aforementioned, stress is a product of variance. Without needing to say more, we all know how much stress can impact our lives. Managing stress is one of the many challenging tasks of being a poker player and each player, has a different way that they handle it best. Downswings, as a result of variance, are simply part of the game and should be embraced. One of the most important aspects of poker is the ability to switch off from the game when not playing. Just like any job being able to de-stress after a long day of work is critical to being able to perform at your best the next day!

Poker Variance Conclusion

Poker Variance is an aspect of poker that no player can ever escape – no matter how hard they try! Dealing with variance is paramount to having a successful career, and it should be embraced with open arms. Those who treat downswings as a way to consolidate their knowledge and sharpen their skills will ultimately become better players. One of the worst ways to deal with variance is to lose confidence in your game. The opposite is also true; it is important to recognise when you’re running well and not become overconfident. Overconfidence can lead players to play stakes they cannot afford or are not skilled enough to play, and this can be financially disastrous. I wish you the best of luck in your poker endeavours and may variance be in your favour!

Patrick Sekinger is from the UK and is an avid poker enthusiast, currently playing both live and online as a professional poker player. Patrick plays all formats of NLHE, however specialises in 100bb cash games and you will find him regularly playing in the small stakes games on Pokerstars.

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