embrace variance

Why You Must Embrace Variance to Succeed in Poker

Nothing invokes larger emotional response to poker players than the word variance.

Defined simply as the expected fluctuation of the average result, variance is meant to quantify the uncertainty around a typical outcome generated by the luck of the draw.

Stochastic events (such as expected amount of money won, number of times making the nuts per session, or even life expectancies and frequencies of car accident) are all susceptible to variance.

In other words, there will be an inevitable difference between the luckiest and the unluckiest of us, even if all else parameters were to remain equal. When doing the exact same thing, some of us will have better/worse results than others simply due to matters of chance beyond our control.

On the one hand, variance is every poker player’s biggest nightmare. Not unlike Murphy’s Law, everything that can go wrong WILL eventually go wrong and in the worst possible way. As a result we should be properly prepared for it!

(Ryan Fee made an excellent case of that in this article.)

Ironically, variance also may be the single greatest gift that poker has to offer. Without it, the thrill of being able to out-luck even the best of the game would dissipate and poker would “degenerate” to a game like chess, where there is absolutely no money to be made, unless one’s skill level is at the top 0.01% or so.

(For anyone interested, I wrote more extensively about this topic here).

Be careful what you wish for

Given that variance is so terrifying, it is tempting to wish it gone or at least find a way to circumvent it.

I would argue that not only this is impossible, but also undesirable. Artistically speaking, variance is the equivalent of having someone like Cerberus as a pet. For those unfamiliar with Greek mythology, I am talking about the terrifying three headed canine that supposedly guarded the underworld.

Interestingly, the portrayal of this fictional beast was purposefully dualistic, featuring attributes of polar opposite character. On the one hand, it was imagined as a dog and thus a loyal and reliable friend. On the other hand, the additional “mutation” of the extra heads was added as a representation of its dangerous and chaotic nature. This meant that nobody – not even its own masters – could ever truly tame it.

However, even if they could, that would not be a wise choice. Cerberus was horrifying for a reason: No souls were to escape the underworld. A petrifying presence such as his is exactly the type of quality one would expect from the guardian of the land of the dead.

This is directly analogous to how the “untamable” variance is the gatekeeper of profitability in poker. Without it, there would be no money to be made.

So what can we do about it?

Step 1: Acceptance

For starters, it should go without saying that we really have to come to terms with the beastly nature of variance.

This may sound obvious, but the vast majority of us are yet to accept the reality that is luck. If we did, we would never complain. Ever! Swings are part of the job description. We signed up for it. Poker is not fair, and the law of large numbers will not bail everyone out exactly the same way.

This is something surprisingly misunderstood across all levels of competency, including successful poker players. In fact, as a rule of thumb, weaker players tend to overestimate the variance/luck factor while better players oftentimes underestimate it.

In reality, there is not enough luck to save any bad player in the long run but more than enough to hurt any good player in the short one. This is not an excuse for avoiding hard work. Quite the opposite! It is just another reminder of our frailty.

We can do everything we can to avoid a car accident but sometimes car accidents do not avoid us! Regardless, practicing safe driving helps. Similarly, persistent poker study and self improvement are among the most effective and long-lasting tools to deal with the ups and downs of the game.

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This brings us to the second point.

Step 2: Perseverance

We may not be able to eliminate variance but we can certainly change how variance is felt. We can do this in two different ways:

In the first case (win-rate increase), variance remains the same but it is felt less. This is because worst-case scenario it just eats up some of our profitability, while best-case scenario it boosts our bottom line further. Either why it is very unlikely it will drag us down to the red.

In the second case (sample size increase) it is actually reduced, but not locally, globally. What this means is that we will experience the same pesky variance on a day to day basis, but in the grand scheme of things – like our long term graph – it will be increasingly harder and harder to spot.

This is essentially what the law of large numbers predicts. The longer we play the more predictable our overall results will be. As good players, the best thing we can do is keep going!

Step 3: Leverage

Another option is to take advantage of the fundamental asymmetries generated by the inevitable swings of the game and see if we can position ourselves in a way that could maximally exploit the benefits of positive variance.

For example, a part-time but winning player may consider the possibility of taking regular but limited shots at tournaments with top-heavy payouts. This may be generally less profitable than say a cash game of the same stakes (at least in terms of expected average returns) but the upside may be worth it, since a big score could give a winning intermediate player access to stakes that they are otherwise prohibitive for their bankroll.

This is essentially turning variance on its head and making it work for us! Incidentally, the above suggestion may not be suitable for a professional player who correctly values their hourly rate more than occasional big scores. This is simply because in the latter case they play long enough to make large payouts irrelevant to their bottom line.

Still, it may be worth occasionally exposing oneself to a high-payoff streak of good luck in an exchange for a small sacrifice in profitability, especially if one knows how to put the extra working capital to good use. (An assumption like this last one is essential in justifying the sacrifice in value. Without it, this whole strategy degrades to a greedy suboptimal gamble).

Two sides of the same coin

To summarize: Like with everything worthwhile, variance is as much of a blessing as it is a curse.

The trick is to learn how to embrace the curse while taking maximal advantage of the blessing. I do not pretend to claim this is easy. However, as always, having a proper theoretical “compass” to guide us seems like the natural first step.

If you’re interested in another article like this, read You Should Feel Pain While Playing Poker – Here’s Why.

Thanks for reading.

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About the Author
Konstantinos "Duncan" Palamourdas

Konstantinos "Duncan" Palamourdas

Duncan is a math professor from UCLA who specializes in the mathematics of poker, as well as in poker education. He currently teaches poker classes at UCLA extension that always fill up early and have long waitlists. In his book Why Alex Beats Bobbie At Poker, he uses simple language to scientifically explain how and why money flows from poker amateurs to professionals. Preorder the book here!

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