• August 1, 2021

Understanding variance

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In statistical terms, variance is used to examine the differences between an individual result and the average for a set of results
Luck vs skill
Poker is almost unique in its blend of luck and skill. If you went 1 on 1 with almost any player in the world and moved all-in, without even looking at your cards, you’d have almost a 40% chance of winning.
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Sounds pretty good, right? Until you realise that if you used that tactic over and over again, you’d end up losing 60% of the time. So, even factoring in the money you’d win, long term you’d almost certainly end up in the red.
It’s all about skill, then? Well, not exactly. You might be the best player in the world, with a hand that’s an 80% odds-on favourite – but there’s still no guarantee you’re going to come out on top.
This is down to a factor called variance, something every poker player needs to understand if they want to get ahead.
Variance and why it matters
Like the angler’s ‘one that got away’, variance has become a bit of a poker in-joke – the excuse when things go pear-shaped. But it has a sound mathematical basis, the idea being that in the real world, results are only predictable in a general way. One-off events tend to vary. It’s as simple as that.
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Take the example of a six-sided dice. If you want to throw a 2, your chances are one in six. But if you throw the dice six times, you might not get a 2 at all. Or you might get three 2s. You might even get six 2s in a row (less likely, but it could happen). That’s variance.
In poker terms, this means that although you’d expect an 80% favourite hand to lose one in five times, in reality, you could lose two, three or even all five times. Should you bet on that hand? Of course you should, because if you played those odds enough, you’d be in the money. Just possibly not today.
Variance and Structure
Some poker games, as well as some betting structures, are prone to have higher variance than others. For instance, a $3/$6 fixed-limit hold’em game will have much less variance than a $1/$2 no-limit hold’em game due almost exclusively to the betting structure. In the $3/$6 limit game, the maximum bet a player can make on the river is $24 (bet-raise-re-raise-cap). In the no-limit game, a player can bet his entire stack at any time, which may be hundreds of dollars. These bet sizes can cause huge swings in variance.
Variance in Poker Tournaments
Despite the allure of fame and glory presented by televised events, no-limit hold’em tournaments are shining examples of the deceptive power of variance. Most professional players (including many famous faces on the tournament circuit) make more of their living through cash games and only enter the most prestigious (and lucrative) tournaments due to the high variance involved. Most major tournament winners are “outliers”, as up to ninety percent of all tournament players walk home empty-handed.
The wrong end of variance
When you’re riding out the statistically rough end of things, you could find yourself losing money game after game, even when you’re getting decent hands and playing like a dream.
For a lot of players, this is too much to take. You lose confidence in your tactics, start playing wildly and, before you know it, it’s not variance that’s the problem – it’s you.
So what are you supposed to do? What all the best poker players do – play strategically, be patient and wait. Because no matter what happens today, tomorrow, next week or even next year, the numbers will work out eventually.
Making variance work for you
Now you know about variance, there are some basic things you can do to build it into your strategy:
Bankroll management. Make sure you’re playing at the right stakes (so you can deal with a potential bad run and still bounce back)
Keep records. Noting down your results over time will help you see a blip for what it is and put things in perspective
Maintain your edge. You know how you should be playing. Keep reading your poker theory, stay calm and trust your methods will pay off
It’s also useful to know how variance affects you personally. For example, textbook players will experience fewer ups and downs than aggressive bluffers. No-limit Hold’em has more variance built into it than limit versions of the game, and so forth.
You can even calculate your own variance if you want to (we’ve included an example below if you want to try it). For a lot of players, it helps them to know everything’s going to plan.
Most importantly, it’s a question of mindset. You need to know that, based on the mathematical laws of the universe (which are never wrong), the more you play, the closer to the predicted odds the results are going to be.
When you take this longer-term view, you’ll see the positive side of variance – that every loss is a stepping stone to a win.
How to Deal with Variance
Shifts in variance can be as unpredictable and dangerous as shifts in the weather: everybody complains about them, but no one can do anything to prevent it. The most important aspect of success in poker lies in treating each session or tournament as a continuation in one long game. Experienced players understand that their success or failure as a player does not lie in the results of a single tournament or a handful of cash-game sessions.
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Steve Carr

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