Learn about variance in poker & how to calculate it

If you want to be successful at poker, it’s important to take the long view. In this section we explain why, covering topics like:

• Luck vs skill
• Variance and why it matters
• The wrong end of variance
• Making variance work for you

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.

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.

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.

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.

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.

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

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.

Let's say you play five sessions of no-limit Hold'em and your winnings are:

Your average win here is 3 € per session (10 - 6 + 14 - 12 + 9) / 5 = 3).

To work out the variance, note how far each session is away from that average:

Then square these values, add them together and divide by the number of sessions (five), then find the square root of the result. In our example it's 9.9 €.