# Unlucky or standard? Understanding variance in poker

Are you plain unlucky, or just experiencing standard variance? Alex Scott reveals the truth about upswings and downswings

There are people in the poker community who consider the word ‘gambling’ unsavoury or distasteful. They prefer to think of poker as a ‘mind sport’, and distinguish our great game from inferior, pure chance games in an attempt to raise its acceptability in the eyes of the public.

Making poker more acceptable is an admirable goal, but it’s impossible to ignore the element of chance in the game. The ups and downs that every player experiences are commonly referred to as ‘variance’, which is a mathematical term used to measure the deviation present in a group of results, such as wins and losses in poker. When you hear somebody say that PLO is a ‘high variance’ game, they mean that the wins and losses tend to be large compared to other games.

Variance affects different players in different ways. Take a beginner, for example, who plays lots of hands and calls a lot of bets. This is a high variance style, which will win big when the beginner catches cards or plays against opponents who bluff too much. At the opposite end of the scale, take a professional tourney player. It’s difficult to consistently cash in tournaments with thousands of players and make a profit. Most of the time, the professional will bust out of the tournament early on, perhaps through sheer bad luck. But when the professional does cash, often it’s for a very large amount of money, which cancels out all the previous losses and puts them in the black for the year. Being a tournament pro is a high variance profession.

You can’t escape variance in poker and you need to prepare for it both mentally and financially.

#### The long run

One of the most common fallacies you hear in poker is the idea that luck ‘evens out over time’. It doesn’t. Luck has no memory, and it doesn’t care that you just lost with Aces against Kings twice in a row. There is no guarantee that you will win with Aces against Kings twice in a row in future, evening out your losses.

What does happen is that over a large sample, your individual wins and losses tend to become insignificant compared to the big picture. When you average out all of your results, you’ll tend to find that your Aces won about 81% of the time that they were all-in against a smaller pair. The more hands you play, the more likely it is that your average result for a situation will be close to the mathematical probability.

In poker, your ‘sample size’ is the number of hands you have played in your career. Beginners tend to underestimate how many hands are required to get into the long run. Take a moment and think to yourself – how many hands do I need to play before I know for sure whether I’m a winner or a loser?

For no-limit hold’em ring games, it’s generally accepted that you need at least 10,000 hands at the same limit under your belt before you can be confident that you’re beating the game, and probably more like 100,000 before you can be absolutely certain. If you’re playing a single table, it might take 125 hours or more to play this many hands! However, if you’ve played fewer hands, variance plays too significant a part in determining the results. Similarly, if you’re playing a higher variance game, such as PLO, you’re going to need more hands before you can be sure that you’re a long-term winner.

#### Tourneys

For tournaments it’s not quite as simple, because there are so many different varieties of tournament – regular, turbo, hyper-turbo and so on. A good way to approach the problem is to look at the average number of hands that you play in a particular tournament type, and then divide 10,000 by that number. So, if in a regular sit-and-go you typically play 80 hands, you’ll need to play at least 125 of them before you know whether you’re a long-term winner or not. If you usually play 20 hands in a hyper-turbo SNG, you’ll need to play 500 of them.

As you can see, the fewer hands are involved in determining the outcome, the more variance is involved. It would be very easy for a complete beginner to win a 20-hand hyper-turbo SNG, for example. However, a 1,000-hand cash game session would be a completely different proposition, and it’s much more likely that a skilful player would pocket the money.

People often ask whether there is more variance in ring games or tournaments, but that’s like asking which is larger, a circle or a square. The important thing is how many hands are played to determine the outcome, and how much money is risked. For example, let’s say you play 100 hands of a no-limit cash game, and wager (on average) \$1 each hand. The variance would be similar to playing a \$100 tournament that lasted for the same 100 hands – in both cases, you’ve wagered the same amount of money over the same number of hands. It’s a simplified example, but an eye-opening one.

Variance goes both ways. If you’re playing a high variance game or style, you’re going to have big wins and big losses. Many players find the big swings difficult to deal with, so they seek ways to reduce variance and simply grind out a consistent profit over time. The simplest way to do this is to play more hands, which can mean playing in faster games, multi-tabling, or simply playing more hours. But there are also more complex ways to reduce variance, such as changing your playing style.

#### Fighting variance

High variance situations in poker tend to be those where you enter the pot with a hand which is close to even against the opposing hands you’re facing – for example, if you enter the pot with 8-8 against an opponent who has A-K. It therefore stands to reason that by playing a tight style in which you enter the pot only with strong hands you’ll reduce your variance, because you’ll usually be a bigger favourite against the competition. Conversely, by playing a loose style and entering the pot with lots of hands, you’ll be less of a favourite and your variance will increase accordingly.

Some players online have taken this to its logical extreme, playing as many as 24 tables (or more!) of excruciatingly tight poker in order to grind out a living. The downside to this type of play, besides the extreme tedium, is that it doesn’t make as much money per hand as a more balanced, prudent style. Not only does extremely tight play mean giving up on potentially profitable situations, it makes you an easier player to read and exploit.

Depending on how risk-averse you are, giving up a bit of profit to lower your variance might be acceptable to you; but to become a truly great player, you need to embrace variance and simply make the optimal play as often as possible.

#### The luck delusion

Finally, a word of caution: it’s easy to chalk up your wins to skilful play on your part and dismiss your losses as variance. It’s exactly this trap that allows so many losing players to delude themselves that they are in fact winners, or at worst ‘breaking even’. While you shouldn’t get too frustrated with short-term fluctuations, it’s never a bad thing to be critical or to analyse your game. It’s much worse to have a leak and never find it than to waste a bit of time looking for a leak that isn’t there.

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