< Understanding Poker Variance


Understanding Poker Variance


Bodog Poker Strategy: Understanding Poker Variance

When they say your results may vary, they aren’t kidding. Every game has some element of luck to it; footballs take crazy bounces, penalty kicks in soccer are essentially coin flips – and with poker, you have to play the hand that’s dealt to you. Maybe it will be pocket Aces this time. Maybe it’ll be Seven-Deuce offsuit. Who knows?


You might not be able to control which cards come off the deck, but you can at least manage your expectations and your online poker strategy by understanding the concept of poker variance. This is an incredibly important concept to nail down if you want to get the most enjoyment and profit out of your online poker sessions at Bodog. We’ll show you what poker variance is all about, and we’ll show you how to deal with the slings and arrows that come with it.


What Is Variance?What Is Variance?

The textbook definitions of variance talk about the difference between things, as well as the degree of difference. But let’s take a moment to look at variance like they do in math class. In this world, variance can be expressed using this formula:


σ² = EV[(x – μ)²]


That’s a bit of a mouthful, but it makes sense when you break down this formula into its component parts. The character on the left side of the equals sign is the lowercase Greek letter sigma, which is squared in this case. By itself, σ is used to represent the standard deviation in a set of data values. This is another very important concept in both math and poker. Think of the IQ bell curve; an average person has an IQ of 100, and more people have this IQ than any other. Every 15 points higher or lower than 100 represents a single standard deviation from the average. About 68% of people have an IQ within one standard deviation of the mean, or between 85 and 115. About 96% of people fall between 70 and 130 on the IQ scale – that’s two standard deviations.


As you move farther and farther away from the mean, you find fewer and fewer people who fit on the curve. Only 4% of people have an IQ either between 55-70 or 130-145, leaving just 0.2% of the population who are more than three standard deviations away from average (below 55 or above 145). This is a lot like how your poker sessions will look over time. If you’re a break-even player overall, you’ll come out slightly ahead or slightly behind in most of your sessions. Sometimes, you’ll win or lose a few buy-ins, and every once in a while, you’ll have an epic session where you either “run like God” or punt off a significant portion of your bankroll.


When you take the square of σ, you get the variance that’s contained within your set of data values. Which brings us to the second half of our magic formula. The big letters EV represent the Expected Value of a random variable x, and the other Greek letter on the right is a lowercase mu, which measures how far from the mean of x you are deviating. The less deviation there is, the closer μ comes to equalling x, and the closer your variance gets to zero.


That last sentence is the big takeaway here. You don’t have to do the actual math (there are calculators for that, which we’ll discuss in a moment), but as long as you get the general idea of how variance is related to deviation, you can start tailoring your online poker strategy to control that variance.


How Does Variance Apply to Poker?How Does Variance Apply to Poker?

Anytime you make an investment that carries some risk, you should consider the variance that comes along with it. There are low-risk investments like index funds, which also carry a low rate of return. And there are high-risk investments like putting your entire bankroll on 20 Black at the roulette wheel. You’re going to get soaked more often than not with these high-risk plays, but when your ship comes in, you’ll be rolling in dough.


When you boil it down, poker is a series of financial investments. Every play you make at the poker table will include a certain amount of variance. Making tight folds with your marginal hands will lower your variance by not further exposing you to the range of results you’d encounter by continuing. Running high-risk bluffs with complete air will do the exact opposite.


The amount of variance in your poker game will depend on a number of factors beyond how risky your poker playing style is. If your game uses the No-Limit poker betting structure, as most do, you have the opportunity to risk your entire stack when it’s your turn. Pot-Limit games have less variance, since you can only bet or raise the amount that’s in the pot. Fixed-Limit games aren’t variance-free, but they’re about as close as you’ll get in poker, since the largest bets available (the big bets) are only twice the size of the big blind – and you can only make them on the turn and river.


Then there’s the poker game itself. If you’re among the thousands of people playing Texas Hold’em at Bodog Poker, your game will naturally have less variance than Omaha poker. That’s because there’s a lot more post-flop play in Omaha poker; with four hole cards instead of two, you have many more ways to connect with the board, and more incentive to continue rather than fold pre-flop. This means bigger pots and more risk, even with the poker Pot-Limit rules in effect.


That all changes when you’re playing Omaha Hi/Lo poker. This is a split-pot poker game, where half the pot goes to the best High hand, and the other half goes to the “best” Low hand, provided there is one. And that’s a very common result in Omaha Hi/Lo poker. Because so many pots get split halfway, there’s less chance of winning or losing a large amount of money during any one poker hand, or any one session.


Finally, we have to consider whether you’re playing a poker cash game or a tournament. Poker cash games generally have less variance; in a poker tournament, the prize pool is split among the top survivors, and on average, you can expect to bust before the money bubble about 80-85% of the time. This invites a giant boatload of deviation when it comes to your results – as we will see shortly.


How to Use Variance CalculatorsHow to Use Variance Calculators

The easiest way for poker players to understand the ramifications of poker variance is to use a poker variance calculator. These are very useful tools to pick up when you download poker software, or you can use free Web-based programs if you prefer. To figure out the poker variance over time playing in a cash game, you simply plug in your expected win rate (in big blinds per 100 hands), the number of hands in your sample, and the standard deviation. It’s okay if you don’t know the exact values for these; just play around with the numbers and see what comes out the other side.


What comes out will be a graph that shows you all the different results from a series of simulations, played out over the number of hands given. Again, most of the results will fall in the middle of the graph, with some very lucky players and some very unlucky players at the two extremes. The calculator will also show you the probability of suffering a loss at the end of your sample, and what your minimum poker bankroll should be if you want a risk of ruin that’s less than a certain percentage – something around 2% or less is recommended for professional poker players.


There are poker variance calculators for tournaments, too, and the variance here is even more sobering. Plug in the number of poker tournaments in your sample, the size of the field, the buy-in and entry fee, how many players get paid, and your expected Return On Investment (ROI). Then let the calculator crunch the numbers, and you’ll get another graph showing you the different results. As you’ll see, even players who have a decent ROI (say, 20% or more) in any one tournament will often finish in the red at the end of the year.


How to Manage Variance in Poker

So how can you tame these poker variance monsters and lower your risk of ruin? Making low-variance choices is your most direct route. You can choose to play a tighter poker style, folding those marginal hands when they arise. You can play more Fixed-Limit poker, and more Omaha Hi/Lo poker. And you can lean more towards poker cash games than tournaments; when you do play a tourney, you can focus on smaller-field events, especially Sit-and-Gos.


Beyond these measures, you can lessen the impact of poker variance by making sure your bankroll is big enough to endure those giant swings in fortune. As the investment gurus say, never put all your eggs in one basket; play at stakes you can afford, especially when you’re playing a high-variance game like Pot-Limit Omaha poker. Be even more stingy with your bankroll when you’re playing a new game, or when you’re playing against tough competition, where your edge at the table will be less than it is at your usual game.


In the end, there’s always going to be some risk involved when you play poker, and you can’t run away from every single high-variance spot if you want to play the game well. But now that you know a little more about what poker variance is, you can manage it to some degree, while also managing your own expectations. Not only will this help protect your poker bankroll, it will keep you from tilting when poker variance does strike – and it will. Remember this the next time you’re running super-hot or ice-cold at the poker tables.