STRATEGY

Standard Deviation in Poker – Tightening Up Your Game

When it comes to playing poker, many people would think that a lot of how you play would be based on instinct and experience. After all, it’s more about reading your opponents and knowing what everyone else is playing, right? Surprisingly, however, there is a lot of math involved in the game, and those who can rake in the big bucks use algorithms and statistics (such as variance and standard deviation) to swing the game in their favor. In fact, online poker winners usually are those who use a computer program to crunch the numbers, not necessarily ones with the best instinct.

One of the most common statistics and numbers involved in poker is the standard deviation. While figuring out this number is somewhat complicated, it can make a big impact on how much you win and what your odds are of improving your win rate. In this article, we aim to help you understand the basics of standard deviation. That way, when confronted with it, you know what you’re seeing as opposed to getting lost in a sea of numbers.

Introduction to Standard Deviation

So what exactly is standard deviation? How can we figure it out and use it to our advantage? Before we can get too far into it, we first need to know what we’re dealing with. Standard deviation is essentially a number that tells us how close together any group of numbers is. There is a complex calculation to determine the standard deviation, but to better understand let’s look at two groups of numbers.

Group 1

3,4,2,5

Group 2

2,8,4,0

In each case, the average (mean) of both groups is 3.5. To calculate the mean you add up all of the numbers, then divide by how many there are. So, in this case, we would do (3+4+2+5) which equals 14, and then divide it by four (four numbers in the set) for an average of 3.5. We do the same for the second set and come up with the same number.

However, as you can see, the second group is much more spread out, which means that although the average is the same, there is more of a variance. Since we cannot tell that based on the average, we need another figure to show us how closely grouped our numbers are. That is where standard deviation would come in.

Looking at the standard deviation, we would instantly be able to tell how spread out or tightly grouped our set of numbers is, which can help us for a variety of reasons. The most important thing to note is how high or low our standard deviation number is.

High and Low Standard Deviation

Because this equation tells us how spread out the numbers in a set are, that means that the higher the standard deviation, the wider the variance. Conversely, the lower the standard deviation, the slimmer the variance. For example, if a set of numbers has a standard deviation of 2.33, compared to another one that has a deviation of 1.33, we know that the lower number indicates a tighter spread.

So how does that help us? Essentially, it will tell us how much our numbers swing from the mean (middle), which can give us the odds of our win rate in poker. It will tell us how tight or loose our game is, as well as how large our win rate could be.

Standard Deviation in Poker and Win Rates

For professional poker players, studying their standard deviation will help them better understand how they play and can help them increase their win rates.

To get data for figuring out your standard deviation, you have to play a lot. The best way to plot your numbers is to know your win rate over 100 hands. Thus, for example, if you play three hundred hands in a given block, you can then start to plot your numbers and figure out a standard deviation.

Let’s say that you win a total of thirty hands out of your first hundred. Then let’s say that you win another forty, then thirty-eight. So based on three hundred hands, you now have three numbers to plug into your calculation. 30, 40, 38.

Looking at those numbers, your average win rate based on these figures is 36. One one side would be the number forty, and on the other side would be the number thirty. For your standard deviation, you would place all of your data on a bell curve, with 36 directly in the center. The reason that we say to put your numbers on a bell curve is that the further you go away from your average, the less likely that you will succeed in getting that win rate. For our example, the odds of you having a win rate of thirty-seven or thirty-five is much greater than having a win rate of fifty.

Standard Deviation

Effects of Standard Deviation

Obviously, the more hands you play and the more data you get over time, your average and your standard deviation will change accordingly. Our example is skewed because the numbers are relatively close together, which is ideal for your win rate. You mostly want your standard deviation to be as small as possible, which means that you have a steady win rate with little fluctuation.

However, if you notice a wider spread in your play (i.e. 10, 37, 22), then your standard deviation will be higher, and it could mean that you have to change your strategy. This is another reason to plot your numbers on a bell curve because you’ll instantly be able to tell how big or small your deviation will be. The fatter the curve, the more variation, and the thinner the curve, the less variance.

There is one other thing to remember about your data as it plots on the curve. Once you have sufficient data to get an accurate average (we suggest at least one thousand hands), you will have a 68% chance of staying right at your average, a 95% chance of being within two standard deviations of your average, and a 99% percent chance of being with three standard deviations from your average. So that means that the tighter your curve, the better chance you have of keeping a steady, optimal win rate.

What Affects Your Standard Deviation?

Assuming that you’re able to track your data and win rates effectively, then you may want to find out how to adjust them. The only thing that can affect your standard deviation, however, is how you play. If you play loosely and like to take risks, then odds are you will be looking at a fat bell curve. However, if you play close to the chest and only bet on premium hands, then your curve might be tighter.

So which is better? A wide and fat curve or a skinny and narrow one? At the end of the day, what really matters is your win rate. If you’re able to hold onto an optimal win rate by playing loose and creating a larger curve, then so be it. Unless you have wildly different numbers that result in a curve that more closely resembles a flat line, then you should be fine.

Difference Between Standard Deviation and Variance

Another common statistic cited by poker players is the variance. We’ve mentioned it here a couple of times, but what exactly does it mean? As with the standard deviation, the variance is a measure to understand how spread out a set of data points is. In fact, you can use both numbers to figure out the variation in your data, but the key difference lies in the numbers themselves. To get the variance, you must add the square of the difference between each number compared to the average.  This will lead to larger numbers overall.

For the most part, the variance is not used because it is dealing in the squares of numbers (a number multiplied by itself), whereas the standard deviation is using the same units as your source data.

For example, the variance of these numbers (10, 22, 32, 18) would be 62.75, while the standard deviation would be 7.92. As you can see, the variance is a much higher number and only tells you the spread. However, the standard deviation tells you how much your win rate could incrementally vary from the average. With those numbers, the average is 20.5. Thus, using the standard deviation, you know that you have a 99% chance of being within three deviations, which means that your win rate would be between -3.26 or +44.25.

Again, this is all somewhat complicated, but looking at your standard variation is much easier to process than looking at your variance. In either case, however, the smaller the number, the tighter your data grouping is.

What is Pokerdope?

To make everything so much easier, there is a website out there called Pokerdope. Instead of trying to crunch your own numbers and do the math yourself, you can enter your data on this site, and it will figure out your variance, as well as tell you what you can expect over so many hands. Overall, this is a fantastic guide to help you understand how your win rate can vary over time as well as assist you in making sure that you keep your win rate as high as possible.

While this site does not offer tips to improve your game strategy, it is a helpful tool to let you know how big your variance is, which can then spur you into action. We highly recommend that you check it out and enter your data whenever possible.

Standard Deviation Conclusion

So what have we learned then? In short, we know that by calculating your standard deviation you can better determine your win rate and see how it varies over time. Ultimately, it will give you an idea of how much your rate can swing over time so that you can be better prepared. For example, if you have a deviation of 70 with an average win rate of 30, then you know that you can have some huge swings up or down over time. Conversely, if you have a deviation of 11 with the same average, then your swing will be much tighter.

Overall, knowing this calculation will help you in the long run. By understanding your typical win/loss pattern you can target areas to improve your game.  For more help like this, check out our other strategy guides.  We hope you enjoyed our article on standard deviation, please leave your comments below and let us know what you thought!


I'm a tech geek who enjoys extreme sports, computing and, of course, an avid poker enthusiast.


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