Before we get into the details, let’s define what we actually mean by variance in poker terms. Without getting too sciency, we can say that variance measures how much data points are spread from the average. In plain English, it means that how much you expect to earn and how much you actually earn will differ over a small sample. Variance A measure of the upswings and downswings your bankroll goes through. Variance is not necessarily a measure of how well you play. However, the higher your variance, the wider swings you'll.
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Our beginners guide to variance explains what it is, why it matters, how you can calculate your acceptable poker variance score, and what to do if you are on the wrong side of it. Our guide is not going to suit every player; but, if it helps you make a few dollars, it should be worth a few minutes of your reading time.
If you read a lot of poker articles, or frequently visit poker forums, you are undoubtedly going to come across the term “variance”. Variance is generally considered to be the upswings and downswings you experience when you play poker. In a way that is true. However, by better understanding variance and what you can do if you are on the wrong side of it, you could experience more upswings and fewer downswings – or, at worse, fewer financially painful downswings. Let´s start by defining variance.
What is Variance in Poker?
Variance in poker relates to short-term results, and one of the best ways to describe how it works is to take a shuffled pack of cards and turn the cards over one-by-one – betting on whether the next card will be black or red. If you were to bet black every time, you would break even by the time all fifty-two cards have been turned over. However, during your break-even run, there will have been times when you won or lost two, three or four bets in a row – maybe more.
Variance in poker is different because you don´t know you will break even at the end of each session. You can calculate the odds of winning each hand, and only bet when the odds are in your favor, but that is no guarantee of short-term success. In theory, your pocket Aces could get busted five times in a row, or you could win against pocket Aces five times in a row – even though the math says pocket Aces will prevail in four-out-of-five hands at the pre-flop stage.
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So, if variance in poker only applies to short-term results, why does it matter? It matters because in order to return a long-term profit you want to have more winning sessions than losing sessions, or at least make sure you win enough during your winning sessions to cover your losses during your losing sessions. In order to do this, you need to calculate your acceptable poker variance score and then decide what you will do if you find yourself on the wrong side of the score.
How to Calculate Your Acceptable Poker Variance Score
The primary objective of calculating your acceptable poker variance score is to determine a stop/loss position at which you say “enough is enough” and end the session. This requires considerable discipline – especially if you are on a sequence of losing sessions – which is why we stated at the very beginning of this article “our guide is not going to suit every player”. To calculate your acceptable poker variance score, you need to collect a sequence of results and then do a little math:
- Take the results from at least your last six sessions. Ideally they should be consecutive sessions with particularly bad days or good days excluded.
- Add up your winning sessions, take away the losses from your losing sessions, and divide the result by the total number of sessions in the calculation.
- The figure you have now is your average win/loss per session, and what you need to do next is work out how far each session is away from the average.
- This is where it gets complicated. Square each “how far each session is away from the average” value, add the results together and divide the result by the number of sessions.
How to Calculate Your Acceptable Poker Variance Score | Total | Average |
Take At Least Your Last Six Results | $10 | $15 | -$12 | $20 | -$15 | $36 | $54 | $9 |
How Far is Each Session from the Average | 1 | 6 | -21 | 11 | -24 | 27 | n/a | n/a |
Square the Values in the Row Above | 1 | 36 | -441 | 121 | -576 | 729 | -130 | -21.66 * |
* To get the figures on the bottom row of calculations, you have to multiple each figure in the middle row by itself.
So, 1×1 = 1, 6×6 =36 -21x-21 =-441, etc.
Then you add all the figures up along the bottom row to get the total of -130, and divide -130 by 6 (because you have used six sets of results in the calculations) to get -21.66.
Therefore if you had the series the results along the top line of the calculations, you should stop playing once you have lost $21.66.
The resulting figure is your acceptable poker variance score – basically your stop/loss position when you are experiencing a losing session. If it looks a bit high to you, it could be because you are playing at the wrong level or because you are an overall losing player. To get back on the right side of variance you should read our article about Poker Bankroll Management for Dummies, work on improving your game, and have the discipline to end a session when the stop/loss position is reached.
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| What is variance? While we could go into the mathematical details we will explain variance on video poker machines using real world examples. Variance is one of the characteristics that makes a big difference in the short term results between one game and another. Lets compare two popular machines. Below you have the pay tables for both full pay Jacks or Better (9/6) and a popular variety of Double Double Bonus (40/10/6). We picked these games for the example as both have a total return in the 99% range and compared side by side make a good example of variance in the real world. | Full Pay Jacks or Better (9/6) | Dbl Dbl Bonus (40/10/6) | Hand | Payout | Return % | Hand | Payout | Return % | Royal Flush | 4000 | 1.98% | Royal Flush | 4000 | 1.95% | Straight Flush | 250 | 0.55% | Straight Flush | 200 | 0.44% | Four of a Kind | 125 | 5.91% | Four Aces +2-4 | 2000 | 2.46% | Full House | 45 | 10.36% | Four Aces | 800 | 2.78% | Flush | 30 | 6.61% | Four 2-4 + A-4 | 800 | 2.29% | Straight | 20 | 4.49% | Four 2 - 4 | 400 | 3.08% | Three of a Kind | 15 | 22.33% | Four 5 - K | 250 | 8.16% | Two Pair | 10 | 25.86% | Full House | 50 | 10.86% | Jacks or Better | 5 | 21.46% | Flush | 30 | 6.77% | Straight | 20 | 5.11% | Three of a Kind | 15 | 22.59% | Two Pair | 5 | 12.31% | Jacks or Better | 5 | 21.16% | Total Return | 99.5439% | Total Return | 99.9577% | Variance | 19.51468 | Variance | 41.96707 |
| Variance Explained | You will notice at the bottom of each pay table we have listed the variance. The first machine shows 19.51468 and the second is over double at 41.96707. The biggest difference when you compare the pays are the four of a kind wins. On the Jacks or Better machine they make up 5.91% of the total return while on the Double Double Bonus machine they make up 18.77% of the total return. You will also notice that on the Double Double Bonus machine the pay for two pair makes up 12.31% of the total while on the Jacks or Better the same pay contributes 25.86% to the overall percentage. It is these changes in the way that pays contribute to the overall pay outs that alter the variance. Let's say you play 1,000 hands on both of the machines above and do not hit a royal flush or any four of a kinds. At the end of the thousand hands it is more likely that you will still have a good amount of credits left if you were playing the Jacks or Better machine compared to the Double Double Bonus. This is because one of the more common hands, the two pairs pay is a win on Jacks or Better while it is simply your bet back on the second game. Comparing the two games you will find that the first game will offer a longer run of smaller pays that keep you going while the second machine will be much harder on your bankroll if you do not hit any of the four of a kind ands. This difference is what variance is all about. The question then comes to mind - Which machine should I play? In the example above the Double Double Bonus would be a better bet over the long term simply because it has a higher overall pay back. But in the short term you have to ask yourself, do you want regular small wins that keep you playing or do you want to have fewer small wins but the chance at the occasional big hit. This is a personal choice so there is no right or wrong answer - it is totally up to you. | Popular Games Compared | Below is a table showing the variance for several popular video poker machine types. This further illustrates the points made above. Note that the higher the number the higher the variance. | Game | Variance | Game | Variance | Pick'em Poker | 15.0055 | All American | 26.7998 | Jacks or Better | 19.5146 | Double Bonus | 28.2555 | Bonus Poker | 20.9040 | Double Double Bonus | 41.9849 | Aces & Eights | 21.7259 | Deuces & Joker | 45.5885 | Deuces Wild | 25.8346 | Loose Deuces | 70.3054 |
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