Video Poker Game Variance

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)
Hand	Payout	Return %
Royal Flush	4000	1.98
Straight Flush	250	0.55
Four of a Kind	125	5.91
Full House	45	10.36
Flush	30	6.61
Straight	20	4.49
Three of a Kind	15	22.33
Two Pair	10	25.86
Jacks or Better	5	21.46





Total Return %		99.5439
Variance		19.51468

Dbl Dbl Bonus (40/10/6)
Hand	Payout	Return %
Royal Flush	4000	1.95
Straight Flush	200	0.44
Four Aces +2-4	2000	2.46
Four Aces	800	2.78
Four 2-4 + A-4	800	2.29
Four 2 - 4	400	3.08
Four 5 - K	250	8.16
Full House	50	10.86
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 %		99.9577
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.