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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)
 
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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