This appendix shall answer the question on the standard deviation for n-play video poker for three types of full pay machines. In general the greater the number of plays the greater the standard deviation. In fact the relationship between number of hands and standard deviation is a linear one. The following table shows the breakdown in variance between the deal and the draw.

Video Poker Variance on Deal and Draw

Game Variance on Deal Variance on Draw Total Variance

Full pay deuces wild 3.140053 22.694565 25.834618

10/7 double bonus 3.391375 24.864165 28.255539

9/6 jacks or better 1.966391 17.548285 19.514676

The formula for the variance per hand of n-play video poker is n*vardeal+vardraw. The following tables show the variance and standard deviation for all three games and 1, 2, 5, 10, 50, and 100 play. All numbers on a per individual hand basis.

 

Full Pay Deuces Wild

Full Pay Deuces Wild

n Variance Standard Dev.

1 25.834618 5.082777

3 32.114723 5.666985

5 38.394829 6.196356

10 54.095093 7.354937

50 179.697201 13.405118

100 336.699837 18.349382

10/7 Double Bonus

10/7 Double Bonus

n Variance Standard Dev.

1 28.255539 5.315594

3 35.038288 5.919315

5 41.821037 6.466919

10 58.77791 7.666675

50 194.43289 13.943919

100 364.001616 19.078826

9/6 Jacks or Better

9/6 Jacks or Better

n Variance Standard Dev.

1 19.514676 4.417542

3 23.447459 4.842258

5 27.380241 5.232613

10 37.212196 6.100180

50 115.867841 10.764193

100 214.187396 14.635143

Let’s look at an example. Consider the total standard deviation of 500 initial hands (5000 total hands) of 10-play jacks or better. This 789bet login would be 50001/2*6.10018 = 431.3479.

 

Another way to look at this is at the variance and covariance between hands in n-play video poker as follows.

 

Variance and Covariance Table

Game Variance Covariance

Full pay deuces wild 25.834618 3.140053

10/7 double bonus 28.255539 3.391375

9/6 jacks or better 19.514676 1.966391

To find the total variance of n hands of n-play video poker use the following formula: n*variance+n*(n-1)*covariance. The variance per hand is variance+(n-1)*covariance. The standard deviation per hand is (variance+(n-1)*covariance)1/2.

 

Sample Problems

For these problems the term “initial hand” refers to the deal (as opposed to the draw). For example if a player played 10-play video poker 5 times he would get 5 initial hands but 50 final hands.

What is the standard deviation of one hand of 1-play jacks or better on a $1 machine with max coins? (answer)

What is the standard deviation of one hand of 1-play jacks or better on a 25 cent machine with max coins? (answer)

What is the standard deviation of 10 hands of 1-play jacks or better on a 25 cent machine with max coins? (answer)

What is the standard deviation of 1 initial hands of 10-play jacks or better on a 25 cent machine with max coins? (answer)

What is the standard deviation of 100 initial hands of 50-play deuces wild on a $5 machine with max coins? (answer)

What is the standard deviation of 50 initial hands of 100-play deuces wild on a $5 machine with max coins? (answer)

What is the standard deviation of 1 initial hand of 8-play 10/7 double bonus on a $2 machine with max coins? (answer)

What is the standard deviation of 2000 initial hands of 23-play double bonus on a $25 machine with max coins? (answer)