Video Poker Appendix 3
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 base hands (5000 total hands) of 10-play jacks or better.
This would be 50001/2*6.10018 = 431.3479.
For another good source on this subject visit Jazbo's article An Analysis of
N-Play Video Poker. The articles includes variance breakdowns
for 13 video poker variations.
