Many online casinos offer huge signup bonuses, but there's a catch. Buried in the fine print is that play on the most popular games doesn't count towards earning the bonus. It's common for blackjack, roulette, baccarat, craps, and Jacks or Better to be excluded. Sometimes everything except slots.
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Finally, in the unlikely event that Bodog feels you've been abusing their bonuses they won't seize your winnings, like some other casinos. In the worst case scenario they will politely tell you that they will not be offering you any future bonuses but you are welcome to keep playing and keep everything you have made already. (Visit Bodog)
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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
8/5 Bonus poker
2.120027
18.784055
20.904082
The formula for the variance per hand (on the draw) of n-play video poker is n*vardeal+vardraw. The following tables show the variance and standard deviation for all three games and 1, 3, 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
25
66.708
8.16750023
39
94.237534
9.707601867
50
115.867841
10.764193
100
214.187396
14.635143
8/5 Bonus Poker
8/5 Bonus Poker
n
Variance
Standard Deviation
1
20.904082
4.572098
3
25.144136
5.014393
5
29.38419
5.420719
10
39.984325
6.323316
50
124.785405
11.170739
100
230.786755
15.191667
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 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)
Spin Poker
The following table compares the standard deviation per hand on the draw in Spin Poker to multi-play video poker, in 9/6 Jacks or Better. For more information, see my section on Spin Poker.
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.
