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Reason #4 why the Wizard likes Bovada:

One-Stop Shopping

Bovada offers the triple crown of gambling: casino, poker, and sports. Many other casinos have tacked on poker as an afterthought, and many poker rooms have tacked on a casino as an afterthought, and the lack of attention shows, sometimes painfully. And very few of these sites let you make sports wagers.

But Bovada doesn’t just offer all three, they do each one well, and everything’s integrated. It’s easy to play all three off one deposit, off just one account.

Another nice thing about Bovada is that you don’t need a separate account to play casino games with fake money. In fact you do not even need an account for that at all, you can just click over there and play. Finally, Bovada usernames are only six or seven characters long making them possible to remember. By contrast some competitors’ usernames are extremely long and cumbersome.

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Standard deviation for multihand video poker

Last Update: Oct 24, 2007


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
GameVariance on DealVariance on DrawTotal Variance
Full pay deuces wild3.14005322.69456525.834618
10/7 double bonus3.39137524.86416528.255539
9/6 jacks or better1.96639117.54828519.514676
8/5 Bonus poker2.12002718.78405520.904082

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
nVarianceStandard Dev.
125.8346185.082777
332.1147235.666985
538.3948296.196356
1054.0950937.354937
50179.69720113.405118
100336.69983718.349382

10/7 Double Bonus

10/7 Double Bonus
nVarianceStandard Dev.
128.2555395.315594
335.0382885.919315
541.8210376.466919
1058.777917.666675
50194.4328913.943919
100364.00161619.078826

9/6 Jacks or Better

9/6 Jacks or Better
nVarianceStandard Dev.
119.5146764.417542
323.4474594.842258
527.3802415.232613
1037.2121966.100180
2566.7080008.167500
3994.2375349.707602
50115.86784110.764193
100214.18739614.635143

8/5 Bonus Poker

8/5 Bonus Poker
nVarianceStandard
Deviation
120.9040824.572098
325.1441365.014393
529.384195.420719
1039.9843256.323316
50124.78540511.170739
100230.78675515.191667

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
GameVarianceCovariance
Full pay deuces wild25.8346183.140053
10/7 double bonus28.2555393.391375
9/6 jacks or better19.5146761.966391

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.

  1. What is the standard deviation of one hand of 1-play jacks or better on a $1 machine with max coins? (answer)
  2. What is the standard deviation of one hand of 1-play jacks or better on a 25 cent machine with max coins? (answer)
  3. What is the standard deviation of 10 hands of 1-play jacks or better on a 25 cent machine with max coins? (answer)
  4. What is the standard deviation of 1 initial hands of 10-play jacks or better on a 25 cent machine with max coins? (answer)
  5. What is the standard deviation of 100 initial hands of 50-play deuces wild on a $5 machine with max coins? (answer)
  6. What is the standard deviation of 50 initial hands of 100-play deuces wild on a $5 machine with max coins? (answer)
  7. What is the standard deviation of 1 initial hand of 8-play 10/7 double bonus on a $2 machine with max coins? (answer)
  8. 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.

Standard Deviation
Lines/PlaysSpin PokerMulti-Play
2 4.64 4.63
3 4.82 4.84
4 5.4 5.04
5 5.90 5.23
6 6.25 5.42
7 6.55 5.60
8 6.89 5.77
9 7.28 5.94

Recommended Reading

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.

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  • Probability of Ruin for single-play video poker

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  • The standard deviation of n-play video poker

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Full-Pay Jacks or Better:

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