WoO VP Strategy Calculator Variance Explanation
June 21st, 2016 at 1:21:17 PM
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Would anyone explain what exactly the variance column means and how it is calculated on the VP Strategy calculator ? https://wizardofodds.com/games/video-poker/strategy/calculator/
Assume the worst, believe no one, and make your move only when you are certain that you are unbeatable or have, at worst, exceptionally good odds in your favor.
June 21st, 2016 at 6:30:33 PM
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I think I figured it out but please correct where I am wrong.
So to calculate variance for the entire game you do:
(probability of getting the hand) * (payout for the hand - Expected return of the entire game)^2 and then add them up for all the possible payouts.
For example for 9/6 jacks:
Nothing: (0.545435) (0-0.995439)^2 +
Jacks or Better: (0.214585) (1-0.995439)^2 +
Two pair: (0.129279) (2-0.995439)^2 +
etc
So for each hand's row in variance is just the individual terms being added to reach the total.
So 9/6 JoB variance is ~19.51, that means the standard deviation is ~4.41701.
So would that mean 9/6 JoB return has a spread of +/- 4.41% ?
So to calculate variance for the entire game you do:
(probability of getting the hand) * (payout for the hand - Expected return of the entire game)^2 and then add them up for all the possible payouts.
For example for 9/6 jacks:
Nothing: (0.545435) (0-0.995439)^2 +
Jacks or Better: (0.214585) (1-0.995439)^2 +
Two pair: (0.129279) (2-0.995439)^2 +
etc
So for each hand's row in variance is just the individual terms being added to reach the total.
So 9/6 JoB variance is ~19.51, that means the standard deviation is ~4.41701.
So would that mean 9/6 JoB return has a spread of +/- 4.41% ?
Assume the worst, believe no one, and make your move only when you are certain that you are unbeatable or have, at worst, exceptionally good odds in your favor.
June 21st, 2016 at 6:45:50 PM
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No.
The return is 99.54%. There is a WoO page about calculating standard deviation.
https://wizardofodds.com/games/video-poker/appendix/3/
The return is 99.54%. There is a WoO page about calculating standard deviation.
https://wizardofodds.com/games/video-poker/appendix/3/
June 21st, 2016 at 7:02:38 PM
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Quote: RSNo.
The return is 99.54%. There is a WoO page about calculating standard deviation.
https://wizardofodds.com/games/video-poker/appendix/3/
So for example:
Q1: What is the standard deviation of one hand of 1-play jacks or better on a $1 machine with max coins?
A1: From the 9/6 table we see the standard deviation is 4.417542. Multiply this by the total bet and the standard deviation is 4.42 × 5 × $1 = $22.09.
So what does that $22.09 actually mean ?
Assume the worst, believe no one, and make your move only when you are certain that you are unbeatable or have, at worst, exceptionally good odds in your favor.
June 21st, 2016 at 7:22:27 PM
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$22.09 is the standard deviation. Being within one standard deviation from the mean means your results would be somewhere between -$0.023 +/- $22.09.
It makes more sense if you do it for 1000 rounds (hands) or more.
It makes more sense if you do it for 1000 rounds (hands) or more.
June 21st, 2016 at 7:34:07 PM
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Quote: RS$22.09 is the standard deviation. Being within one standard deviation from the mean means your results would be somewhere between -$0.023 +/- $22.09.
It makes more sense if you do it for 1000 rounds (hands) or more.
Thank you. Tons of places on the net like to talk about variance but none of them actually tell you what it means.
Assume the worst, believe no one, and make your move only when you are certain that you are unbeatable or have, at worst, exceptionally good odds in your favor.
