sza
sza
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June 4th, 2023 at 2:06:48 AM permalink
In 9/6 JOB, the covariance is 1.966389 according to this Standard Deviation for Multihand Video Poker

Is it calculated by enumerating all possible dealt hands? Or how to calculate it? Thanks!
Dieter
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Dieter
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June 4th, 2023 at 2:19:17 AM permalink
Quote: sza

In 9/6 JOB, the covariance is 1.966389 according to this Standard Deviation for Multihand Video Poker

Is it calculated by enumerating all possible dealt hands? Or how to calculate it? Thanks!
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Blessing the link.
May the cards fall in your favor.
CrystalMath
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sza
June 6th, 2023 at 8:22:41 AM permalink
The covariance in video poker is the same as the variance on the deal; this is the part of the variance shared by all of the hands.

To get this variance, loop through all C(52,5) deal hands and calculate the EV of each hand. Calculate the variance of those EVs. For 9/6 JOB, I get 1.966388673520996, which corroborates the Wizard's work.
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UP84
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June 6th, 2023 at 8:54:59 AM permalink
In order to calculate the covariance in n-play VP you first need to derive the probability pairs matrix for the given strategy, which is not easy.
sza
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CrystalMath
June 9th, 2023 at 2:31:15 PM permalink
CrystalMath, thank you very much!

I got a very close number using your approach. 1.9663894301318172.

Your number seems to be the sum of the square differences divided by 2598960, not 2598960-1. Please correct me if I am wrong.
CrystalMath
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sza
June 9th, 2023 at 6:10:05 PM permalink
Quote: sza

CrystalMath, thank you very much!

I got a very close number using your approach. 1.9663894301318172.

Your number seems to be the sum of the square differences divided by 2598960, not 2598960-1. Please correct me if I am wrong.
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Youíre welcome. Mine are all divided by 2598960. Since we are looking at every outcome, itís the entire population, so we donít need to subtract 1.
I heart Crystal Math.
sza
sza
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CrystalMath
June 10th, 2023 at 11:21:31 AM permalink
Make sense. Thank you very much, CrystalMath!
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