Question about Calculating Standard Deviation for a given hand in Full Pay Deuces Wild Video Poker
April 28th, 2010 at 8:20:28 AM
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I am trying to understand the exact formula for calculating Standard Deviation for a given hand in full pay Deuces Wild video poker. If you look at the example posted at the bottom of the Wizard of Odds website page that defines the correct strategy for Full Pay Deuces Wild You will find an example of how to play the hand made up of 5H, 6S, 8H, 9H, KC.
The Wizard of Odds site states that the expected value of .3404 for playing the 4 card straight: 5H, 6S, 8H, 9H
is exactly the same as that for playing the 3 card straight flush: 5H, 8H, 9H
The Wizard of Odds site further gives the breakdown of all the possible hands you can get from the 47 one card draws to 5H, 6S, 8H, 9H and the 1081 hands you can get from two card draws to 5H, 8H, 9H
Lastly the Wizard of Odds site stated that the standard deviation for the one card draw to the straight is: 0.751639223, and the standard deviation for the two card draw is: 1.182169177
I have tried to determine the exact formula for calcuating these two values for Standard Deviation, but I could not get any of my attempts to match the numbers posted on the web site.
I am hoping that someone can take a look at the link above, and look at the data for these two hands (seen at the bottom of the site page), and let me know what the proper formula for clcualting standard dev for these two poker hands actually is.
The Wizard of Odds site states that the expected value of .3404 for playing the 4 card straight: 5H, 6S, 8H, 9H
is exactly the same as that for playing the 3 card straight flush: 5H, 8H, 9H
The Wizard of Odds site further gives the breakdown of all the possible hands you can get from the 47 one card draws to 5H, 6S, 8H, 9H and the 1081 hands you can get from two card draws to 5H, 8H, 9H
Lastly the Wizard of Odds site stated that the standard deviation for the one card draw to the straight is: 0.751639223, and the standard deviation for the two card draw is: 1.182169177
I have tried to determine the exact formula for calcuating these two values for Standard Deviation, but I could not get any of my attempts to match the numbers posted on the web site.
I am hoping that someone can take a look at the link above, and look at the data for these two hands (seen at the bottom of the site page), and let me know what the proper formula for clcualting standard dev for these two poker hands actually is.
April 28th, 2010 at 10:54:38 AM
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1. calculate the return. It is 16/47 for both. I'm going to show the math for the 3 to a straigh flush.
2 For each posible pay take pay - return.
s.f. 9 - 16/47 = 8 31/47
flush 2 - 16/47 = 1 31/47
st. 2 - 16/47 = 1 31/47
3ok 1 - 16/47 = 31/47
Loser 0 - 16/47 = -16/47
3. square these numbers
s.f. 165649/2209
flush 15625/2209
st. 15625/2209
3ok 961/2209
Loser 256/2209
4. multiply by how often they occur (ok rounding here)
s.f. 165649/2209 * 15 = 1124.82344952467
flush 15625/2209 * 63 = 173.513807152558
st. 15625/2209 * 31 = 85.3798098687189
3ok 961/2209 * 45 = 19.5767315527388
Loser 256/2209 * 927 = 107.429606156632
5. add them
1510.72340425532
6. divide by total combo
1510.72340425532/1081= 1.39752396323341
7. The squareroot is the standard standard dev.
1.18216917707806
2 For each posible pay take pay - return.
s.f. 9 - 16/47 = 8 31/47
flush 2 - 16/47 = 1 31/47
st. 2 - 16/47 = 1 31/47
3ok 1 - 16/47 = 31/47
Loser 0 - 16/47 = -16/47
3. square these numbers
s.f. 165649/2209
flush 15625/2209
st. 15625/2209
3ok 961/2209
Loser 256/2209
4. multiply by how often they occur (ok rounding here)
s.f. 165649/2209 * 15 = 1124.82344952467
flush 15625/2209 * 63 = 173.513807152558
st. 15625/2209 * 31 = 85.3798098687189
3ok 961/2209 * 45 = 19.5767315527388
Loser 256/2209 * 927 = 107.429606156632
5. add them
1510.72340425532
6. divide by total combo
1510.72340425532/1081= 1.39752396323341
7. The squareroot is the standard standard dev.
1.18216917707806
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