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variance in 6 max LHE pt. 3 - estimating your win rate

  
 
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DrivingDog
Old 02-26-2008, 12:14 AM     Post subject: variance in 6 max LHE pt. 3 - estimating your win rate #1 (permalink)  
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Because of variance, you can never get a 100% accurate reading of what your exact win rate is, but you can fix it within a given range with a reasonable degree of certainty.

For this you need:

a) Your win rate (WR) for the set of hands in your database (use BB/100)
b) The standard deviation (SD) of your win rate (in PT 'session's' page, under 'more details' button)
c) The number of hands (n) you've played in 100s. E.g., 5000 hands = 5 x 100

Step 1) Use your SD and n to determine the standard error (SE) of your win rate

SE = SD/sqrt(n) - where 'sqrt' means 'take the square root of the number in brackets''

e.g., if your SD = 15 and you have played 160,000 (1600 x 100) hands, then your SE = 15/sqrt(1600)
SE =15/40
SE =0.375

Step 2) find the confidence interval (CI) that you want to use by looking at the following table to obtain the necessary z-score (Z)

CI.........................Z
99%...................2.57
95%...................1.96
90%...................1.64
75%...................1.15

(scientists use 95% CI, or a z -score of 1.96)

3) multiply the z-score by your SE (in the above example, using a 95% CI, you would multiply 1.96 *0.35 = 0.686

4) Subtract this number from your win rate to determine the lower boundary of your CI

e.g., if your win rate is 1.0 BB, then the lower boundary is 1.0 - .686 = 0.314

5) Add this number to your win rate to determine the upper boundary
e.g., 1.0+ 0.686 = 1.686

Thus, given the data from this person's PT (1.0 BB/100 WR over 160k hands, with an SD = 15), we can be 95% confident that their true win rate lies within the range of 0.314 to 1.686.
"You can fool some of the people all of the time, and those are the ones you want to concentrate on." (George Bush).
 
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asdpikas
Old 03-14-2009, 03:26 PM #2 (permalink)  
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UP!
"could I take out every woman and child in a border town?"
For the right to be governed, waste them without mercy.
When you've decided. Meet me at the airport.
 
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Jamjoe
Old 03-17-2009, 10:38 PM #3 (permalink)  

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Jamjoe
how come this doesnt work for FR as well as 6max?
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asdpikas
Old 03-17-2009, 11:30 PM #4 (permalink)  
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it should work
"could I take out every woman and child in a border town?"
For the right to be governed, waste them without mercy.
When you've decided. Meet me at the airport.
 
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DrivingDog
Old 03-18-2009, 12:12 AM #5 (permalink)  
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Because I dont play FR

Srsly, it does work for any game.
"You can fool some of the people all of the time, and those are the ones you want to concentrate on." (George Bush).
 
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KoRnholio
Old 03-18-2009, 12:47 AM #6 (permalink)  
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KoRnholio will become famous soon enough
 Indeed it will work for any game. You should just find that the SD of shorthanded games is higher than for full ring.
Some days it feels like I've been standing forever, waiting for the bank teller to return so I can cash in all these Sklansky Bucks.
 
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