un epeu pour les matheux masi trs explicite toriuve sur 2+2 ecrit par un frenchy
I wanted to make a post about variance for my 1k post. I know i have just 500 posts but this thread can be a direct answer to the SneakyFerret thread. So i think it’s better to post this now than in a few months.
First, i apologize for my bad english
I come from video games. I played CounterStrike at « international level » for 7 years in differents french team (famous: Goodgame (same team as elky) and aAa). One movie @ me: Kabal 2002 - YouTube .
I have discovered poker end of 2006. I’ve started to read lots of poker book before moving to realmoney with my first deposit of 50$. In 2007, i tried lots of poker rooms and all possible style like cashgame, sng, tourney. Since september 2007, i’ve choosen my style: STT => It’s fast, no tilting, and clear for me. On january 2008, i cashout all my BR and start again with 50$ on february on absolute. I moved on pokerstars on april in order to make decent volume (8+ tablings). Now i’m playing 16 tables on 27$ and i hope i will maintain at least a 5% ROI.
After this few word about me, go back to the main subject: the variance.
There is some mathematics formula for calculate variance, standard deviation, confidence interval.
You can find all of them on wikipedia.
As you know (or not), variance is the average of the distance between (median and result)² of a data’s sample.
Standard deviation is the square root of variance.
Let see all these concepts in a real case.
This is my real data (16$ BI):
2,149 11%
ITM:
- 288 first
- 259 second
- 305 thrid
- And so 1297 not ITM
16$ prizepool:
- 1st: 67.5$ so +51.5$ = +3.21875 BI
- 2nd: 40.5$ so +24.5$ = +1.53125 BI
- 3rd: 27$ so 11$ = +0.6875 BI
ROI is +11% so +0.11 BI.
Variance:
(288*(0.11-3.21875)²+259*(0.11-1.53125)²+305*(0.11-0.6875)²+1297*(0.11-(-1))²)/2149=2.329570 BI
squrt = square root
standard deviation sDev = squrt(Variance) = 1.526292
Confidance intervals for « N » games played
You are:
- 68% sure that you ROI is on the interval [ROI-(sDev/squrt(N)); ROI+(sDev/squrt(N))]
- 95% sure that you ROI is on the interval [ROI-2*(sDev/squrt(N)); ROI+2*(sDev/squrt(N))]
- 99% sure that you ROI is on the interval [ROI-3*(sDev/squrt(N)); ROI+3*(sDev/squrt(N))]
If you plan to play 1000 games per month (a decent volumes), what is your expected ROI ?
- at 68% you can say your ROI will be on [+6.17%; +15.83%] that’s means an deviation of 4.83% !!
- at 95% you can say your ROI will be on [+1.34%;+20.7%], so a deviation of 9.66% !!
Now let’s see another example:
This is another real data (27$ BI):
542 6%
ITM:
- 67 first
- 67 second
- 76 thrid
- And so 332 not ITM
27$ prizepool:
- 1st: 112.5$ so +85.5$ = +3.1667 BI
- 2nd: 67.5$ so +40.5$ = +1.5000 BI
- 3rd: 45$ so 18$ = +0.6667 BI
ROI is +6% so +0.06 BI.
Variance:
(67*(0.06-3.1667)²+67*(0.06-1.5)²+76*(0.06-0.6667)²+332*(0.06-(-1))²)/542=2.189293 BI
standard deviation sDev = squrt(Variance) = 1.479625
Confidance intervals with 1000 games:
- 68% => [+1.32%; +10.7%]
- 95% => [-3.4%; +15.4%]
So a 6% winning reg at 27$ can finish a month @ -3.4% or +15.4%.
The deviation is 9.4% it’s a + or -150% on his expected winnings.
To get a deviation of 1% in this case, we need to increase the number of games played by 100.
That’s 100 000 games !
I hope some people will understand now the brutal nature of the variance in STT.
I want to thank 2+2, all the 2+2 STT communities and specially a thanks to:
AMT, staffy, luisgallo, little john, Scotty_12, darinvg, sippin_criss, simplicity8, 7castle, juandadi, dave_w11, eurythmech, emperor_norton, drzen, NJD77 and wobuffet for the quality of their posts.
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