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variance in 6 max LHE pt. 2 - how many hands...

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DrivingDog

02-25-2008, 11:54 PM Post subject: variance in 6 max LHE pt. 2 - how many hands...

#1 (permalink)

Full House

Join Date: Jul 2007

Location: UK

Posts: 923

...do you need to be 95% confident of showing a profit?

To estimate this you need:

a) the standard deviation (SD) of your win rate/100 hands in PT under the 'more detail' button on the 'sessions' page.

b) your estimated win rate (WR) in BB/100

Here's how it's done:

1) find SD*1.96/WR
2) square it
3) multiply by 100

this gives you the number of hands before you can be 95% confident that, if your WR estimate is correct, you will have a winning record.

as one formula it looks like this:

((SD*1.96/WR) sqrd)*100 - where 'sqrd' means 'square what's in these brackets'

e.g., if your SD =15 and your WR = 1.0 BB/100, then you need

((15*1.96/1.0)sqrd)*100 = 86436 hands to be 95% confident of showing a profit.

The table below gives a few calcs I've done in excel. The leftmost column is 1000s of hands, the other columns are the SD. The values in the table are the win rate at which this person could be 95% confident of showing a profit.

hands.............................SD=10..........S D=15..........SD=20..........SD=25
25k.................................1.24.......... ....1.86.............2.48.............3.10
50k.................................0.88.......... ....1.31.............1.75..............2.19
75k.................................0.72.......... ....1.07.............1.43..............1.79
100k...............................0.62........... ...0.93.............1.24..............1.55
150k................................0.51.......... ....0.76.............1.01..............1.27
250k................................0.39.......... ....0.59.............0.78.............0.98
400k................................0.31.......... ....0.46.............0.62.............0.77
600k................................0.25.......... .....0.38.............0.51.............0.63
1000k (1 million hands)....0.20...............0.29............0.39. ............0.49

So basically, for small samples you need an enormous win rate to be 95% confident of showing a profit in the short term, and for small win rates you need an enormous sample size.

The corollary of this is that for any given WR and SD, you can expect to be a loser over the same number of hands 5% of the time. E.g., if your WR if 1.31 BB/100 and your SD = 15, you can expect to lose money one out of every twenty sets of 50k hands.

"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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