Question about Winrate

Lmn55d · #1 11-13-2004, 03:37 AM

Ok, if I have a winrate of 1.42BB/100 after 4000 hands, what would you guys say is the range of my true winrate. Like, is it possible that I'm a 3BB/100 player and just have a sample size that is too small?

uuDevil · #2 11-13-2004, 05:06 AM

You have to provide your standard deviation as well. But this is such a small sample I'd guess the answer is easily yes.

pzhon · #3 11-13-2004, 06:30 AM

[ QUOTE ]
You have to provide your standard deviation as well. But this is such a small sample I'd guess the answer is easily yes.

[/ QUOTE ]
The standard deviation changes from player to player and game to game, but usually not by a huge amount.

Let's assume the standard deviation in 100 hands is 15. In 40x100 hands, the standard deviation of the win rate should be about 15/sqrt(40)~2.4. After 4000 hands, your true strength is very likely to be within 2 standard deviations, 1.4+-4.7 BB/100. That's not a very tight estimate. It is hard to conclude anything from only 4000 hands.

jason1990 · #4 11-13-2004, 11:58 AM

[ QUOTE ]
The standard deviation changes from player to player and game to game, but usually not by a huge amount.

[/ QUOTE ]
If we're talking about "good" players, I would probably agree. But a weak-tight player, or a LAG, or perhaps anyone with a true winrate that is negative, could likely have a standard deviation that differs significantly from the "norm".

I just wanted to mention this because the OP might be trying to decide if he's a "good" player. And, it seems to me, the assumption of a 15BB/100 SD presupposes this fact to some degree.

Lmn55d · #5 11-13-2004, 12:37 PM

how do I find out my standard deviation?

uuDevil · #6 11-13-2004, 04:20 PM

[ QUOTE ]
how do I find out my standard deviation?

[/ QUOTE ]
If you have PokerTracker, it's under
"Session Notes" tab -> "More Detail..." button

Lmn55d · #7 11-13-2004, 08:08 PM

ah cool. So say I know my current winrate after a small sample size of hands and my standard deviation. How can I find out the range of my true winrate?

ode · #8 11-13-2004, 08:27 PM

How much is large enough sample size to draw a conclusion on if you are or aren't a winning player at a certain limit (on let's say 97% certainty).

Is it 50k+ hands, 100k+ hands?

I currently have 29,138 hands of $2/4, BB/100 of 3.52, SD/100 of 15.2394.

I'm pretty certain I'm a winner, since I've been playing and winning for quite a long time. Those are just since I recently started logging with PT.

But so, how much is enough when speaking of sample size?

/ode

uuDevil · #9 11-14-2004, 03:13 AM

[ QUOTE ]
ah cool. So say I know my current winrate after a small sample size of hands and my standard deviation. How can I find out the range of my true winrate?

[/ QUOTE ]

pzhon showed the idea above.

The interval

WR +/- 2*SE

will include your true win rate with 95.4% confidence, where SE= SD/sqrt(N), SD and WR are in BB/100, and N= #hands (in hundreds)

The factor 2 can be varied depending on the desired confidence:

1 -> 68% confidence
1.96 -> 95% confidence
3 -> 99.7% confidence

The greater the desired confidence, the wider the interval.

uuDevil · #10 11-14-2004, 04:13 AM

[ QUOTE ]
How much is large enough sample size to draw a conclusion on if you are or aren't a winning player at a certain limit (on let's say 97% certainty).

Is it 50k+ hands, 100k+ hands?

[/ QUOTE ]

Whether or not you are a winning player depends on WR, SD, and N (#hands). Calculate the quantity

WR/(SD/sqrt(N))

This is the distance from breakeven in # of SD. For >= 97% confidence, this quantity >= 2.17.

[ QUOTE ]

I currently have 29,138 hands of $2/4, BB/100 of 3.52, SD/100 of 15.2394.

I'm pretty certain I'm a winner, since I've been playing and winning for quite a long time. Those are just since I recently started logging with PT.

But so, how much is enough when speaking of sample size?

[/ QUOTE ]

It's relative, but 3.52/(15.2/sqrt(291))=3.95 so you can be better than 99.9% confident you are a winning player.