General Philosophy

[Aaron W.]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Over 20k hands, your WR doesn't mean much.

[/ QUOTE ]

This is complete BS.

There are 3 factors: winrate, # of hands played, and standard deviation. We know two of the factors already, and even using a grossly inflated standard deviation of 55BB/100, he is still a winning player out to 99.99999% confidence. Using a more normal, but still inflated standard deviation of 21BB/100 we can say with 99.9% confidence that he's earning at least 1.5BB/100.

This is basic stuff you can find in the FAQ.

[/ QUOTE ]

Hmmm, I am open to the idea that you are correct, but I have often seen people saying WR doesn't start to converge until like 100k hands. Maybe you could go over a little bit of the math for me, or just quote where you saw it in the FAQ (I looked but did not find it). FWIW, I recall a post where one of the more veteran posters (Josh. perhaps) ran 10 100k hand samples for players with 2BB/100, and got results as low as 1BB/100 and as high as 3BB/100 over that sample. I do have a very limited knowledge of stats and am familiar with terminology, but am not exactly sure how you came to these conclusions. Please help. Thanks.

Brad

[/ QUOTE ]

If I recall correctly, the point was to point out that you don't actually ever know your true winrate. This is different from saying that winrate doesn't carry information. Your winrate after 10k hands gives you enough information to reasonably say you are a winning player (assuming your BB/100 is above 1 or 1.5 -- someone else can figure that out because I'm not a statistician). After 20k hands, you can say it with even more confidence with the same BB/100.

[PokerSlut]

This post is linked at the bottom of the Micro-limits FAQ as "Homer's confidence interval calculations for winrates":

How many hands do I need to play...

What is meant by "converge" is that the more hands you play, the more narrow your confidence interval becomes. However, you can still establish reasonable lower and upper bounds with fewer hands. The difference is that you will see a wider range of possible winrates over fewer hands. e.g. 1.5BB-2.6BB for our friend here if we use a 99.9% confdence. If I change his 20k hands played to 100k hands, his interval is much tighter: 1.87BB-2.32BB.

[jaxUp]

[ QUOTE ]
If I recall correctly, the point was to point out that you don't actually ever know your true winrate. This is different from saying that winrate doesn't carry information. Your winrate after 10k hands gives you enough information to reasonably say you are a winning player (assuming your BB/100 is above 1 or 1.5 -- someone else can figure that out because I'm not a statistician). After 20k hands, you can say it with even more confidence with the same BB/100.

[/ QUOTE ]

Ok, so I went into that link I posted above and played around a bit in Excel. After 20k hands, with a SD/100 of 15BB @ 2BB/100 we can be 95% sure that our BB/100 is somewhere between 0 and 4. This is not too accurate and hence I don't think you can rely too heavily on it. We know OP is a winning player (well, we almost "know), but that's about it. I guess I should have phrased my initial response differently. Over 20k hands, the WR doesn't give us "no information" but it certainly isn't necessarily accurate at all.

[jaxUp]

[ QUOTE ]
This post is linked at the bottom of the Micro-limits FAQ as "Homer's confidence interval calculations for winrates":

How many hands do I need to play...

What is meant by "converge" is that the more hands you play, the more narrow your confidence interval becomes. However, you can still establish reasonable lower and upper bounds with fewer hands. The difference is that you will see a wider range of possible winrates over fewer hands. e.g. 1.5BB-2.6BB for our friend here if we use a 99.9% confdence. If I change his 20k hands played to 100k hands, his interval is much tighter: 1.87BB-2.32BB.


[/ QUOTE ]

I went through that link and got WAY different numbers for upper and lower bounds. I copy and pasted the formulas that Bison posted a bit into the thread and used a SD/100 of 15BB ,CI of 95, and still got 0 and 4 for bounds.

[PokerSlut]

[ QUOTE ]
I went through that link and got WAY different numbers for upper and lower bounds.

[/ QUOTE ]

Then you need to check what you did wrong. I did exactly that just to make sure, and I get 1.90BB-2.32BB for 15BB standard deviation, 20k hands, and 95% confidence.



EDIT:
By "exactly that" I mean I copy & pasted the formulas into cells A5 and A6. I put "20000" in A1, "2.11" in A2, "15" in A3, and ".95" in A4.

[PokerSlut]

You made a mistake somehwere. You need to check your work.

[jaxUp]

[ QUOTE ]
[ QUOTE ]
I went through that link and got WAY different numbers for upper and lower bounds.

[/ QUOTE ]

Then you need to check what you did wrong. I did exactly that just to make sure, and I get 1.90BB-2.32BB for 15BB standard deviation, 20k hands, and 95% confidence.

[/ QUOTE ]

Cell B1 -> 20000
Cell B2 -> 2.1
Cell B3 -> 15
Cell B4 -> 95
Cell B5 -> =B2-NORMSINV((100-B4)/200)*B3*(1/SQRT(B1/100))
Cell B6 -> =B2+NORMSINV((100-B4)/200)*B3*(1/SQRT(B1/100))

Is this what you have? I get 0.02 for Lower Bound, and 4.17 for Upper bound. Thanks.

[PokerSlut]

Your confidence is a percentage, and should be ".95" not "95". You used 9500%.

[jaxUp]

[ QUOTE ]
Your confidence is a percentage, and should be ".95" not "95". You used 9500%.

[/ QUOTE ]

Hmm, okay. Then there is a problem in Homer's thread. Bisonbison rewrote the formulas using an integer rather than a number between 0 and 1. To compensate for this he subtracted it from 100, which would of course yeild different results.

Here's exactly what bison wrote :

[ QUOTE ]
For those working in BB/100 and Pokertracker:

A1: Hands
B1: Hand Count from PT
A2: EV/100
B2: BB/100 from PT
A3: SD/100
B3: SD/100 from PT session tab, 'more detail' button.
A4: Confidence Interval
B4: an integer between 0-99 (note: Homer originally used 0-.99)
A5: Upper Bound
B5: =B2-NORMSINV((100-B4)/200)*B3*(1/SQRT(B1/100))
A6: Lower Bound
B6: =B2+NORMSINV((100-B4)/200)*B3*(1/SQRT(B1/100))


[/ QUOTE ]

EDIT: STOP THE TRAIN

OK, I think the problem is that we are using 20000. That is the number of hands, but since we are doing BB/100 we should do groups of 100 hans in B1. This would mean that we put 200 instead of 20000, yeilding a lower bound of 0 and upper of 4 (with CI of .95).

[jaxUp]

So just to clarify, use groups of 100 hands if you are using Homer's formulas, and total # of hands when using Bison's formulas.