Variance, winrates, and expectation (long)

[Surfbullet]

Just to tack on to some other posters queries about 2-3BB/100 players running bad...

Schnieds has posted graphs of 30k breakeven stretches. Sxb who has a winrate of 3BB/100 at 10/20 over 300k+ hands, has posted a 650 BB downswing.

Davidross, longtime poker pro, who is estimated at 2+BB/100 has had a 600BB downswing that lasted almost 30k hands.

These things are rare, but they happen. The CI is by no means a bound(as another poster noted) and results outside of the 99% CI are not as uncommon as we would like to think, especially given how many hands of poker most play.

Surf

[tallstack]

I think I will be getting out of my league pretty soon here, but I still have a few comments.

[ QUOTE ]
I think I can explain your concerns. Let's consider looking at a 20,000 hand sample within a 100,000 hand sample. Are there 5 20,000 samples we can choose from? Not really, there are 80,000 20,000 hand samples. 1-20,000, 2-20,001, 3-20,002, 4-20,003,...,79,999-99,998, and 80,000-99,999.

[/ QUOTE ]

There certainly are 5 20,000 hand 'independent' samples. The 80,000 20,000 hand samples are about as dependent as can be. If we are going to normal distribution assumptions for our data then I believe that they need to be independent data points. Thus, using 80,000 20,000 hand samples is not valid. Using 5 20,000 hand samples would be valid, but 20,000 hand samples are likely too large to analyze a peak-to-valley downswing. It is better than using a single 100,000 sample, but not by much. We could use say 1000 100 hand samples and get a more refined answer, or we could take it down to a single hand level. My central argument is that this analysis method you have shown, while valid for determining a probable range of end values, is not suited to determining the probable range of paths taken to get there. If we want to determine swings along the way, we need to use a method that models paths within a sample size.

[ QUOTE ]
I guess my point is, instead of blaming variance, turn the focus inward and see where our play has been suboptimal.

[/ QUOTE ]

I agree with you here. [img]/images/graemlins/smile.gif[/img]

[Justin A]

The fact that the -99% line in the bottom graph intersects 0 just short of the 40,000 hand mark doesn't mean that there is only a 1% chance that a 2BB/100 winner will have a breakeven stretch of that length at some point. It only means that he only has a 1% chance of breaking even on his VERY NEXT 40,000 HAND STRETCH STARTING RIGHT NOW! That is entirely different than having a 1% chance of ever breaking even for 40,000 hands.

Just thought that this should be repeated. Nice post cartman.

[beachbum]

[ QUOTE ]
I'd love it if you could run another set using a SD of 17 and a SD of 19, since a SD of 15 would be more indicative of, say, a 5/10 full ring player.

[/ QUOTE ]

LOL. So is my 14.6 SD at 5/10 6-max a little low? [img]/images/graemlins/laugh.gif[/img] There's never been a question about my being risk averse.

Anyway, here ya go.








The 1 BB graph at 19 SD is just painful to look at.

[Surfbullet]

Thanks for doing that, beachbum.

It's very telling that after a mere 50k hands the same 1BB/100 player w/ 17 SD(mine is 16.8) could either be down 200BB or up 1250BB! That's a STAGGERING range, and really something to think about before anyone judges the quality of a person's play based solely on their winrate over a small hand sample.

Surf

[MrBig30]

Very nice. I have this thread bookmarked now, and I think whenever someone new complains about running bad he should be told to take a look at these graphs.... [img]/images/graemlins/smile.gif[/img]

Love your work Beachbum.

It is very scary to look at the 1BB/100 WR on the 19SD graph. If your running bad it could nearly take a life time of poker to come out of it. A 1BB/100 WR with 19SD suxs. Its basically break even poker.

I'm thinking that you can't comprimise on your WR. Multi-tabling will have its dangers in decreasing your WR.

Trent.

[ggbman]

Excellent post here. I am not a math guy, so its always nice to have people simplify things for us common folk. I think the key thing here to take away is that very good players can have uncharecteristic downswings that are more severe than their peers.

The important thing to do is focus on styaing condifident and playing within the parameteres of your game. Obvioulsy, during a downswing, you might need to move down so as not to comprimise your bankroll. Gigabet said it well in one of his fews posts. "At some point, everyone will run worse than they ever thought was possible". This is very true, and for some people it will be in the form of a 500 or 600 BB downswing and for others it might be kick starting your 100/200 career with a 200BB downswing (not I! [img]/images/graemlins/smile.gif[/img]) Anyway, it should be reassuring to people going therough these downswings that it's a normal part of variance and that it will go away after about 17 million hands.

Gabe