Variance

[cartman]

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You guys are funny. How is this not EXACTLY linear?


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You cant just put % on one of the axes. Linear means that for each 1 unit increase in one axis, there is a fixed amount of increase or decrease on the other axis. (As an aside, this comparison should probably be win rate vs risk of ruin instead of win rate vs required bankroll). For this example, for the relationship to be linear the additional amount of bankroll required for a decrease in win rate from 2.0 to 1.5, for example, should be the equal to the additional amount of bankroll required for a decrease in win rate from 1.5 to 1.0. That isn't the case here.

Cartman

[DpR]

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You cant just put % on one of the axes.

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I know, I didnt suggest only using it one axis.

[ QUOTE ]
Linear means that for each 1 unit increase in one axis, there is a fixed amount of increase or decrease on the other axis. (As an aside, this comparison should probably be win rate vs risk of ruin instead of win rate vs required bankroll). For this example, for the relationship to be linear the additional amount of bankroll required for a decrease in win rate from 2.0 to 1.5, for example, should be the equal to the additional amount of bankroll required for a decrease in win rate from 1.5 to 1.0. That isn't the case here.

[/ QUOTE ]

Well duh, no one should ever consider that to be what anyone is referring to if they said there was a linear relationship between WR and Bankroll required. Obviously, the scenario you describe for any poker scenario since the BR required will be infinity for all WR <0, thus it will be assymptotic as x->0. Percentage are clearly implied in this conversation (or use natural logs if u like).

The interesting question is, does variance increase with a decrease in WR.

[Abbaddabba]

The actual figure of STDV/100 is independent of your winrate.


The swings seem smaller when you have a higher winrate because they tend to gravitate towards a higher average.

If you're a 3BB/100 winner historically and run at 2BB/100, it's not going to be busting your balls like it would for a 0.5BB/100 winner to run at -0.5BB/100.

[DpR]

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The actual figure of STDV/100 is independent of your winrate.



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What makes you so certain? ( I do not mean from a statistical perspective on a given sample)

[Abbaddabba]

Are you saying that you think there's a positive or negative relationship between the two figures?

[PartyGirlUK]

There aer some very good posts in this thread. I guess you could say I belong to the 'aba' school of thinking. Imo people underestimate the impact of skill on swings.

Consider a marginal winner goes on a terrible run over 15k hands. He loses 500bb. He makes a couple of posts in BBV and they do indeed consider a number of sick, sick beats, hands where any good player would have lost the same amount. In fact, every single on of the bad beat hands was played perfectly by him. A number of experts chime in to say this. I think it might be easy for him to consider it proof that 500bb hands happen. Lets say he is .5bb long term winner. Someone else is 2bb/100. If the latter had gone on the same run of sick sick beats over 15k hands, he would 'only' be down 275bb.

Thinking about the 4 high profile limit posters that immediately spring to mind that went on long (>100k) breakeven or worse stretches, with the exception of JoshW they all play a ludicrous number of tables (6 to 8). I can't help but thinking that they were table selecting bad + playing too sessions in order to get unstuck. They also going to have a smaller edge playing that many tables. Someone 8 tabling at 1bb/100 is gonna make twice the hourly of someone 2 tabling at 2bb/100, but is gonna have way bigger downswings. Which isnt to criticise people who do this - I'm in awe of anyone able to play 6+ tables of sh limit successfully, but they will have longer (in terms of hands) breakeven stretches.

It's extremely difficult to play well when you are running really bad. Every single person Ive played lots with plays better when running well. Almost everyone I know plays more when stuck than after a nice score. I am more guilty than most of these sins. Because of this, I remain incredibly skeptical of claims such as 'I lost 450BB and played me A++ game throughout'. If the player in question wants to send me his hand histories for the stretch in question I would be happy to look through them btw. Also, I dont want people to think Im preaching/claiming to be superior. It's possible I've never been on a prolonged run of lack as bad as some of these guys, and if I did, my game may well go to bits without me knowing it.

I'm more risk averse than the clear majority of 2p2ers, and one really useful thing from this thread is that Im gonna keep focusing hard on game selection. For me, it's not worth playing in a game where my edge is only 1bb/100, even if I am super duper comfortably rolled for the level. Just too much variance, I hate losing for a long time, and the best way to avoid long breakeven stretches is to play in games where your edge is big. Maybe I'll just be content grinding it out at 30/60 and playing higher when the games are really juicy?

fsuplayer mentioned something about me running well in NL. I made a stat post in MSNL a month or so ago where I openly admitted this. I do stand by the statement that most people at 3/6 NL blow though. I also still believe that 2bb/100 is doable in the 100/200 stars limit game with minimal table selection, but Im definitely not good enough to achieve that rate.

[PartyGirlUK]

Should add, most of my work is based around analysing poker stuff in stata, so Im not totally clueless, and am aware that anything is possible. It *could* be that BK lost 1200bb while playing 1bb+/100 poker. It's possible. It's possible aba will go on a 60 buyin downswing while playing his A game. Anything is possible. But using bayes theorem leads me to the conclusions I make about how likely it is that most people who go on these massive downswings are deluding themselves.

Dean

[Hobbs.]

Dean,

Something I've been thinking a decent amount over the last couple of days is the idea that winrates in limit hold'em are normally distributed. I think it's pretty clear that winrate is not, but I'm stuck on how much this will have an effect on the things like bankroll requirements and downswing frequencies. I don't play nearly enough poker to have a large enough database to start looking at some of these things, but my best guess is that a lot of individual hands are going to have winrate distributions that have fairly fat tails. AA will likely have a fat tail on the negative side due to times you lose with it it is usually more than a couple of bbs, while 78s will a fat tail on the positive side (occasionally smash flushes, but fold early in hands otherwise). I'd further guess, but could be way off here, is that if ones winrate distribution has a fairly fat tail on the negative side the severity of downswings is likely going to be higher than common thought.

Anybody done any work on this or have any useful links?

[El Diablo]

Dean,

People who run better than average underestimate how much variance there is. People who run worse than average overestimate how much variance there is.

[PartyGirlUK]

Diablo that's a great (and true) aphorism.