Does a decreased winrate have an exponential effect on variance?
 

Take a player whose style and game selection yield standard deviation X.

As he tilts and his winrate decreases, in what way does his variance increase? Linearly? Exponentially?

I know variance is a function of standard deviation and winrate...but exactly what sort of function is it?

Re: Does a decreased winrate have an exponential effect on variance?
 

-EV decisions can be lower variance or higher variance depending on what they are.

Tilters who "steam raise" will probably have higher swings. Tilters who make hasty folds but otherwise play correctly will probably lose money slowly but steadily.

Re: Does a decreased winrate have an exponential effect on variance?
 

While I agree with this in theory, in my experience a tilt is actually a low standard deviation event. The reason is most people keep tilting until they lose. It's true they'll have some big wins along the way, but they'll keep pushing their luck until losses either bring them to their senses or extinguish their bankroll. Also, they'll play more hands, which means their negative EV is more significant relative to their standard deviation over 100 hands or an hour. So both wild betting tilters and demoralized folders will tend to see their standard deviation go down.

If that's not true, if someone starts betting wildly but pays attention to wins and losses, it may only look like a tilt, it may be positive EV.

Re: Does a decreased winrate have an exponential effect on variance?
 

It's effect on true variance can be positive, negative or neutral, depending on how you tilt. True variance here is defined as deviation from expectation.

However, when most people talk about 'variance', they really mean downswings (cause nobody talk about up variance, they just assume they're that good). And tilting will of course have big impact on your downswing, hence heightening the illusion of 'variance'.

Re: Does a decreased winrate have an exponential effect on variance?
 

To me, variance is just a range above and below your expectation. As you expectation drops, the range still stays about the same, it's just a range around a different number. If my expectation is 2BB/100 with a SD of 17, then most of the time I'll have a result around -15 to +19. If I tilt and my expectation drops to -1BB/100, I'll have a range of -18 to +16. I don't see why tilting, in and of itself, would have a tremendous effect on my standard deviation.

Re: Does a decreased winrate have an exponential effect on variance?
 

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Also, they'll play more hands, which means their negative EV is more significant relative to their standard deviation over 100 hands or an hour. So both wild betting tilters and demoralized folders will tend to see their standard deviation go down.

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This is where we disagree; tilt can also be not making enough isolation raises, blind steals or bluffs. This is definitely the minority case but it does happen to some people.

Re: Does a decreased winrate have an exponential effect on variance?
 

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I know variance is a function of standard deviation and winrate...but exactly what sort of function is it?

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Variance is a function of standard deviation only in the sense that variance = the square of standard deviation.

In actual fact, variance is a calculable property of a statistical data set. If EV(q(x)) is the expected value of quantity q that depends on random variable x, then variance is

V = EV((x - EV(x)^2)

Variance is a property of the probability distribution governing the behavior of a random variable. Different probability distributions will have, in general, a different mean and a different variance.

In particular, in a poker game, the hand-by-hand results of a winning player playing her 'A' game might have one probability distribution and those of the same player when she's on tilt might have another. Both the variance and the mean (the win rate) of the tilt distribution will in general be different from those of the 'A'-game distribution.

If you invoke the Central Limit Theorem to cover the results of many, many hands, the theorem asserts that long term results will governed by a normal (Gaussian) probability distribution, no matter what the underlying distribution for hand-by-hand results. Gaussian distributions are parameterized independently by their means and their variances. You can't say a priori that changing the mean will change the variance, or vice versa.

Re: Does a decreased winrate have an exponential effect on variance?
 

It depends on what one means by "tilt".

If "tilt" is a particular sort of anger or rage induced by bad beats or other losing experience, then it seems to me that a tilter is more likely to become overly aggressive than overly passive.

If "tilt" is, as some poker thinkers assert, any emotional state that moves a player to playing anything other than correct play to the best of their knowledge, than timid, weak-tight play as a result of the fear of getting big hands like aces cracked also counts as tilt.

To an extent, it's a philosophical question, if not psychological: What is the nature of tilt?

Re: Does a decreased winrate have an exponential effect on variance?
 

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What is the nature of tilt?

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Bad dialogue?

Re: Does a decreased winrate have an exponential effect on variance?
 

If we define tilt as a deviation from optimal play - that is, we don't specify whether its victim is raising too often (loose agressive) and on whim rather than in selected spots, calling too often (loose passive) or folding too often (tight passive) - there should be no generic correlation between WR and varience.

In theory this describes the situation.

I think there is substantial truth to Aaron's description (tilt being a one-directional and fairly stabile trip) though I'm wondering if the numbers back this up.

- I'm not sure they do but I'm equally unconvinced they do not.

I see alot of bad (as in REALLY bad) players with expectedly high loss rates who, nonetheless have significant and frequent upswings.

All this is merely food for thought - I have neither proof nor even a strong belief that either statement is true; while my gut instinct is that tilt has either no effect or at most a negligible effect on varience, the truth is I'm just not sure.

Question for the masses . . .

If tilt does correlate to a lower varience does it then follow that a sudden burst in performance would raise one's varience - in ways other than the well understood concept of expert play including a huge number of high varience/low profit moves ?

Re: Does a decreased winrate have an exponential effect on variance?
 

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It depends on what one means by "tilt".

If "tilt" is a particular sort of anger or rage induced by bad beats or other losing experience, then it seems to me that a tilter is more likely to become overly aggressive than overly passive.

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I agree with this, except I would not characterize any tilter as overly aggressive. Most tilters get more aggressive in the sense of bluffing more, raising higher and folding less (although as Xhad said, there is also the player who gets timid and cautious after a bad beat). But this is really passive, despite the appearances. The play is predictable, and not designed to give other players hard choices. It's like closing your eyes and charging in battle. It may look fierce, but it's a lot easier to beat than the guy who advances rapidly but carefully, zigging and zagging randomly and keeping under cover.

Re: Does a decreased winrate have an exponential effect on variance?
 

Hey guys, there is a mathematical reason your "swinginess" goes up when your winrate goes down as a result of tilt or other factors. Your swinginess is measured by your coefficient of variation, the ratio of your standard deviation to your winrate. As a result, your "swinginess" increases exponentially as your winrate approaches zero, even though your standard deviation stays the same.

Re: Does a decreased winrate have an exponential effect on variance?
 

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I know variance is a function of standard deviation and winrate...but exactly what sort of function is it?

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i don't know if that has been said yet, but variance is NOT a function of SD and winrate.

standard deviation is the square root of variance.

variance is not a function of winrate at all.

Re: Does a decreased winrate have an exponential effect on variance?
 

yea, apparently I was confusing variance with "swinginess" which is the coefficient of variation or SD/winrate

Re: Does a decreased winrate have an exponential effect on variance?
 

By variance you actually mean "swings." Variance is the square of standard deviation; it is NOT a function of winrate.

Let's say you wanted to calculate what your worst possible downswing could be.

Let's assume a 3 SD downswing for "worst possible".
The equation you want to minimize is:

Winnings = Winrate_per_100hands*(N) - 3*SD_per_100hands*SQRT(N)

This is how much you're up (down if negative) after N blocks of 100 hands.
We take the derivative with respect to N (abbreviate Winrate_per_100hands as WR and SD_per_100hands as SD):

D(winnings)/Dn = WR - (3/2)SD/[SQRT(N)].

We set this derivative equal to 0 and solve for N:

N= [1.5SD/WR]^2

Now plug this back into your Winnings equation:

Winnings = 2.25SD^2/WR - 4.5*SD^2/WR = -2.25SD^2/WR

So...we see that your worst possible downswing is proportional to the square of your SD and inversely proportional to your WR. So halving your winrate doubles your worst possible downswing. Going from 2bb/100 to 0.2bb/100 multiplies your worst possible downswing by a factor of 10.

Hope this helps.

Re: Does a decreased winrate have an exponential effect on variance?
 

[ QUOTE ]
Hey guys, there is a mathematical reason your "swinginess" goes up when your winrate goes down as a result of tilt or other factors. Your swinginess is measured by your coefficient of variation, the ratio of your standard deviation to your winrate. As a result, your "swinginess" increases exponentially as your winrate approaches zero, even though your standard deviation stays the same.

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BZZZT! Thank you for playing.

Swinginess increases without limit as win rate goes to zero, but it most assuredly does not increase exponentially.

Re: Does a decreased winrate have an exponential effect on variance?
 

If I have a gun and you have a knife, and you run towards me brandishing the knife in your hand, the fact that it is very easy for me to gun you down before you get close to me does not alter the fact that attacking someone with a knife is an act of aggression.

Despite the fact that nearly all competent poker players are aggressive, this does not make aggression identically equal to competence. It is very easy to be incompetently aggressive.

Betting and raising are aggressive. Checking, calling, and folding are passive.

An out-of-control angry player is more likely to be aggressive than passive. This is the nature of anger.

Re: Does a decreased winrate have an exponential effect on variance?
 

Let me put all this math into English for our poker player readers.

It does not take many hands lost to affect your win rate. When you win you win what the other players put into the pot and you KEEP you what put into the pot. Your share is not won money. When you lose you lose the money you should have won from other players and your money. So you lose more than you win when you lose.

Other factors. If you run good players fear you. They think your lucky. They will play predictable against you and NOT bluff. So you know where you stand at all times. You can bluff more. All you need is one extra bluff an hour to increase your BB/100 a large amount. Look at it this way if you bluff just one $25 pot in 3/6 extra every hour thats at least 2-3 BB extra an hour.

Now look at the other side of the coin. Your losing. Now you CAN'T bluff, other players get unpredictable and try to bluff. You slightly tilt can't believing you got drawn out again so you may call a bit more. Even if you just lose just one extra pot an hour due to a well placed semibluff you decrease your win rate 2-3 BB. Now add lets say 1 BB of tilt. Well look at the shift.

Running hot: Bluff +2-3 BB, Plays well -0 BB, Players predictable thus saves you bets +1 BB
Running poorly: No bluff -?, Players bluff you -2 to -3 BB, Tilt -1 BB.

Its simple but it gets the point accross.

Thats why I...

Always buy in for more: New players entering the table see you are already lucky. Also good players coming to the table will usually leave once they see a couple big stacks. I do.

Switch tables: If you're running bad switch tables. I don't care how fishy they are those players are feeling "lucky" and are playing comfortable. They might get some balls and bluff you now and then. I've seen VPIP 50, PRF 0.4, TAF.6 start bluffing at the table when this fish is feeling good. When he feels bad he NEVER bluffs and only raises when he's got it. You want the other guy on tilt not you. Move to a new table.

Quit for 30 mins: If all your tables are bad, quit go do some excersize, have sex with the wife/gf, step outside and get some air, go eat something. Get away from the mindset and environment that is frustrating you.

Nufsed.

Re: Does a decreased winrate have an exponential effect on variance?
 

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What is the nature of tilt?

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Bad dialogue?

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NH, sir.

Re: Does a decreased winrate have an exponential effect on variance?
 

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It does not take many hands lost to affect your win rate. When you win you win what the other players put into the pot and you KEEP you what put into the pot. Your share is not won money. When you lose you lose the money you should have won from other players and your money. So you lose more than you win when you lose.

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LOL. that has to be the funniest thing ive ever read on 2p2. ever.

just to clarify so people dont listen to this:

in a 4 bet capped internet game, what is the most you can lose in 1 hand? 12bbs

what is the most you can possibly win (net) in 1 hand? 108bbs.

on average, when you win, you win way more than you lose when you lose.

what OP was trying to get at is that when you lose, you lose the bets you put in + the bets you would have won from the opponents had you won. but OP doesn't take it the OTHER way. i.e. when you win, the swing could be just as large b/c had you lost, you'd lose all the bets you won + the bets you got to "keep" from your stack.

silliest logic ever by OP.

Barron

Re: Does a decreased winrate have an exponential effect on variance?
 

This poker player reader thanks you for putting his post into English.