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 ?