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#1
10-20-2007, 08:02 AM
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Variance is Fractal
You cant get a truthful picture of the "variance" of a thing unless you have the mean to that thing. If you do not document wins/losses and keep stats then you have no way of calculating your mean, variance or EV (unless you are annette_15).
(fixed variance) example: The mean (long run) win rate for AA vs KK HU seeing all 5 cards is 83%. A measured sample over say 200 games of a win rate of 72% is variance. The more sessions, or iterations the closer you get to the true "mean" of that thing. The mean is the truth of an equation. In this example the mean was the win rate of AA vs KK HU while seeing all five cards. There is (fixed) variance (odds), and there is variance of your theoretical "edge" (dynamic) and tilt (dynamic).... By using solid bankroll management, variance will rarely have you lifting an eyebrow unless you've been on tilt. It often makes the hair on the back of your neck stand on end with or without tilt! 
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#5
10-21-2007, 11:56 AM
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Re: Variance is Fractal
[ QUOTE ]
You cant get a truthful picture of the "variance" of a thing unless you have the mean to that thing. [/ QUOTE ] That depends entirely on the relative size of the mean and standard deviation. An error of 1% on the mean causes an error of 1% of the mean on the standard deviation. If the mean is small compared to the standard deviation (say on a one-day stock return), this is a trivial error and you can estimate the variance far more accurately than the mean. If the mean is large compared to the standard deviation (say on heights of healthy adult males), this is a large effect. [ QUOTE ] If you do not document wins/losses and keep stats then you have no way of calculating your mean, variance or EV (unless you are annette_15). [/ QUOTE ] I half agree. You don't have to document anything, but you do have to keep some statistics. You don't need to record every hand result, but you should keep at least open, high, low and close bankrolls per session. I know of no way to compute poker win parameters without data. [ QUOTE ] (fixed variance) example: The mean (long run) win rate for AA vs KK HU seeing all 5 cards is 83%. A measured sample over say 200 games of a win rate of 72% is variance. The more sessions, or iterations the closer you get to the true "mean" of that thing. The mean is the truth of an equation. In this example the mean was the win rate of AA vs KK HU while seeing all five cards. [/ QUOTE ] Actually, AA beats KK 1,399,204 out of 1,712,304 times, for 81.7%. It also ties 7,923 times which gives equity (tie counts as half win) of 82.2%. In this example, the mean (82.2%) is high compared to the standard deviation (37.8%). If you measure a 72% win rate for AA, you will estimate a 44.9% standard deviation. Your 14% error on the mean will correspond to a 41% error on the variance. But this is only because you postulate a mean higher than the standard deviation. Suppose you measured the KK win rate instead of the AA win rate. Now your error on the mean is 57% (you measured 28% instead of the correct 17.8%). So now the error on the mean is larger than the error on the variance. [ QUOTE ] There is (fixed) variance (odds), and there is variance of your theoretical "edge" (dynamic) and tilt (dynamic).... By using solid bankroll management, variance will rarely have you lifting an eyebrow unless you've been on tilt. [/ QUOTE ] I agree the first sentence is a reasonable way to analyze edge. The second is a matter of preference. If you play poker to grow your bankroll, it often makes sense to take risk with it. Poker without bankroll risk is called "penny ante." It's a fun game for kids and people who hate risk. [ QUOTE ] It often makes the hair on the back of your neck stand on end with or without tilt! [/ QUOTE ] This seems to be the opposite of what you said above. If it's true for you, I suggest you shave your neck to get rid of the tell.
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#7
10-21-2007, 06:27 PM
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Re: Variance is Fractal
[ QUOTE ]
[ QUOTE ] You cant get a truthful picture of the "variance" of a thing unless you have the mean to that thing. [/ QUOTE ] That depends entirely on the relative size of the mean and standard deviation. An error of 1% on the mean causes an error of 1% of the mean on the standard deviation. If the mean is small compared to the standard deviation (say on a one-day stock return), this is a trivial error and you can estimate the variance far more accurately than the mean. If the mean is large compared to the standard deviation (say on heights of healthy adult males), this is a large effect. [ QUOTE ] If you do not document wins/losses and keep stats then you have no way of calculating your mean, variance or EV (unless you are annette_15). [/ QUOTE ] I half agree. You don't have to document anything, but you do have to keep some statistics. You don't need to record every hand result, but you should keep at least open, high, low and close bankrolls per session. I know of no way to compute poker win parameters without data. [ QUOTE ] (fixed variance) example: The mean (long run) win rate for AA vs KK HU seeing all 5 cards is 83%. A measured sample over say 200 games of a win rate of 72% is variance. The more sessions, or iterations the closer you get to the true "mean" of that thing. The mean is the truth of an equation. In this example the mean was the win rate of AA vs KK HU while seeing all five cards. [/ QUOTE ] Actually, AA beats KK 1,399,204 out of 1,712,304 times, for 81.7%. It also ties 7,923 times which gives equity (tie counts as half win) of 82.2%. In this example, the mean (82.2%) is high compared to the standard deviation (37.8%). If you measure a 72% win rate for AA, you will estimate a 44.9% standard deviation. Your 14% error on the mean will correspond to a 41% error on the variance. But this is only because you postulate a mean higher than the standard deviation. Suppose you measured the KK win rate instead of the AA win rate. Now your error on the mean is 57% (you measured 28% instead of the correct 17.8%). So now the error on the mean is larger than the error on the variance. [ QUOTE ] There is (fixed) variance (odds), and there is variance of your theoretical "edge" (dynamic) and tilt (dynamic).... By using solid bankroll management, variance will rarely have you lifting an eyebrow unless you've been on tilt. [/ QUOTE ] I agree the first sentence is a reasonable way to analyze edge. The second is a matter of preference. If you play poker to grow your bankroll, it often makes sense to take risk with it. Poker without bankroll risk is called "penny ante." It's a fun game for kids and people who hate risk. [ QUOTE ] It often makes the hair on the back of your neck stand on end with or without tilt! [/ QUOTE ] This seems to be the opposite of what you said above. If it's true for you, I suggest you shave your neck to get rid of the tell. [/ QUOTE ] Good post Arron, clarified a few things for me. I used poker stove for the aa vs kk. The comment didn't refer to a session or any one group of things. More of a "looking back" chill watching the 15ft surf roll by. Some waves are shredable 10 footers while every now and then you catch and ride a monster. Whether you barely survive the wipe out or hold a 6 second barrel you'll always remember and "re live" it looking back, once the high/low is gone. Once you come back "home".
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#8
10-21-2007, 06:30 PM
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Re: Variance is Fractal
[ QUOTE ]
[ QUOTE ] Can you say Mandelbrot backwards? [/ QUOTE ] Can you explain what fractals have to do with simple variance? [/ QUOTE ] Who said variance was simple?
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#10
10-21-2007, 07:07 PM
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Re: Variance is Fractal
The very nature of what variance "IS", is fractal. This makes every process both of the transparent and non transparent kind also fractal.
My point is that by knowing this and by being aware of this fractal nature of variance, we can consciously keep "the math" in harmony (which includes various "standard deviations" with various magnitudes) which can improve our game. I think that through a deeper understanding of what variance "is", we can all but remove the "tilt" factor which for most, is our biggest enemy. By realizing that variance IS fractal, we take it out of a box that we have sub consciously put it in, which makes it tough to analyze and fix leaks un in an unbiased way (which should be a goal). By putting variance in perspective, we can see why anyone who "hates" variance is not a long term consistent winner, in this "game".
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