Questions about PT4 and variance

Variance is one of my favourite subjects.

Every single card dealt in every hand is subject to variance, because it is an random event. Using software like PT4, we can look at Cwon all in adj and our luck bell curve and say we are lucky or unlucky but these are really only tiny aspects of your total variance which cannot be measured. However, we can calculate the likelihood of how far we are away from our actual/real winrate, which over large sample sizes is likely to be pretty close to our winrate we see in PT4.

We can still be really unlucky or lucky over 150K hands but the vast majority of the population (approx 95%) will be between slightly unlucky and slightly lucky.

As the number of hands we play tends towards infinity then variance tends towards zero.

In conclusion, in Poker, we shouldn't dwell on how lucky or unlucky we are as we cannot control it and we cannot measure it.

Originally Posted by DJAbacus

Variance is one of my favourite subjects.

You should study it, then. I'm happy to answer questions on the subjects of math and physics. Fire away.

Originally Posted by DJAbacus

As the number of hands we play tends towards infinity then variance tends towards zero.

Umm.... What? That statement is incredibly misleading - and flat out false for non-convergent statistics.

Props for correct use of "tends toward infinity" there, though.

Originally Posted by DJAbacus

In conclusion, in Poker, we shouldn't dwell on how lucky or unlucky we are as we cannot control it and we cannot measure it.

You just described how it is measured.

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I'm guessing you've had some college level calculus, but you haven't taken either a Probability or a Statistics class, yet.
?

You have the passion, so buy a book. Study this stuff for yourself, even if you're not in school. If you are in school, then you'll be miles ahead of your own education. It's win-win.

Watch out everyone it's the Variance police. I'm guessing you don't get out much.

If you play an infinite number of hands then variance will be equal to zero and therefore our winrate is therefore our 'true winrate' or 'skill level' if you like.

In the following video, over an infinite sample size the 'normal distribution' curve will be effectively an infinitely thin line.

https://www.youtube.com/watch?v=5416oRqykJw

So all we need to realise is that the more hands we play the more likely our winrate reflects our skill level.

So if we play 250K hands and our winrate is 5BBs/100 then it is likely that our skill level is closer to this than if we have a 5BBs/100 winrate over 50K hands.

Originally Posted by MadMojoMonkey

You just described how it is measured.

Ok, maybe I should have said it cannot be measured exactly



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Originally Posted by DJAbacus

Watch out everyone it's the Variance police. I'm guessing you don't get out much.

I could explain the finer points between convergent and non-convergent stats.

I could explain why that video has nothing to do with poker or any stat you'd like to estimate that would help guide your decisions in a poker hand.

I could explain why the normal distribution is NOT an unbiased estimator for statistics based on Bernoulli trials.

I could, but I see that you've got it all figured out.

Sorry to have wasted your time, DJ. Where can I buy your book on probability and statistics?


@renegaderob: If there's anything you'd like clarification on, please keep asking questions until you fully understand.

Originally Posted by MadMojoMonkey

I could explain why that video has nothing to do with poker or any stat you'd like to estimate that would help guide your decisions in a poker hand.

It's simple really.

You bet on tails.

You flip a coin 30 times and it comes up tails 20 times. You have been lucky.

It comes up heads 20 times. You have been unlucky.

You flip the coin an infinite number of times and you will win 50% of the time, neither lucky or unlucky.

Poker is a more complicated scenario, with many variables but over an infinite number of hands we win or lose based on our 'Poker Skills' as we are neither lucky nor unlucky over an infinite sample.