Short-Handed Flucuations

[chief444]

One standard deviation means 66% of the times you play 100 hands you're somewhere in this range. I think...dude it's been like 10 yrs + since I actually opened a book on this so maybe some of the younger ivey leagers can explain better and correct me if this is wrong. Basically, you're not ALWAYS within that range. You're just withing that range most of the time. There will always be very extreme data/sessions. If the 66% is right, it's just sort of a random standard used evaluating data.

[Octopus]

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A greater edge doesn't mean your variance will change. It just mean your winrate will be higher.

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Gotcha! Your variance is simply a measure of short-term luck (for both you and your opponents), right? The edge you have over your opponents would not change that. That would simply change the fact that you're going to win more. Is it more complicated than that or am I right on?

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You are right on and it is more complicated than that. The two things are not unrelated.

For example, if your edge over your opponents came from them betting/raising everytime it was their turn to act, regardless of their holdings, then both your winrate and your variance would be much higher than it they are now.

In other words, how your opponents play has a direct effect on your own variance.

[QTip]

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One standard deviation means 66% of the times you play 100 hands you're somewhere in this range. I think...dude it's been like 10 yrs + since I actually opened a book on this so maybe some of the younger ivey leagers can explain better and correct me if this is wrong. Basically, you're not ALWAYS within that range. You're just withing that range most of the time. There will always be very extreme data/sessions. If the 66% is right, it's just sort of a random standard used evaluating data.

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oh...ok...it's not any math that we did with our PT numbers. 66% (or whatever it is) is what's been figured out by the math geeks to say what SD means.

[QTip]

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[ QUOTE ]
A greater edge doesn't mean your variance will change. It just mean your winrate will be higher.

[/ QUOTE ]

Gotcha! Your variance is simply a measure of short-term luck (for both you and your opponents), right? The edge you have over your opponents would not change that. That would simply change the fact that you're going to win more. Is it more complicated than that or am I right on?

[/ QUOTE ]

You are right on and it is more complicated than that. The two things are not unrelated.

For example, if your edge over your opponents came from them betting/raising everytime it was their turn to act, regardless of their holdings, then both your winrate and your variance would be much higher than it they are now.

In other words, how your opponents play has a direct effect on your own variance.

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OK..now THAT'S why I've always felt that variance is generally higher in the 6 max games...because people tend to play much more aggressively.

[chief444]

Yeah, and as Octopus pointed out it's actually 68.2%. It's funny...when I went through school I learned so much terminology and specifics that it was sometimes difficult to recognize applications and keep focus on the general concepts. Now I forget half of the specifics/terminology but the applications and concepts are far more obvious.

Obviously a slow day at work. [img]/images/graemlins/grin.gif[/img]

[QTip]

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Obviously a slow day at work.

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I'll get fired if I keep this up! [img]/images/graemlins/frown.gif[/img] But, there are so many good things going on in here today, I can't get myself to leave. Soon, I'll have to pull a Josh and have someone change my password...

[JoshuaD]

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I GOT IT!!!!! YEAH BABY!! THANKS SO MUCH!

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[img]/images/graemlins/laugh.gif[/img]

[Octopus]

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oh...ok...it's not any math that we did with our PT numbers. 66% (or whatever it is) is what's been figured out by the math geeks to say what SD means.

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Exactly. Here is one way to think about it. (This is somewhat technical, but you seem interested.)

Suppose everytime you play 100 hands, what actually happens is that you reach into a bag and draw a number which is the amount you win or lose. What we are talking about is what numbers are in the bag. Note that there are a lot more numbers close to your true win rate than there are numbers far from your win rate. (You will win about 5BB far more often than you will win about 25BB.) This is generally true; the further from the win rate, the less likely you are to draw that number. Whatever is in the bag is called the 'distribution'.

The percentages come from a "normal distribution" - the so called bell-curve. This distribution is special. It turns out that if you take a bunch of draws from a non-normal distribution (say, winnings in a hand of poker) and average the results and you do this a bunch of times, the distribution of the averages will be approximately normal. As I say in another post in this thread, winnings per hand or winnings per 100 hands are not particularly normal, but winnings per 1,000 or 10,000 hands are much closer.

We know exactly the probability of being a certain distance (or further) from the mean for a normal distribution and these are the probabilities that you see all the time here. A normal distribution is completely described by its mean and its standard deviation. Here are some probabilities, for your reference:

There is a 31.8% chance of being more than 1 SD above or below the mean.
There is a 4.55% chance of being more than 2 SD above or below the mean.
There is a 0.27% chance of being more than 3 SD above or below the mean.
There is a 0.00634% chance of being more than 4 SD above or below the mean.

[chief444]

Nice explanation. And thanks for the refresher on the exact #'s. [img]/images/graemlins/grin.gif[/img]

[QTip]

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oh...ok...it's not any math that we did with our PT numbers. 66% (or whatever it is) is what's been figured out by the math geeks to say what SD means.

[/ QUOTE ]

Exactly. Here is one way to think about it. (This is somewhat technical, but you seem interested.)

Suppose everytime you play 100 hands, what actually happens is that you reach into a bag and draw a number which is the amount you win or lose. What we are talking about is what numbers are in the bag. Note that there are a lot more numbers close to your true win rate than there are numbers far from your win rate. (You will win about 5BB far more often than you will win about 25BB.) This is generally true; the further from the win rate, the less likely you are to draw that number. Whatever is in the bag is called the 'distribution'.

The percentages come from a "normal distribution" - the so called bell-curve. This distribution is special. It turns out that if you take a bunch of draws from a non-normal distribution (say, winnings in a hand of poker) and average the results and you do this a bunch of times, the distribution of the averages will be approximately normal. As I say in another post in this thread, winnings per hand or winnings per 100 hands are not particularly normal, but winnings per 1,000 or 10,000 hands are much closer.

We know exactly the probability of being a certain distance (or further) from the mean for a normal distribution and these are the probabilities that you see all the time here. A normal distribution is completely described by its mean and its standard deviation. Here are some probabilities, for your reference:

There is a 31.8% chance of being more than 1 SD above or below the mean.
There is a 4.55% chance of being more than 2 SD above or below the mean.
There is a 0.27% chance of being more than 3 SD above or below the mean.
There is a 0.00634% chance of being more than 4 SD above or below the mean.

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Really interesting stuff. So, when I go on 200BB downswing over 5 sessions, that's because I was lucky enough (assuming my play has not changed) to reach into the bag and pull out these negative # far from my expected winrate?