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Old 05-19-2005, 01:18 PM
QTip QTip is offline
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Join Date: Sep 2004
Posts: 31
Default Re: Short-Handed Flucuations

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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.

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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?
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