ich zitiere mal direkt von dort:
"First, the winners. We have 10 of these guys; they win at 2BB/100, and the sd is 12 as usual. But we assume we have more data on them as winners play more, so they've all done ten sessions. Generating random variates from the appropriate normal distribution, and then multiplying by 10 to turn win rate numbers into actual winnings, here are their bank balances:
Those are their scores in big bets after 1000 hands. Let's assume the game is 0.50c / $1, so that these numbers can be treated as actual dollar amounts. Now a 2BB/100 winner expects to make $20 if he plays 1000 hands of 0.50/$1, right? So hopefully you agree that the above looks like a perfectly plausible distribution of wins / losses. Two guys get lucky and make more than $50, two guys have a bad run and lose money, etc. It's a picture I'm sure you're all familiar with.
Now let's do the losers. In line with our assumptions there will be 90 of them in the database. They don't play as much, so we only have a single 100 hand session on each of these guys. Let's assume they are significant losers: they expect to drop 2 BB/100. Their sd is 12 BB/100. So it's easy to generate their wins/losses from the appropriate normal distribution. Here are the numbers:
Notice it's true that idiots get lucky sometimes. There's one guy in there who made $24.35 in 100 hands, despite being an awful player. But the average win/loss is very close to what we'd expect: -$1.96. The part you might find hard to swallow is that 41 of the 90 (nearly half!) are actually winners over the 100 hands. But think for a minute about a bell curve centred on -2, with arms extending all the way out to about -38 on the left and +34 on the right (i.e., plus or minus 3 standard deviations). It's obvious that close to half the area of that curve will be in positive territory. In the short run (100 hands) many idiots don't actually lose. But in the long run the law of large numbers will catch up to them, don't worry.
So anyway, the final step is that we add the two groups of players (theoretical winners and theoretical losers) together. Then count the number of actual winners. This is easy: with 8 winners in the winning players group, and 41 winners in the losing players group, we have a 49% winners figure for our imaginary poker tracker database. This number, obviously, bears little relation to the underlying truth that only 10% of those players know what they're doing.
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