Hi Chomp,
The worst/best/ run line is simply the line of the player(trial) who had the worst/best results out of that group of simulators...not the worst run possible. So in the graph above, the green line is from the player who ran the best out of the 1000 trials simulated, and the blue is the line of the player who had the worst results out of the 1000.
If you look at the distribution of winrates graph the green line corresponds to the bin at the far right of that graph (winrate of ~17bb/100) and the blue line corresponds to the bin at the far left of the graph (winrate ~ -1).
This can be interpreted as around 1 in 1000 players will run that bad. If we increased the number of trials to 1 000 000, the worst/best runs would be even more dramatic.
2. That is exactly right.
3. A meaningful sample size is largely determined by your standard deviation If we look at a plot for an 8bb/100 with a 40bb/100 SD then I think that anyone looking at any of these lines in isolation would conclude that it was the graph of a winning poker player:
So we can say that 100 000 hands is a "meaningful" sample in this case.
If however we crank up the sd to 140 (say for something like hu plo):
then looking at many of these lines in isolation we would be hard pressed to convince someone that the person was a winning poker player (we however know they are, because we know their theoretical winrate is 8bb/100). So in this case 100 000 hands likely isn't big enough to be considered a "meaningful sample".
Make sense?
Last edited by Neko; 02-11-2010 at 05:25 AM.
Reason: added pic.