Variance/Winrate Simulator
01-03-2010
, 08:33 AM
Hey Guys,
Thought some of you might be interested in this. I've set up an online variance simulator that you can input a winrate and standard deviation and then run a set of trials to see how well/poorly you could possibly run over a given number of hands. Output looks like this:
You can increase the number of trials and plot the worst/best runs from those trials:
The frequency of having a downswing of at least X bb:
The above is a cumulative histogram of the distribution of largest downswings from all the runs. The far left (probability of 1) represents the smallest downswing from all the runs (ie. everyone will experience a downswing at least this big). The far right (probability close to zero) represents the largest downswing from all runs.
And the distribution of all winrates for the simulated runs:
Hope somebody finds this useful or has a bit of fun with it
Thought some of you might be interested in this. I've set up an online variance simulator that you can input a winrate and standard deviation and then run a set of trials to see how well/poorly you could possibly run over a given number of hands. Output looks like this:
You can increase the number of trials and plot the worst/best runs from those trials:
The frequency of having a downswing of at least X bb:
The above is a cumulative histogram of the distribution of largest downswings from all the runs. The far left (probability of 1) represents the smallest downswing from all the runs (ie. everyone will experience a downswing at least this big). The far right (probability close to zero) represents the largest downswing from all runs.
And the distribution of all winrates for the simulated runs:
Hope somebody finds this useful or has a bit of fun with it
01-08-2010
, 02:05 PM
Why here is the best run lower than the worst run, shouldn't it be the other way around?
[/QUOTE]
So looking at this graph I can say the the chances of this player going on a 20 buyin downswing (2000 bb's) in 100,000 hands in 20%? Is that correct?
[/QUOTE]So looking at this graph I can say the the chances of this player going on a 20 buyin downswing (2000 bb's) in 100,000 hands in 20%? Is that correct?
01-08-2010
, 02:30 PM
Hey Green,
It's 40% (follow gridline at 2000bb's up and it almost exactly hits the .4 mark) but yes that is roughly the correct way to interpret that graph.
To be more precise it is not strictly a probability but a frequency from the sample of trials; to generate that graph I ran a 100 000 hand sample (nhands = 100 000) for 1000 different players (ntrials=1000) who all win at exactly 8bb/100 hands. Out of those particular trials every single one of the players experienced a downswing of ~8bi, 40% of the players underwent a downswing of 20 bi's and roughly 2% of players underwent a downswing of 40 b.i.'s. The worst downswing experienced by a single player is in the neighbourhood of 53 bis.
Now if we run that calculation again for a different 1000 players:
Then we see a slightly different graph since the individual results for the 1000 players are different.
It's 40% (follow gridline at 2000bb's up and it almost exactly hits the .4 mark) but yes that is roughly the correct way to interpret that graph.
To be more precise it is not strictly a probability but a frequency from the sample of trials; to generate that graph I ran a 100 000 hand sample (nhands = 100 000) for 1000 different players (ntrials=1000) who all win at exactly 8bb/100 hands. Out of those particular trials every single one of the players experienced a downswing of ~8bi, 40% of the players underwent a downswing of 20 bi's and roughly 2% of players underwent a downswing of 40 b.i.'s. The worst downswing experienced by a single player is in the neighbourhood of 53 bis.
Now if we run that calculation again for a different 1000 players:
Then we see a slightly different graph since the individual results for the 1000 players are different.
02-11-2010
, 05:24 AM
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?
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.
04-23-2010
, 03:46 PM
