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Old 01-03-2010, 08:33 AM   #1
Neko
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Variance/Winrate Simulator

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
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Old 01-03-2010, 09:22 AM   #2
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Re: Variance/Winrate Simulator

oops link is http://www.evplusplus.com/poker_tool...nce_simulator/
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Old 01-03-2010, 09:56 AM   #3
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Re: Variance/Winrate Simulator

Cool.
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Old 01-08-2010, 02:05 PM   #4
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Re: Variance/Winrate Simulator

Quote:
Originally Posted by Neko View Post
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?
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Old 01-08-2010, 02:30 PM   #5
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Re: Variance/Winrate Simulator

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.
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Old 01-08-2010, 03:43 PM   #6
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Re: Variance/Winrate Simulator

ok I see now, thanks.
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Old 02-04-2010, 03:10 PM   #7
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Re: Variance/Winrate Simulator

Yup, my 3500bb downswing definitely makes me a special boy.

I find this really handy btw. Thanks for making it.
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Old 02-04-2010, 05:48 PM   #8
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Re: Variance/Winrate Simulator

My pleasure 8N. I'm glad so many people are enjoying it...theres been about 3500 simulations run since I posted this thread!
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Old 02-05-2010, 11:33 PM   #9
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Re: Variance/Winrate Simulator

Me and a friend actually found it on google. And then google lead me back to this thread lol
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Old 02-09-2010, 09:10 AM   #10
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Re: Variance/Winrate Simulator

Just added Longest-Breakeven-Stretch graphs as well. Thanks to Moshiach for the suggestion!

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Old 02-10-2010, 09:46 PM   #11
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Re: Variance/Winrate Simulator

Interesting tool. Three quick questions if I may.

1. In the main sample graph in OP the "worst run" line for the player is showing something like -1000bb's over the 100k sample. Now, say that player is indeed -10BI's over that 100k hands - what does that mean? That he has run as badly as he possibly could have over that sample for his wr & SD? (It's possible I'm totally misunderstanding SD here btw).

2. On the graph just above this post am I reading it correctly: "Over a 100k sample, the chances of this player having a 40k hand breakeven during those 100k hands is about 30%". Is that right?

3. Having looked at these large samples, have you come to any conclusions as to meaningful sample sizes?


Thanks.
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Old 02-11-2010, 05:24 AM   #12
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Re: Variance/Winrate Simulator

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.
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Old 02-11-2010, 06:20 AM   #13
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Re: Variance/Winrate Simulator

Makes perfect sense, thanks very much Neko. Seems like a really nifty creation, congrats.
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Old 02-11-2010, 06:27 AM   #14
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Re: Variance/Winrate Simulator

Thanks Chomp
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Old 02-13-2010, 11:12 PM   #15
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Re: Variance/Winrate Simulator

Excellent program.

Are SDs of 100bb/100 actually typical at all? Seems a bit high to me...
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Old 02-14-2010, 07:11 AM   #16
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Re: Variance/Winrate Simulator

Thanks foal. 100bb/100 would be probably very high in some games but my SD in 1/2 6max PLO over 50k hands is something like 110bb/100. Crazy game.
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Old 02-14-2010, 07:23 AM   #17
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Re: Variance/Winrate Simulator

ah PLO, that makes sense.
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Old 04-20-2010, 04:26 PM   #18
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Re: Variance/Winrate Simulator

source available for personal use?

Johan
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Old 04-20-2010, 06:39 PM   #19
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Re: Variance/Winrate Simulator

Will this work for SnGs? Or is there something similar that will?
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Old 04-20-2010, 07:38 PM   #20
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Re: Variance/Winrate Simulator

Quote:
Originally Posted by johan313 View Post
source available for personal use?

Johan
Hadn't considered releasing the source before now but I wouldn't mind doing so when I get some free time to clean it up a bit (It's only ~200 lines of python code fwiw). Bug me in a week if I haven't got to it by then.

Quote:
Originally Posted by mtnpoker View Post
Will this work for SnGs? Or is there something similar that will?
Check these two threads for sng specific tools:
https://forumserver.twoplustwo.com/36...ariance-73786/

https://forumserver.twoplustwo.com/sh...6&postcount=12
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Old 04-21-2010, 06:36 AM   #21
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Re: Variance/Winrate Simulator

Quote:
Originally Posted by Neko View Post
Hadn't considered releasing the source before now but I wouldn't mind doing so when I get some free time to clean it up a bit (It's only ~200 lines of python code fwiw). Bug me in a week if I haven't got to it by then.

Ok, thx, ill bug you in a week =)
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Old 04-21-2010, 06:43 PM   #22
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Re: Variance/Winrate Simulator

Quote:
Originally Posted by foal View Post
Excellent program.

Are SDs of 100bb/100 actually typical at all? Seems a bit high to me...
at 6max NLHE (200nl and 400nl) my SD averages between 100-110 bb/100. at plo over a small sample i average like 130-140 bb/100 but that's cause i just started playing it and for most of my hands i played way too loose/spazzy

if u play full ring, or play pretty tight 6max, i guess you'd get a smaller SD but 100bb/100 isn't unreasonable at all for 6max
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Old 04-21-2010, 06:57 PM   #23
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Re: Variance/Winrate Simulator

Quote:
Originally Posted by DarkMagus View Post
at 6max NLHE (200nl and 400nl) my SD averages between 100-110 bb/100. at plo over a small sample i average like 130-140 bb/100 but that's cause i just started playing it and for most of my hands i played way too loose/spazzy

if u play full ring, or play pretty tight 6max, i guess you'd get a smaller SD but 100bb/100 isn't unreasonable at all for 6max
Ya, at HUNL I have around 8bb/100 WR with 122bb/100 SD. Yikes!
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Old 04-23-2010, 03:46 PM   #24
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Re: Variance/Winrate Simulator

Quote:
Originally Posted by johan313 View Post
Ok, thx, ill bug you in a week =)
Didn't want you bugging me in a week

http://www.evplusplus.com/poker_tool...ator/download/
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Old 04-26-2010, 02:19 PM   #25
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Re: Variance/Winrate Simulator

awesome tool. ty!
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