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 Probability Discussions of probability theory

 01-03-2010, 08:33 AM #1 Neko Pooh-Bah   Join Date: Jul 2005 Posts: 4,000 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
 01-03-2010, 09:22 AM #2 Neko Pooh-Bah   Join Date: Jul 2005 Posts: 4,000 Re: Variance/Winrate Simulator
 01-03-2010, 09:56 AM #3 Karganeth old hand     Join Date: Jun 2008 Posts: 1,305 Re: Variance/Winrate Simulator Cool.
01-08-2010, 02:05 PM   #4
Green_29
veteran

Join Date: Apr 2009
Location: running out of cash
Posts: 3,037
Re: Variance/Winrate Simulator

Quote:
 Originally Posted by Neko
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?

 01-08-2010, 02:30 PM #5 Neko Pooh-Bah   Join Date: Jul 2005 Posts: 4,000 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.
 01-08-2010, 03:43 PM #6 Green_29 veteran     Join Date: Apr 2009 Location: running out of cash Posts: 3,037 Re: Variance/Winrate Simulator ok I see now, thanks.
 02-04-2010, 03:10 PM #7 8Nilor old hand     Join Date: Jun 2009 Posts: 1,543 Re: Variance/Winrate Simulator Yup, my 3500bb downswing definitely makes me a special boy. I find this really handy btw. Thanks for making it.
 02-04-2010, 05:48 PM #8 Neko Pooh-Bah   Join Date: Jul 2005 Posts: 4,000 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!
 02-05-2010, 11:33 PM #9 8Nilor old hand     Join Date: Jun 2009 Posts: 1,543 Re: Variance/Winrate Simulator Me and a friend actually found it on google. And then google lead me back to this thread lol
 02-09-2010, 09:10 AM #10 Neko Pooh-Bah   Join Date: Jul 2005 Posts: 4,000 Re: Variance/Winrate Simulator Just added Longest-Breakeven-Stretch graphs as well. Thanks to Moshiach for the suggestion!
 02-10-2010, 09:46 PM #11 Chomp Pooh-Bah     Join Date: May 2006 Location: Pretty terrible at poker Posts: 3,716 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.
 02-11-2010, 05:24 AM #12 Neko Pooh-Bah   Join Date: Jul 2005 Posts: 4,000 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.
 02-11-2010, 06:20 AM #13 Chomp Pooh-Bah     Join Date: May 2006 Location: Pretty terrible at poker Posts: 3,716 Re: Variance/Winrate Simulator Makes perfect sense, thanks very much Neko. Seems like a really nifty creation, congrats.
 02-11-2010, 06:27 AM #14 Neko Pooh-Bah   Join Date: Jul 2005 Posts: 4,000 Re: Variance/Winrate Simulator Thanks Chomp
 02-13-2010, 11:12 PM #15 foal Pooh-Bah     Join Date: Apr 2007 Location: half villain, half good player Posts: 3,588 Re: Variance/Winrate Simulator Excellent program. Are SDs of 100bb/100 actually typical at all? Seems a bit high to me...
 02-14-2010, 07:11 AM #16 Neko Pooh-Bah   Join Date: Jul 2005 Posts: 4,000 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.
 02-14-2010, 07:23 AM #17 foal Pooh-Bah     Join Date: Apr 2007 Location: half villain, half good player Posts: 3,588 Re: Variance/Winrate Simulator ah PLO, that makes sense.
 04-20-2010, 04:26 PM #18 johan313 journeyman   Join Date: Jul 2008 Posts: 295 Re: Variance/Winrate Simulator source available for personal use? Johan
 04-20-2010, 06:39 PM #19 mtnpoker journeyman     Join Date: Nov 2007 Location: Los Angeles Posts: 204 Re: Variance/Winrate Simulator Will this work for SnGs? Or is there something similar that will?
04-20-2010, 07:38 PM   #20
Neko
Pooh-Bah

Join Date: Jul 2005
Posts: 4,000
Re: Variance/Winrate Simulator

Quote:
 Originally Posted by johan313 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 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

04-21-2010, 06:36 AM   #21
johan313
journeyman

Join Date: Jul 2008
Posts: 295
Re: Variance/Winrate Simulator

Quote:
 Originally Posted by Neko 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 =)

04-21-2010, 06:43 PM   #22
DarkMagus
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Join Date: Jul 2007
Posts: 8,389
Re: Variance/Winrate Simulator

Quote:
 Originally Posted by foal 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

04-21-2010, 06:57 PM   #23
Sherman
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Join Date: Jun 2005
Location: Psychology Department
Posts: 7,764
Re: Variance/Winrate Simulator

Quote:
 Originally Posted by DarkMagus 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!

04-23-2010, 03:46 PM   #24
Neko
Pooh-Bah

Join Date: Jul 2005
Posts: 4,000
Re: Variance/Winrate Simulator

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

 04-26-2010, 02:19 PM #25 black666 Pooh-Bah     Join Date: Dec 2006 Location: cut that meat Posts: 4,287 Re: Variance/Winrate Simulator awesome tool. ty!

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