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Old 04-26-2015, 10:34 PM   #101
MrBubbleBoy
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Can op maybe add cash variance or suggest a simulator that does?
BTW great work

Is it possible to create an easier way to reduce our ROI though?

I.e. just putting in roi of 3% and letting the numbers do the work instead of having to play around with 1st % 2nd % 3rd % ?
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Old 04-27-2015, 08:00 AM   #102
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Quote:
Originally Posted by MrBubbleBoy View Post
Can op maybe add cash variance or suggest a simulator that does?
Pokerdope does the job (for MTTs as well).
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Old 04-27-2015, 09:28 AM   #103
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Quote:
Originally Posted by MrBubbleBoy View Post
Can op maybe add cash variance or suggest a simulator that does?
BTW great work

Is it possible to create an easier way to reduce our ROI though?

I.e. just putting in roi of 3% and letting the numbers do the work instead of having to play around with 1st % 2nd % 3rd % ?
Thanks for the relevant link, coon74. It's unlikely that I will add any cash simulation.

As for generating a finish distribution based on an input ROI, I like the idea for the winner-take-all formats. For most non-WTA formats I would have to make assumptions, since there can be multiple finish distributions that yield the same ROI but can have differing variance. It's also more involved to put it into the program. So the current status of this potential feature is that it's on the list and I'm still thinking about it.
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Old 04-27-2015, 10:04 AM   #104
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Strictly speaking, ITM distributions that are dependent on the multiplier are also possible in JP SnGs (e.g. I try to play higher multipliers more focused and neglect the 2x that are running at the same time when I'm multitabling; but otoh, recreationals spew more in 2x's), but their influence turns out small, so the ITM auto-fill basing on the ROI would be quite accurate. (But still allow users to put custom ITM distributions in like you do now.)
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Old 04-27-2015, 10:15 AM   #105
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Good points, tyty.
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Old 05-16-2015, 10:08 AM   #106
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0

Just a couple small bug fixes.
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Old 05-21-2015, 09:39 PM   #107
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

thanks for the nice tool.

Is it possible to have some quantitative measure of the variance of the prices after a given number of tournaments? In the text output I only see the mean value, it would be great to have some value for the variance or std deviation as well as the statistical error on both the mean and the std deviation.

Thanks
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Old 05-21-2015, 11:04 PM   #108
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Mean, sum sq dev, mean sq dev, and root mean sq dev were inadvertently added in a previous update when I was considering having summary stats in the output. Ultimately, I decided not to add them because I had concerns that they might be misleading due to the weird result distributions on these games. (Apparently I left mean in by mistake. Now fixed -- ty!)

My statistics knowledge is not extensive enough to know if those concerns are warranted and I chose to err on the side of caution. Would be happy to hear from stats-knowledgeable persons about what would be proper to report.
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Old 05-22-2015, 07:53 AM   #109
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

xkcd, you can define a personal 'utility function' that will account for your risk aversion.

I haven't measured my risk aversion that precisely, so I use the standard (accurate for most people and stock price dynamics) utility function - the (natural) logarithm of the (end) net worth.

I plug SwongSim output into an Excel sheet and calculate the exponential of the mean value of this logarithm to obtain the 'risk-adjusted end bankroll'.

That said, I've stopped believing into the accuracy of log-utility for poker players because, even in the current games, they can quickly recuperate after a big loss by crushing lower limits (as witnessed by the numerous SSPLO comebacks of urubu111 aka urubu222), while at the high stakes, their money isn't working that effectively because ROIs are lower.

Thus, imo, BRM should be looser than most people think at the <=€25 limits; at the >=$30s, look rather to maximise the hourly (which is a nontrivial problem) than minimise the risk, just make sure that you'll have enough money left in the worst case to grind back up at the low stakes.

Last edited by coon74; 05-22-2015 at 08:08 AM.
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Old 05-22-2015, 09:29 AM   #110
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Hi guys,

thanks for your answers. But actually I really need some measure if variance, since I want to check how that deviates from the expected std. dev in a 1-dimensional random walk, with expected roi "r" (s_N ~ sqrt(N)*(1-r)*(1+r)).

For that, I would need to have, in the txt output, something like:

mean +/- err_mean
stddev +/- err_stddev


I'm no statistician but definitions should be pretty straightforward:

If I run N simulations, each path will lead, after n games, to profit x_i (i = 1..N).
You can easily compute the four quantities I need as:
  • m = mean = 1/N*(x_1 + x_2 + ... + x_N)
  • s = stddev = sqrt( 1/(N-1)*( (x_1 - m)^2 + (x_2 - m)^2 + ... + (x_N - m)^2 ) )
  • err_mean = s/sqrt(N)
  • err_stddev = sqrt( 1/N*( m4 - s⁴ (N-3)/(N-1)),

where in the last equation m4 is the fourth moment of the sample:

m4 = sqrt( 1/(N-1)*( (x_1 - m)^4 + (x_2 - m)^4 + ... + (x_N - m)^4 ) )

If needed I can send some pseudo-code that does this. Let me know;
Thanks.
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Old 05-22-2015, 09:54 AM   #111
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Over reasonable samples, Spin & Go winnings deviate a lot from a simple random walk, because they're very skewed. Millions of games, if not more, are needed to make the total distribution close to normal.

Theoretical higher moments of winnings can be calculated directly, there's no need to simulate.

Edit: I've simulated a sample of 4M $15+ Spins (on an old version) and the distribution has visibly heavier tails than normal.
Code:
---------------------------------------------------------------------------------------
Effective	Specified		Simulation
Place	Finish Distribution	Finish Distribution
1	0,00036%          	0,000366%
2	0,00033%          	0,00033%
3	0,00031%          	0,000311%
4	0,0018%          	0,001807%
5	0,00165%          	0,001643%
6	0,00155%          	0,00155%
7	0,0036%          	0,003606%
8	0,0033%          	0,003306%
9	0,0031%          	0,003103%
10	0,036%          	0,035988%
11	0,18%          	0,180023%
12	2,7%          	2,700129%
13	7,69176%          	7,691692%
14	25,38648%          	25,385435%
ITM	36,01024%          	36,009289%
---------------------------------------------------------------------------------------
1000  simulations of  4000000  games
Expected ROI (with 0% rakeback): 2,56%  (102399 Buyins)
---------------------------------------------------------------------------------------
Mean 103144,15
Sum square deviation 154557974321,48
Mean square deviation (Sample variance) 154712687,01
Root mean square deviation 12438,36
99% 	had ROI below   3,38%	(135202 Buyins)
97.5% 	had ROI below   3,24%	(129486 Buyins)
95% 	had ROI below   3,09%	(123649 Buyins)
90% 	had ROI below   2,97%	(118616 Buyins)
80% 	had ROI below   2,83%	(113362 Buyins)
70% 	had ROI below   2,73%	(109238 Buyins)
60% 	had ROI below   2,64%	(105721 Buyins)
50% 	had ROI below   2,57%	(102999 Buyins)
40% 	had ROI below   2,49%	(99778 Buyins)
30% 	had ROI below   2,42%	(96875 Buyins)
20% 	had ROI below   2,33%	(93252 Buyins)
10% 	had ROI below   2,17%	(86947 Buyins)
  5% 	had ROI below   2,09%	(83491 Buyins)
  2.5% 	had ROI below   1,99%	(79557 Buyins)
  1% 	had ROI below   1,92%	(76679 Buyins)
---------------------------------------------------------------------------------------
  99% 	had a downswing greater than   548 buyins
  97.5% 	had a downswing greater than   569 buyins
  95% 	had a downswing greater than   591 buyins
  90% 	had a downswing greater than   630 buyins
  80% 	had a downswing greater than   663 buyins
  70% 	had a downswing greater than   699 buyins
  60% 	had a downswing greater than   728 buyins
  50% 	had a downswing greater than   761 buyins
  40% 	had a downswing greater than   796 buyins
  30% 	had a downswing greater than   841 buyins
  20% 	had a downswing greater than   908 buyins
  10% 	had a downswing greater than   994 buyins
  5% 	had a downswing greater than   1099 buyins
  2.5% 	had a downswing greater than   1197 buyins
  1% 	had a downswing greater than   1292 buyins
---------------------------------------------------------------------------------------
  99% 	had a low point lower than   -1 buyins
  97.5% 	had a low point lower than   -3 buyins
  95% 	had a low point lower than   -5 buyins
  90% 	had a low point lower than   -11 buyins
  80% 	had a low point lower than   -23 buyins
  70% 	had a low point lower than   -39 buyins
  60% 	had a low point lower than   -57 buyins
  50% 	had a low point lower than   -82 buyins
  40% 	had a low point lower than   -108 buyins
  30% 	had a low point lower than   -143 buyins
  20% 	had a low point lower than   -194 buyins
  10% 	had a low point lower than   -278 buyins
  5% 	had a low point lower than   -372 buyins
  2.5% 	had a low point lower than   -463 buyins
  1% 	had a low point lower than   -565 buyins
---------------------------------------------------------------------------------------
The observed (sample) root mean square deviation is pretty close to its theoretical value. But look at the top 1% and top 99% ROI values - they're 2.2-2.7 standard deviations away from the mean, which of course shouldn't happen if the distribution is close to normal (recall the 'three sigmas' rule). I haven't run a Kolmogorov-Smirnov test directly, but I'm pretty sure the simulated cdf wouldn't 'pass' as normal.

Last edited by coon74; 05-22-2015 at 10:23 AM.
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Old 05-22-2015, 10:26 AM   #112
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

^ The version that I've used is the one from post #91 itt (04.04.2015). (I didn't add rakeback because it would alter the mean only; so don't be scared by the low points and downswings, they're far less dramatic with RB). It yet has the standard deviation figures, but lacks the option of second rakeback. It's a good idea to use the old and new versions parallelly (which is possible because the executables are independent and don't require installation).
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Old 05-22-2015, 11:22 AM   #113
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Hey Coon74,

great thanks! However I am not able to download that specific version. Seems that DB forces me to take the last one...
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Old 05-22-2015, 12:01 PM   #114
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Np, I've rehosted the April 3 version for you.

Speaking of normality of the distribution, I've just run a mammoth batch of 40K sims for 4M games and it fails the Lilliefors test with significance level 0.001, i.e. I conclude with 99.9% confidence that the distribution is not close enough to normal even after 4M games.
Code:
---------------------------------------------------------------------------------------
Effective	Specified		Simulation
Place	Finish Distribution	Finish Distribution
1	0,00036%          	0,000359%
2	0,00033%          	0,000329%
3	0,00031%          	0,00031%
4	0,0018%          	0,0018%
5	0,00165%          	0,001649%
6	0,00155%          	0,001549%
7	0,0036%          	0,003601%
8	0,0033%          	0,003301%
9	0,0031%          	0,0031%
10	0,036%          	0,036004%
11	0,18%          	0,180015%
12	2,7%          	2,700035%
13	7,69176%          	7,691678%
14	25,38648%          	25,386423%
ITM	36,01024%          	36,010154%
---------------------------------------------------------------------------------------
40000  simulations of  4000000  games
Expected ROI (with 40% rakeback): 4,56%  (182399 Buyins)
---------------------------------------------------------------------------------------
Mean 182317,86
Sum square deviation 5820952022726,84
Mean square deviation (Sample variance) 145527438,75
Root mean square deviation 12063,48
99% 	had ROI below   5,32%	(212739 Buyins)
97.5% 	had ROI below   5,18%	(207282 Buyins)
95% 	had ROI below   5,07%	(202770 Buyins)
90% 	had ROI below   4,95%	(197912 Buyins)
80% 	had ROI below   4,81%	(192241 Buyins)
70% 	had ROI below   4,71%	(188272 Buyins)
60% 	had ROI below   4,63%	(185015 Buyins)
50% 	had ROI below   4,55%	(181897 Buyins)
40% 	had ROI below   4,47%	(178854 Buyins)
30% 	had ROI below   4,39%	(175690 Buyins)
20% 	had ROI below   4,30%	(172062 Buyins)
10% 	had ROI below   4,18%	(167242 Buyins)
  5% 	had ROI below   4,08%	(163295 Buyins)
  2.5% 	had ROI below   4,00%	(160027 Buyins)
  1% 	had ROI below   3,90%	(156120 Buyins)
---------------------------------------------------------------------------------------
  99% 	had a downswing greater than   283 buyins
  97.5% 	had a downswing greater than   293 buyins
  95% 	had a downswing greater than   302 buyins
  90% 	had a downswing greater than   313 buyins
  80% 	had a downswing greater than   329 buyins
  70% 	had a downswing greater than   342 buyins
  60% 	had a downswing greater than   354 buyins
  50% 	had a downswing greater than   366 buyins
  40% 	had a downswing greater than   380 buyins
  30% 	had a downswing greater than   396 buyins
  20% 	had a downswing greater than   416 buyins
  10% 	had a downswing greater than   450 buyins
  5% 	had a downswing greater than   482 buyins
  2.5% 	had a downswing greater than   512 buyins
  1% 	had a downswing greater than   552 buyins
---------------------------------------------------------------------------------------
  99% 	had a low point lower than   0 buyins
  97.5% 	had a low point lower than   -1 buyins
  95% 	had a low point lower than   -2 buyins
  90% 	had a low point lower than   -4 buyins
  80% 	had a low point lower than   -10 buyins
  70% 	had a low point lower than   -16 buyins
  60% 	had a low point lower than   -23 buyins
  50% 	had a low point lower than   -31 buyins
  40% 	had a low point lower than   -41 buyins
  30% 	had a low point lower than   -53 buyins
  20% 	had a low point lower than   -71 buyins
  10% 	had a low point lower than   -102 buyins
  5% 	had a low point lower than   -134 buyins
  2.5% 	had a low point lower than   -164 buyins
  1% 	had a low point lower than   -206 buyins
---------------------------------------------------------------------------------------
It's distinctly skew-positive: the top winners run much better than in a cash game with the same winrate and variance, the top losers run much better too, while the middle runs significantly worse than in a cash game. The discrepancy is especially stark at the top 5% and bottom 5%: the top 5% runs at least ~1.7 standard deviations above the mean, which, under the normal distribution, would happen to the top 4.5% only; the bottom 5% run not better than ~1.58 std devs below the mean, but under the normal distribution, that would happen to as many as 5.7% of the population.

Last edited by coon74; 05-22-2015 at 12:15 PM. Reason: typo
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Old 05-22-2015, 12:52 PM   #115
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Hi Man,

thanks for hosting.
I have been computing the stddev (what he calls "Root mean square deviation") for various evROI%, and I find surprisingly find some trend, but opposite to what I was expecting. I have been using default PS settings, with 3k games per simulation, run with 500k simulations.

Can you make sense of this?




Thanks for help
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Old 05-22-2015, 01:04 PM   #116
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0

Added option to show summary stats (use at your own risk!).


xkcd, I'll add in the others you asked for when I get a chance.
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Old 05-22-2015, 01:05 PM   #117
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

@xkcd: Yes, this trend exists. The single biggest main component in the variance is the 3K BI jackpot squared, multiplied by the probability of getting it, which is 1stplace%/10000000. Hence the variance is roughly proportional to the ITM, and its square root (the standard deviation) is roughly proportional to the square root of the ITM. But as the ITM doesn't differ much from one player to another (is in the 34-40% region for regs), its square root and hence the std dev grows almost linearly.

But don't confuse the variance in its mathematical definition with the risk of ruin and the bankroll required to have a RoR below 10/5/1/whatever %. As the ROI/ITM grows, the risk of ruin falls (hence poker players say 'the variance is lower'), but in fact, the variance in the strict sense grows slightly in all kinds of SnGs except HUSnGs as the ROI grows (as long as it stays 'humanly reasonable' - of course, the variance falls to 0 when the ITM grows from 99% to 100%), just in non-jackpot ones, the growth rate is lower.

Last edited by coon74; 05-22-2015 at 01:21 PM. Reason: clarified to whom I responded
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Old 05-22-2015, 01:12 PM   #118
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Hi guys,

thanks for your explanation/implementation!
Actually coon74, I need some reasonable estimate of variance, as an input for another calculation, that I tried to explain here:

https://forumserver.twoplustwo.com/25...rofit-1533621/

Maybe if you think I am doing something wrong you can post an answer directly there (sorry if I abuse of your kindness, but you seem very proficient with these matters )
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Old 05-31-2015, 12:27 PM   #119
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0

Added PokerStars.fr structures to the presets list and fixed a few cosmetic bugs.
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Old 05-31-2015, 12:49 PM   #120
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Wow, you're the person who has pointed me to the fact that Stars.fr now have the €25s and €50s They must have appeared this month because I checked them at its beginning and the top BI was €20 back then. Awesome job
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Old 05-31-2015, 01:07 PM   #121
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Quote:
Originally Posted by coon74 View Post
Wow, you're the person who has pointed me to the fact that Stars.fr now have the €25s and €50s They must have appeared this month because I checked them at its beginning and the top BI was €20 back then. Awesome job
Thanks go to 7a.m.@hu for the info.
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Old 06-04-2015, 09:17 AM   #122
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

First off, this is a fantastic tool and the results are very enlightening and helpful in setting realistic expectations for spins (and a great way to bolster our mental game). So thanks for all the hard work in putting it together.

It seems like EV ROI is a pretty common measurement for success in spins. Also, players can have variance in the fact that (a) $ results could be much different that EV ROI results, but also from (b) EV ROI being negative over some duration even though you might be a good player overall (say if you were to get coolered continuously).

So two questions:
1) Is there a way to know how much of the variance reported in Swongsim can be tied back to each of (a) vs (b) above? Is there any mathematical assumption that could be made?
2) Over what sample size is it realistic for EV ROI to be negative even though someone might still be a solid player?

FWIW, I am not making illusions about my own play - I have just started playing spins and know I have a lot to learn before I would call myself solid. But I would also like some tool or ability to more independently assess my play overall to determine if I am at least moving in the right direction since these games are so extremely swingy.

Hope that makes sense - thanks in advance.
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Old 06-04-2015, 09:31 AM   #123
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Maybe another way of asking this question is roughly what the longest period (of games) of negative EV ROI has been for some solid players?
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Old 06-04-2015, 11:07 AM   #124
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Hi zilblitz, thanks for the kind words. Will respond later since I'll be out most or all of today.
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Old 06-04-2015, 04:36 PM   #125
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

My estimate is that the difference between the true EV and the chip EV accounts for 1.5-2% of the overall variance in stars.com Spins.

Even if we ignore all-in equities and calculate expected winnings as ((ITM%/100%)*2.85-1)*BI*#tourneys (i.e. as if there was no lottery and the prize always equaled its average - 2.85 BI for $15s+, 2.82 for $3-7, 2.79 for $1), then the difference between them and the true EV accounts merely for 5-6% of the overall variance. (You can actually see this yourself if you run SwongSim for the fixed-prize winner-take-all 3-max structure.)

To answer the question about bad runs of a 'solid player' (I'm not sure how you define a 'solid ROI'), run SwongSim for the fixed-prize structure and divide the needed samples by 3-4 (as the difference between the true and chip EV would account for 25-35% of the variance if the prize were fixed, as far as my PT4 analysis shows).

Or just use the following formula for the one-tailed 95% confidence interval for the chip EV winrate per tourney:

true_chip_EV_wr > observed_chip_EV_wr - 600/sqrt(#games)

where sqrt is the square root.

For 90% or 80% confidence, replace 600 by 500 or 300, respectively.

The formula is based on the estimate that the standard deviation of the chip EV in a single tourney is about 350 chips. (I'm serious here.) [The standard deviation of the actual number of chips won (i.e. +1000 or -500) is about 700 chips, so its square (variance) is about 4 times bigger as said above.] I've multiplied 350 by the quantiles from the z-test table and rounded the numbers to get 600, 500 and 300.

So, if you, say, define a solid player as someone who wins 40 or more chips per tourney, then, over 225 games (=(600/40)^2), there's a 95% chance of him winning a positive number of chips overall; over (500/25)^2=625 games, there's a 90% chance of him winning over 40-25=15 chips per tourney.

Last edited by coon74; 06-04-2015 at 04:57 PM.
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