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06-04-2015, 09:36 PM   #126
Max Cut
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Thanks, as always coon74! I like the idea of comparing to a similar non-lottery payout structure, but hadn't thought about how to further quantify the comparison.

Quote:
 Originally Posted by zilblitz 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?
I think I'm going to add numbers for length of "longest" break-even stretch. This would be similar to worst buyin downswing, but would record the number of games (until back into profit relative to the start of the downswing; i.e., break-even stretch) rather than the deepest. Then you can simulate a "solid" player and see numbers.

For example:
99% had a break-even stretch longer than ___
95% had a break-even stretch longer than ___
.
.
.
5% had a break-even stretch longer than ___
1% had a break-even stretch longer than ___

06-04-2015, 09:39 PM   #127
zilblitz
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

You rock, c o o n - very helpful information (not sure I understand everything but I think I get it).

Quote:
 Originally Posted by coon74 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.
Does that mean, inversely, that the other approx 98% of variance is due to actual \$ ROI results being different that EV ROI results?

Quote:
 Originally Posted by coon74 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.
Ok, so let's take someone whose skill should win them 50 chips per game - if we wanted to know the time period over which they should get at least 45 chips per game, the formula for 95% confidence would be (600/5)^2=14400.

And your first example (225 games (=(600/40)^2)) suggests that a skilled player could very well be close to break-even over 225 games (or slightly losing when you factor in rake).

Am I understanding you correctly?

Last edited by zilblitz; 06-04-2015 at 09:40 PM. Reason: Being prevented from quoting your sn - lol

06-04-2015, 09:51 PM   #128
zilblitz
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Join Date: Jun 2013
Posts: 391
Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Quote:
 Originally Posted by Max Cut Thanks, as always coon74! I like the idea of comparing to a similar non-lottery payout structure, but hadn't thought about how to further quantify the comparison. I think I'm going to add numbers for length of "longest" break-even stretch. This would be similar to worst buyin downswing, but would record the number of games (until back into profit relative to the start of the downswing; i.e., break-even stretch) rather than the deepest. Then you can simulate a "solid" player and see numbers. For example: 99% had a break-even stretch longer than ___ 95% had a break-even stretch longer than ___ . . . 5% had a break-even stretch longer than ___ 1% had a break-even stretch longer than ___
Sorry, I hadn't intended to give you more work , but i like that idea a lot. Players who are just starting with the spin format can get discouraged pretty easily if they feel like they can't win even though they may actually be playing well - but they should have awareness of what an appropriate sample size to look at might be to actually make a strong assessment.

06-04-2015, 10:56 PM   #129
coon74
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Quote:
 Originally Posted by zilblitz Does that mean, inversely, that the other approx 98% of variance is due to actual \$ ROI results being different that EV ROI results?
Yes, that's because 1) the difference between the chip EV and the actual chip winnings depends only on the board cards that fall after the betting action ends (everyone either has folded or is all-in) but is independent of players' strategies and 2) the players' strategies are almost independent of the prize multipliers.

The variance of the sum of two (or several) probabilistically independent random variables (the EV and the difference in our case) always equals the sum of their variances.

Quote:
 Originally Posted by zilblitz Ok, so let's take someone whose skill should win them 50 chips per game - if we wanted to know the time period over which they should get at least 45 chips per game, the formula for 95% confidence would be (600/5)^2=14400. And your first example (225 games (=(600/40)^2)) suggests that a skilled player could very well be close to break-even over 225 games (or slightly losing when you factor in rake). Am I understanding you correctly?
Yes, it's correct, except one clarification: the solid player can be breakeven even in terms of the chip EV after 225 games; of course he might end up losing a lot of BIs over this sample because of getting too many 2x multipliers (those times when he wins). If you wish to assess the probabilities of certain monetary losses, just use SwongSim.

 06-04-2015, 11:17 PM #130 zilblitz journeyman     Join Date: Jun 2013 Posts: 391 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) Cool - thanks for the clarification. It is interesting then that someone whose skill should garner them an EV of 50 chips per game would most likely not have a negative EV ROI in a sample size as ridiculously small as 144 games.
 06-05-2015, 01:12 PM #131 Max Cut Carpal \'Tunnel     Join Date: Apr 2010 Location: exiledpolitics.freeforums.net Posts: 10,338 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0 Added numbers to the text output for longest breakeven stretch. Good thing we have chip EV!
 06-05-2015, 04:14 PM #132 zilblitz journeyman     Join Date: Jun 2013 Posts: 391 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) 50% probability of break-even stretch of 4600 games (or more) - showers.... Thanks, Max Cut - looks good.
 06-06-2015, 07:32 AM #133 CheckN0rris grinder   Join Date: May 2015 Posts: 412 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) Thx Max Cut for making and sharing this software, its awesome, much appreciated!
 06-06-2015, 06:04 PM #134 Max Cut Carpal \'Tunnel     Join Date: Apr 2010 Location: exiledpolitics.freeforums.net Posts: 10,338 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0 Fixed bug for break-even stretch when using \$ mode instead of buyin mode.
 06-11-2015, 05:28 PM #135 coon74 Carpal \'Tunnel   Join Date: Apr 2011 Posts: 10,681 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) The iPoker network has just started dividing Twister prize pools of €1000 or more, regardless of the buy-in, between all the three participants in the 80%/10%/10% proportion (e.g. €800/€100/€100). The frequencies stay the same. So there should now be separate built-in structures for €1-2 (where only the top tier enjoys the 80/10/10 split), €5 (where the top two tiers have it) and €10 Twister (where the top three tiers have it).
 06-11-2015, 05:55 PM #136 Max Cut Carpal \'Tunnel     Join Date: Apr 2010 Location: exiledpolitics.freeforums.net Posts: 10,338 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) Thanks for the info! Can you verify that the bottom tier is 2.01 buyins? www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0 Updated iPoker structures.
 06-11-2015, 09:50 PM #137 coon74 Carpal \'Tunnel   Join Date: Apr 2011 Posts: 10,681 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) Yes, it's all correct, the bottom tier awards 2.01 BIs, as witnessed by my cashier. Thanks! Last edited by coon74; 06-11-2015 at 09:58 PM.
 07-10-2015, 11:59 AM #138 Max Cut Carpal \'Tunnel     Join Date: Apr 2010 Location: exiledpolitics.freeforums.net Posts: 10,338 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0 Speed up for drawing graphs with large numbers of games.
 07-10-2015, 04:07 PM #139 Max Cut Carpal \'Tunnel     Join Date: Apr 2010 Location: exiledpolitics.freeforums.net Posts: 10,338 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0 Bug fix. (Crash when drawing graph for very few games.)
 07-15-2015, 08:53 PM #140 Max Cut Carpal \'Tunnel     Join Date: Apr 2010 Location: exiledpolitics.freeforums.net Posts: 10,338 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0 Updated FTP Jackpot frequencies.
 07-15-2015, 10:53 PM #141 coon74 Carpal \'Tunnel   Join Date: Apr 2011 Posts: 10,681 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) That rake Speaking of the prize structures, the Winamax ones have changed too (which I've recorded in text files importable into SwongSim). Winamax (all the buy-ins - €1/2/5/10/25/50): https://www.dropbox.com/s/5chzbyaf1z...o_new.txt?dl=0 | Screenshot Pokerstars.es Spins split the 100x and 200x prize pools in the 80%/10%/10% proportion. Otherwise they follow the structure that you have labeled as 'XXL' (the 1200x and 6000x ones are indeed split as 83.3%/8.3%/8.3% and 25x and lower are winner-take-all). Screenshot Pokerstars.fr has set a promotional rake rate of 5% for €50 and €100 Spins https://www.dropbox.com/s/kf80ihjggq...promo.txt?dl=0 ; on September 1, they're likely to revert to the structure identical to the €25 one with 6% rake. Screenshot
 07-16-2015, 04:08 PM #142 Max Cut Carpal \'Tunnel     Join Date: Apr 2010 Location: exiledpolitics.freeforums.net Posts: 10,338 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) Thanks very much for the info. Will get these updated ASAP.
 07-17-2015, 02:20 PM #143 Max Cut Carpal \'Tunnel     Join Date: Apr 2010 Location: exiledpolitics.freeforums.net Posts: 10,338 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0 Updated Winamax, PokerStars.es, and PokerStars.fr structures. (Wow, that Winamax structure looks intimidating, haha.) Thanks again, coon74.
 07-17-2015, 03:50 PM #144 coon74 Carpal \'Tunnel   Join Date: Apr 2011 Posts: 10,681 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) You didn't pay attention to the bottom part of my Winamax screenshot. The prize pool at the top 4 tiers (50x's and higher, at each BI level) is split in the 80%/12%/8% proportion, i.e. 40/6/4 BIs in 50x's etc. So the structure is only about as much scary as the Stars.fr non-promotional one. Yes, it has become so top-heavy that I'm not going to switch to Winamax to play the €25s until I have a roll of about €50K, lol.
 07-17-2015, 04:05 PM #145 Max Cut Carpal \'Tunnel     Join Date: Apr 2010 Location: exiledpolitics.freeforums.net Posts: 10,338 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0 Whoops; thanks!
 07-17-2015, 04:27 PM #146 coon74 Carpal \'Tunnel   Join Date: Apr 2011 Posts: 10,681 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) The 'PokerStars Spin&Go (France, 50€)' structure name should read 'PokerStars Spin&Go (France, 25€)'. Also, I've just found out that the Stars.it rake has been reduced for the €10 and €25 BIs, and made a screenshot. (I hope it's understandable without knowledge of Italian.) Note that: Rake = 9% for BI=€1/2/5 (the 1st paytable), 8% for €10 (2nd), 7% for €25 (3rd). Tiers A and B (12000x and 1200x) split the winnings as 83.33%/8.33%/8.33%. Tiers C and D (2000x and 1000x) split them as 80%/10%/10%. The other tiers (E and lower) are winner-take-all. As usual, no deals are available. Edit: speaking of Italy, here's the paytable of the Shake&Go tourneys of the Dollaro network (which have 1-minute blind levels, ugh, and as far as I've understood, all the tiers are winner-take-all): (Lol, there are of course misprints in the €5 and €10 columns; I guess the structure is the same in terms of multipliers for all the stakes; the misprints show the level of Dollaro's legitimacy, lol.) Last edited by coon74; 07-17-2015 at 04:37 PM.
 07-17-2015, 05:09 PM #147 Max Cut Carpal \'Tunnel     Join Date: Apr 2010 Location: exiledpolitics.freeforums.net Posts: 10,338 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) Thank you, kind sir. Yeah, I left Dollaro out on purpose because I consider them silly (1-minute blinds) and they can't even be bothered to correct their tables. Will add if asked for. www.dropbox.com/s/ukpadqy24se12th/SwongSim.exe?dl=0 France 25€ fixed; Italy updated.
 07-17-2015, 06:02 PM #148 coon74 Carpal \'Tunnel   Join Date: Apr 2011 Posts: 10,681 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) It's all OK now, thanks Edit: if I were living in Italy, I'd try out both available options, though. Judging by the edges people have on iPoker with 2-minute blind levels and sizeable antes on slow software, Shake & Gos might be sufficiently beatable if the fish-to-reg ratio is good - fish have glaring push/fold leaks and ridiculously weak minraise/calling ranges. Plus 1.5 times more tourneys can be played per hour with the same number of tables opened, which positively affects the hourly. Plus the rake (with RB up to 40%, I believe) is lower for those who can't get SNE at Stars.it (which is hardly possible at the €10 level anyway). Last edited by coon74; 07-17-2015 at 06:25 PM.
 07-20-2015, 09:36 AM #149 sharko newbie   Join Date: Jan 2015 Location: Scotland - France Posts: 19 Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post) Hey Max Cut! Just wanted to say thank you for your program, it's very nice, easy to use and good to see graphs too. Very useful to visualize and understand variance and project potential winrate. Also well done for keeeping it updated, coon74 too. Edit: I noticed small differences between winnings amongs different sites while the rake is the same. For example Pokerstars.com \$1 gives you \$40 winnings, while pokerstars.fr 1€ gives you \$38, then \$35 for Winamax Expresso, all 3 are at 7% rake. Are they due to a mistake in your program or maybe the actual rake is 6.99..% or 7.00..1% depending on the sites? Last edited by sharko; 07-20-2015 at 09:48 AM.
07-20-2015, 11:11 AM   #150
Max Cut
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Re: SwongSim -- ROI/variance simulator for lottery-payout SNGs (2k post)

Quote:
 Originally Posted by sharko Hey Max Cut! Just wanted to say thank you for your program, it's very nice, easy to use and good to see graphs too. Very useful to visualize and understand variance and project potential winrate. Also well done for keeeping it updated, coon74 too. Edit: I noticed small differences between winnings amongs different sites while the rake is the same. For example Pokerstars.com \$1 gives you \$40 winnings, while pokerstars.fr 1€ gives you \$38, then \$35 for Winamax Expresso, all 3 are at 7% rake. Are they due to a mistake in your program or maybe the actual rake is 6.99..% or 7.00..1% depending on the sites?

Cheers, sharko. Glad to hear you find it useful.

The differences you notice are due to differences in payout structure. More specifically, differences in the tiers that are not winner-take-all. When a higher proportion of the total buyins awarded go to 2nd and 3rd place, then ROI will be slightly lowered for players that finish in 1st place more than 1/3 of the time. You can see this by changing the player finish distribution so 1st, 2nd, and 3rd are all 33.33%, and then comparing sites with the same rake. Another check would be changing all the tiers to a 100/0/0 prize pool distribution.

This is the same reason the common formula for expected ROI that is based on expected win rate (from chip EV) is very slightly too high (but negligible for practical purposes.)

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