SnG ROI Confidence Intervals--Monte Carlo results

[Pokerscott]

This post is meant to be a quick reference if you are interested in determining the confidence level surrounding key questions such as:

Suppose you have played 50 SnGs and are up 11 units, how confident are you that:
-You are better than the average player that consistently loses the rake?
-You are good enough to overcome the rake?
-You are an ROI 10%+ player? 20%? 30%? 40%? 50%?

The following tables help you answer these questions.

Background on this analysis and some discussion can be found in my original thread here (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=1562473&page=1&view=colla psed&sb=5&o=14&fpart=1)

People requested I run the analysis not just for testing whether or not you are above average, but also looking at various levels of ROI. Here are the tables for those results.

First the average player results (note the average player should have an ROI corresponding to the rake or in this case an ROI of -9.09%)

http://www.imagevenue.com/loc183/972_ROIneg909.GIF

Here are the tables for testing your confidence that you are able to overcome the rake (ROI 0%)

http://img3.imagevenue.com/loc143/610_ROIzero.GIF

And finally, here are the tables for ROI 10% - 50%

10% ROI

http://img2.imagevenue.com/loc203/e68_ROI10.GIF

20% ROI
http://img3.imagevenue.com/loc183/2e0_ROI20.GIF

30% ROI

http://img3.imagevenue.com/loc186/e47_ROI30.GIF

40% ROI

http://img1.imagevenue.com/loc156/bd4_ROI40.GIF

50% ROI

http://www.imagevenue.com/loc211/33c_ROI50.GIF

Cheers,

Pokerscott

[rachelwxm]

Good job!
I have not follow your work closely, so my question might sounds stupid.
Is typical confidence level in original spreadsheet still a good one for decent sample size? /images/graemlins/smile.gif

Assume if you have enough sample size, your distribution approach normal and the question whether your ROI is above x% is merely a t-test.

Is there any other inefficiency of using the original fomula comparing with your method? /images/graemlins/smile.gif

[Pokerscott]

The large Monte Carlo should be superior for the small number of SnGs since the normality assumption would be weakest here. Having said that, normality seems like a pretty good assumption to me (especially at 100 SnGs and above), so the analytic approach with a normality assumption is good too.

Pokerscott

[rachelwxm]

Thanks very much.

[Irieguy]

Thank you Pokerscott.

I think the interesting practical application is that if you have a 20% ROI and play 500 SNGs a month... you will never have a losing month.

Little perspective on the variance of SNGs vs. live play there. I wonder how many ring game players have never had a losing month.

Irieguy

[lorinda]

Thanks for taking the time to do this.

Lori

[bball904]

Excellent point! It appears also that 15% ROI and 500 sng's a month would provide about 97-98% (rough guess from extrapolation) or so confidence in not having a losing month.

[Daliman]

WHy are these called "Monte Carlo" results?

[Pokerscott]

[ QUOTE ]
WHy are these called "Monte Carlo" results?

[/ QUOTE ]

Monte carlo simulation is a method for getting approximate solutions to many mathematical problems. Here is a link describing some details on the history of the name 'Monte Carlo'
monte carlo history link (http://www.geocities.com/CollegePark/Quad/2435/history.html)

[The Yugoslavian]

[ QUOTE ]
WHy are these called "Monte Carlo" results?

[/ QUOTE ]

It sounds a helluva lot cooler than saying 'results,' doesn't it?

I thought it was cooler anyway. And if anyone knows what's cool, it's obviously me. /images/graemlins/cool.gif <-- I'm so cool that I'm wearing shades right now.

I'm going to start calling any results of anything I post 'Montevideo Prix results' -- mainly for my own amusement.

Yugoslav

[lacky]

I've played full time for 18 months now, about 2/3 ring, 1/3 sng's and I've never had a losing month. When you figure in rackback as well, it takes a serioes prolonged run to have a losing month. The only times I have come close is when I have been spanked at a higher limit and had to drop down and make it up.

Steve

[Maulik]

[ QUOTE ]
Excellent point! It appears also that 15% ROI and 500 sng's a month would provide about 97-98% (rough guess from extrapolation) or so confidence in not having a losing month.

[/ QUOTE ]

Are you suggesting people 2+2ers play 16-17 sit-n-gos daily to hit 500? Wow.

[jackdaniels]

And you didnt account for any days off, sick time or anything else! If you want to make it more appealing, 4 table the SNG's, play 20 days a month (giving you weakends off for good behaviour) and you'll wind up playing about 25 a day or (assuming an average of 1 hour per game/4 tabling) - 6-7 hours of work, 5 days a week.

Assuming you are playing the 20's and have a 35% ROI you are looking at making about $3,500/month or roughly $28/hour. Sure beats that McDicks gig for min wage but most people good enough to make that coin in poker can do a lot better with a dumb corporate job (where you get benefits and slack off most of the day - heck, I'm writing this while "working" at my dumb corporate job /images/graemlins/cool.gif). You really have to enjoy playing the game to do it for a living - otherwise, you'll find yourself hating it very soon and possibly being short of other options when the realization dawns on you.

[valenzuela]

Your graphic is:
-useful to ppl like who have played like only 80 sngs( since i started counting winnings)
-entertaining.
-slightly disapointing, what was the worst and the best simulation you got in each set of ROIs? I would really love to know( even though its totally unpractical unless you play sngs for the next 8000 years. )

[Pokerscott]

[ QUOTE ]
Your graphic is:
-slightly disapointing, what was the worst and the best simulation you got in each set of ROIs? I would really love to know( even though its totally unpractical unless you play sngs for the next 8000 years. )

[/ QUOTE ]

This one I can answer without looking back at the analysis /images/graemlins/smile.gif

The min/max results are just the best/worst possible (e.g. The 50 SnG max is a first in all 50 and the min is a blank in all 50). In other words, if you did enough Monte Carlo trials, you would eventually get a trial that was the 'best' and a trial that was the 'worst'.

The percentiles are helpful in that they can tell you how likely you are to be better or worse than a given outcome. The min/max are not very helpful since if you give me enough trials I can get any outcome.

I guess maybe having more of the tail results could be interesting (such as the 99.9% and 99.99%). That part of the distribution is probably least likely to be normal, but do you really want to know it /images/graemlins/smile.gif

Pokerscott

[valenzuela]

YES!

[ReDeYES88]

. .is it just me, or is anyone else having problems seeing the pretty pictures. . .they won't load. . /images/graemlins/frown.gif

[Pokerscott]

If you are having trouble seeing the images in this post, I updated the images and reposted the information in this (http://forumserver.twoplustwo.com/showflat.php?Cat=&Number=1941324&page=3&view=colla psed&sb=5&o=14&fpart=1) thread.

Pokerscott