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

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%)



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



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

10% ROI



20% ROI


30% ROI



40% ROI



50% ROI



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? [img]/images/graemlins/smile.gif[/img]

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? [img]/images/graemlins/smile.gif[/img]

[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

[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. [img]/images/graemlins/cool.gif[/img] <-- 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