Accuracy of $$$/hr in SNGs

[AleoMagus]

I am a sng player. I want to know how to figure the % accuracy of my average $$$/tourney to within X dollars based upon my sample size.

Wow, I thought it would take more to express that question

Put (perhaps) more clearly, if I have played in 100 $10+1 sngs and I make $5/tourney on average, to what degree of accuracy (%) can I say this is true +/- $1?

Note: these are just hypothetical results and I'd really like a general equation that I can use to figure any accuracy to any +/- for any sample.

Thanks,
Brad S

[Bozeman]

Standard deviation per tourney is SD1=Sqrt(SUM(Px*$x^2)) [Px=probability of xth place, $x is net for that finish]

Standard deviation after n tourneys is SD1*Sqrt(n).

Your results will be within one SD about 68% of the time. Equations are approximate, accuracy increases with n.

SDofAVE$/tourney=SD1/Sqrt(n)

For an average player, SD1=$16.8, so would get 68% confidence in +-$1 after 281 tourneys.

For winning players, SD1 is somewhat higher, my SD1 at $109 is ~$180, and for 50% ROI would be even higher.

Craig

There may be corrections of order 1+1/n.

[AleoMagus]

Thanks. One more question.

I can see how SDofAVE$/tourney=SD1/Sqrt(n), and how Sqrt(n) will need to equal the number of tourneys played to have 68% confidence in +/-$1/tourney (32400 tourneys in your case!) ...but how would I calculate my confidence in a given +/- after any number of tourneys, or number of tourneys needed for any % confidence.

Thanks for the help
Brad S

Edit: Oh, I also am not sure what you mean by the ccorrection of order 1+1/n. Thanks again

[Bozeman]

Just use an normal distribution calculator (for example: web page (http://www.swogstat.org/stat/public/normal_calculator.htm) ). While the distribution is not quite normal, the approximation is good for any reasonably large n (~>20). To use this one, convert twosided interval (eg 95% confidence) to one sided (1-(1-.95)/2=.975), and it will give you the number of sd's for that in critical value. For a two way confidence, like this, 1 sd is 68%, 2 sd's is 95%.

[Bozeman]

"SDofAVE$/tourney=SD1/Sqrt(n) "

For example, if you win, 2nd, and 3rd 15% each at $10+1, your win rate is $4, and your SD1 is $19 (units are $/sqrt(sng)).

After 100, you can say that your true win rate is $4+-1.9 with 68% confidence, and $4+-3.8 with 95% confidence. Or using a one sided measure, you can say that you are a winning player with 98.2% confidence.

Craig