• Bronze
Joined: 14.06.2008
Wondering if anyone has a excel spreadsheet to give us information about how true our roi's are for our sample sizes?

Want to find out things like "How likely is it that my true roi might be 0% or lower if I have 15% roi after 300 games?"

"How likely is it that my true roi is 15% after playing 500 sng's with 15% roi??"

I've seen a lot of more complicated poker related excel spreadsheets so I'm wondering if anyone knows if something like this exist...

When playing around with some numbers and finding out how big of a factor variance is in sng's I'm kinda excited to find out how likely it is that I might actually be a loosing player lol
• 6 replies
• Bronze
Joined: 17.06.2010
In theory, the probability your true ROI is 0% or lower depends on a nonmathematical prior distribution. However, what you might ask instead is how likely it is that a break-even player would have an ROI as good or better than the ROI you have had. If this probability is low, then you can say that you have strong statistical evidence that you are a winning player.

As long as you have played more than a few dozen tournaments, you can use a normal approximation. I don't know whether people have made a spreadsheet for that yet, and it would not be hard to make one, but I'll tell you how to do the calculation.

Almost regardless of your playing style as a serious player, your standard deviation in a 9-player SNG is between 150% and 155% of a buy-in per tournament. In other forms of poker, you can make plays which break-even in \$ which greatly reduce your variance, but despite common misconceptions, those rarely occur in SNGs. So, let us assume that your standard deviation is 155% per tournament.

After n tournaments, the standard deviation of your ROI is about 155%/squareroot(n).

Express your observed ROI in terms of standard deviations: Divide your observed ROI by 155%/sqrt(n). This tells you the number of standard deviations by which you are ahead of breaking even. You can enter that value into the first line of this web calculator. The reported cumulative probability is the chance that a break-even player would have worse results than you have seen. 100% minus this is the chance that a break-even player would have better results.

For example, after 300 tournaments with an ROI of 15%, your standard deviation is about 155%/sqrt(300) = 8.95%. You are 15%/8.95% = 1.68 standard deviations ahead of breaking even. The chance that a break-even player would have results worse than that is about 0.95 = 95%, so there is about a 5% chance that a break-even player would have better results. That's close to the boundary of when people would start to say that you have strong statistical evidence that you are a winning player, but you don't yet have a good idea what your ROI is.
• Bronze
Joined: 18.03.2008
• Bronze
Joined: 01.01.2010
how do you get to the value of 155% ?
I play 10-man SNGs, how much does it change there? And how much can I expect it to be in a double- or nothing tournament?
• Bronze
Joined: 17.06.2010
To calculate the standard deviation from a finishing distribution, you can do the following:

-- Compute the average prize A.

-- Compute the average of the square of the prize won B.

-- Variance is B-(A^2).

-- Standard deviation is sqrt(Variance).

For example, suppose you play \$10+\$1 SNGs with a finish distribution of 13% firsts, 12% seconds, and 14% thirds.

A = \$45 * 0.13 + \$27 * 0.12 + \$18 * 0.14 = \$11.61

B = 2025 * 0.13 + 729 * 0.12 + 324 * 0.14 = 396.09

variance = B - A^2 = 261.3

standard deviation = sqrt(261.3) = \$16.16, or 147% of an \$11 buy-in.

If you do this for other finishing distributions, you will find that playing style does not make a large difference in your standard deviation. It is different for cash games or multitable tournaments, where your playing style might significantly affect your variance.

You will tend to get slightly higher values for 10-player SNGs.

For Double or Nothings, you can follow the same procedure if you want, although there are simpler methods for computing the standard deviation when there are only two outcomes possible. Suppose you play \$5.20 Double-or-Nothings and cash 55% of the time.

A = \$10 * 0.55 = \$5.50

B = 100 * 0.55 = 55.

variance = 55 - 30.25 = 24.75

standard deviation = sqrt(24.75) = \$4.97 = 96% of a \$5.20 buy-in.
• Bronze
Joined: 01.01.2010
Wow thanks for the exact answer:-) Well I will try to calculate it later
• Bronze
Joined: 01.01.2010
winning:-)
just want to add: in some countries, as mine, excel gives numbers in the format 1,23 in the calculator it needs to be changed to 1.23 ;-)