I did a sample size analysis for a STT sit’n’go. 10k tournamemts for a MTT seems to me quite a stretch.
The table below displays the number of STT sit’n’go s you should play to determine with a 90% confidence that you are a winning player. It uses the central limit theorem to justify assuming a normal profit distribution with profit determined by the equation Profit = ROI*Total Buy-in (includes entry fee). The situation assumed is a 9-man SNG with a $9 prize-pool buy-in and a $1 entry fee. The prize structure is 50% for 1st, 30% for 2nd and 20% for 3rd. Given that data and the placing distribution when in-the-money (ITM), it is possible to calculate the standard deviation. Four placing distributions were analyzed
Uniform - each placing equally likely with relative weights of 1,1,1 when in the money.
Symmetrical – relative weights of 1,2,1, signifying that 2nd place is twice as likely as first and third places
First place most likely – relative weights of 3,2,1 signifying that first place is 1.5 times as likely as 2nd place and 3 times as likely as third place when in the money
Third place most likely – relative weights of 1,2,3
For each of these placing distributions, there is also a fourth result and that is out of the money meaning a loss of the total buy-in. This results in the First Place Most Likely placing distribution having the highest standard deviation and thus the largest sample size requirement. As one would expect, the largest sample size requirement to show you are a SNG winner is for the smallest ROI. The sample size range for the cases examined is 417 for a 10% ROI with first place money as the most frequently occurring prize while the smallest required sample size is just 17 when the ROI is a high 40% and third place is most likely.
[B]
| | 9-Man SNG/ Sample Size | for 90% Confidence | WR>0 vs. ROI | |
| | | Return on Investment, ROI | | |
ITM Placing Distrib. | 10% | 15% | 20% | 30% | 40% |
Uniform 1-1-1 | 350 | 162 | 92 | 42 | 24 |
Symmetrical 1-2-1 | 331 | 149 | 85 | 39 | 22 |
First Likely 3-2-1 | 417 | 189 | 109 | 50 | 29 |
Third Likely 1-2-3 | 275 | 124 | 70 | 31 | 17 |
Example: If you are equally likely to finish in first, second or third place if ITM, and if your ROI is 15%, to be 90% confident you are a winning player, you need to play 162 SNG tournaments.