Hyper-Turbo SNG

ROI and variance in tournaments

ROI (return on investment) shows what percentage of the buy-in amount was returned in prizes: ROI = (prizes − buy-ins) / buy-ins × 100 %. A positive ROI means that over the long term the player takes back more than he puts in; negative — that tournaments are unprofitable for him.

The main trap is the short distance. In hyper-turbo, almost the entire prize pool is concentrated in the top places, so a dozen tournaments can give an ROI of hundreds of percent or minus one hundred percent without any change in the quality of play. Only a few thousand tournaments provide an estimate that you can rely on.

The simulator builds a bankroll through tournaments: each tournament is an independent random event with given probabilities for first and third place. The graph line shows how the same ROI can look completely different on the way to the expected value.

Where does the scatter come from

The variance of the result of a single tournament depends on the size of the prizes and their probabilities. The larger the prize for first place relative to the buy-in, the more a single win "skews" the graph. Therefore, in hyper-turbo, the bankroll looks like steps: long declines and rare sharp rises.

What can be checked

• how ROI changes with a change in the probability of first place;
• how many tournaments are needed for the schedule to look like a straight line;
• what happens to the bankroll if the prize for third place is close to the buy-in;
• why the same parameters give different trajectories with each run.