Tournament Variance Calculator

Tournament results are a distribution, not a line

Cash game variance is a bell curve with your win rate at the center. Tournament variance is something uglier: a heavily right-skewed distribution where nearly all your profit comes from rare deep runs, and the majority of your tournaments end in a registration fee written off as an expense. The math here is different, and treating it like cash game variance is one of the more expensive errors a tournament player can make.

The model

The calculator uses a Monte Carlo approach rather than a closed-form normal distribution, because MTT results don't follow a normal distribution. For each simulated tournament, it draws a finish position from a payout-weighted distribution shaped by your ROI input. Over N tournaments, it aggregates the results and plots the profit/loss distribution across all simulation runs.

The core inputs: buy-in (in dollars), rake percentage, field size, your ROI as a percentage, and number of tournaments. ROI is defined as:

ROI = (total_winnings - total_invested) / total_invested * 100

A 10% ROI means that for every $100 you invest in buy-ins plus rake, you expect to receive $110 back in prize money over a large sample. The variance around that expectation is enormous.

Worked example

Player runs a schedule of 200 tournaments: $100 buy-in (10% rake, so $90 goes to the prize pool), 1,000-player field, claimed ROI of 30%.

• Total invested: 200 * $100 = $20,000
• Expected return: $20,000 * 1.30 = $26,000
• Expected profit: $6,000
• Standard deviation of that profit over 200 tournaments: approximately $18,000-$25,000 depending on the payout structure steepness

The 95% confidence interval on 200 tournaments at 30% ROI easily includes losing $30,000. That is not a hypothetical. Players with genuine edges go bankrupt in tournaments because they underestimated variance and overbought their schedule.

What each output means

Probability of profit over N tournaments is the headline number: the percentage of simulated runs that ended in the black. At 200 tournaments with a real 30% ROI, this is likely around 55-60%, meaning you lose money in roughly 4 out of 10 comparable sample stretches. Confidence bands show the typical and worst-case ranges. Best and worst runs show the extremes from the simulated population: useful for understanding that a huge score is not a statistical accident but a predictable feature of the distribution. Break-even sample tells you approximately how many tournaments you need to play before your results start reliably reflecting your edge.

Where the model breaks

ROI is not a stable number. It changes with field composition, your study habits, stake levels, and the payout structure of events you're targeting. A player running 20% ROI in small-field turbos may run 5% or negative in deep-stacked majors with the same strategy. Inputting a single ROI treats your skill as static across all formats.

The payout structure shape matters enormously. A flat top-heavy payout structure (winner takes 20% of the pool) produces far more variance than a flatter structure. The default model approximates a typical tournament payout curve, but field-specific payout structures can deviate substantially.

Progressive knockout events break the model in a specific way: bounties are paid incrementally throughout the tournament, not just at the money. The expected value from bounties is correlated with survival depth, meaning your results in PKO events are even more right-skewed than standard MTTs. See the ICM deal calculator for how PKO structures affect late-game deal math.

Sample size is the deepest problem. The calculator will honestly show you that 500-1,000 tournaments are needed before your results meaningfully constrain your true ROI estimate. Most players never play that many events at a single stake. If you want to understand variance across your actual game mix, the bankroll calculator translates tournament variance into the buy-in count you need to survive it.