Expected Profit over N Bets

The expectation is straightforward. Work out what one bet is worth on average, multiply by the number of bets, and you have the profit the edge produces in the long run. It is exact arithmetic and it needs no simulation.

What it does not tell you is what your season will look like, and that is the part people take away. The expected figure is an average across every possible season, and no individual season is the average. That is what the simulation is for.

The percentile table is the useful half of this page. A real edge over a real number of bets still produces a wide spread of outcomes, and the 10th percentile — the season that goes badly without anything being wrong — is usually far below the expectation and frequently below zero. Planning around the average is how people end up with bankrolls sized for a season that never arrives.

The assumptions are worth naming because they all point the same way. Constant price, constant edge, independent results, fixed stake. Real betting has none of them: prices vary, edges drift, and same-day results correlate. Every one of those makes the real distribution wider than the simulated one, so the spread here is a floor.

The analytic figure appears immediately and the simulation runs on request. That split is deliberate — the expectation should never depend on a random process, and putting a simulated number where an exact one belongs would be a strange thing to do.

500 bets at $100, at −110, winning 55% of the time. Break-even is 52.38%, so the edge is 2.62 points.

EV per bet is 0.55 × $90.91 − 0.45 × $100 = $5.00, so expected profit is $2,500 on $50,000 of handle — an expected ROI of +5.00%. A very good season.

Then run the distribution. The median lands right on the expectation at +$2,500 — but the 10th percentile is −$173, a losing season, and the 90th is +$5,173, more than double it. Same edge, same 500 bets. That spread is what variance does over a sample this size.

The lesson is not that the edge is unreliable. It is that a season is a small sample, and the bankroll has to be sized for the 10th percentile rather than the average.

Why is my actual profit so different from the expected figure?

Because the expected figure is an average across every possible season, and you only get one. Over a few hundred bets, variance dominates a two-or-three-point edge completely — the percentile table shows how wide that spread really is.

How many bets before results converge on the expectation?

Thousands. The sample size calculator gives the number for your specific edge, and it is almost always larger than a season. Convergence is slow because the edge is small relative to the noise.

Why does the calculator use analytic expectation instead of the simulation?

Because the expectation has an exact closed form and should never depend on a random process. The simulation adds the distribution around that number — it does not produce the number itself.

What if my odds and stakes vary?

Use your averages and read the result as an approximation. Varying prices and stakes widen the real distribution beyond what is shown, so treat the spread here as a floor rather than a range.

Which percentile should I plan around?

The 10th, for bankroll purposes. It is the season that goes badly without anything having gone wrong, and it is the one your staking has to survive. Planning around the median is how bankrolls run out.

• How to Track Your Betting Results HonestlyWin rate, ROI and units measure different things, and quoting the flattering one is how most records get inflated without anybody lying.9 min read

• Bankroll SimulatorTen thousand seasons of the same edge, and where they end up.
• Expected Value (EV) CalculatorWhat a bet is worth on average, given a price and your own probability.
• Sample Size CalculatorHow many bets it takes before a result means anything.
• Betting ROI CalculatorReturn on everything you put through, not just the bets that won.