Probability of profit in options: an estimate, not a promise

Almost every options platform shows a "probability of profit" next to the strategy. It is a useful number and also the most misread thing on the screen, because it is taken as a promise when it is an estimate resting on assumptions the market breaks daily.

What is probability of profit?

It is the estimated probability that AT EXPIRY the underlying sits in the region where your strategy makes money — beyond your breakeven, or between your two breakevens if the strategy has two, as an iron condor does.

It is computed assuming the future price follows a lognormal distribution: take the current price, project it with a drift and a diffusion that depend on time remaining and volatility, and measure how much of that bell sits inside your profit region. It is the same mathematical frame as Black-Scholes.

The assumptions it hides, one by one

• Returns are lognormal. In reality they have fat tails: extreme moves happen considerably more often than the model says, and they are exactly the ones that destroy option sellers.
• Volatility is constant to expiry. It is not, and you know it if you have ever watched implied volatility before and after an earnings report.
• It only looks at expiry. It ignores the path entirely: a position can go through a drawdown that forces you out and still finish "profitable" in the simulation.
• It ignores the volatility smile. The market prices far strikes at different volatilities precisely because it does NOT believe in a symmetric bell, and the calculation usually uses a single volatility.
• It knows nothing about early assignment or dividends, which on American options change the ending.

A number being an estimate does not make it useless: it makes it comparable. It is good for ranking two strategies against each other under the same assumptions. It is not good as a forecast of what will happen to you.

Why a high probability is not a good trade

Here is the part that is almost never said, and the part that costs money: probability of profit says NOTHING about how much you win or how much you lose. It ignores magnitude entirely.

Selling a far out-of-the-money option can give you a 90% chance of making $50 and a 10% chance of losing $950. The expectancy is 0.90 × 50 − 0.10 × 950 = −$50. Nine times out of ten you collect and feel clever; the tenth takes the previous nine and a bit more.

The calculation that matters is expectancy: probability × average win − (1 − probability) × average loss. A strategy that is right 40% of the time at 3-to-1 makes money; one that is right 90% of the time at 1-to-19 loses it. Probability alone is half a formula.

So what do I use it for?

• To compare variants of the SAME idea: two iron condors of different widths, under identical assumptions.
• To spot what is too good: a very high probability paired with a huge maximum loss is the signature of a negative-expectancy trade.
• To size: if you cannot afford the maximum loss, the percentage is irrelevant — that is the part of the analysis that depends on no model at all.
• Never as the sole reason to open. If the only argument is "it has an 85% probability", half the calculation is missing.

Any tool that hands you this number — ours included — is handing you an estimate under a model, not a measurement of the world. A platform presenting it as a real probability is telling you a cleaner story than the data supports.