What is expected value?

Expected value is the probability-weighted average of every possible outcome of a bet · what you would get back on average if you could repeat it many times. You compute it by multiplying each result by its chance and adding the products together.

How do I calculate it quickly?

Multiply each result by its probability (as a decimal) and sum them. For example, a 50% chance of $200 plus a 10% chance of $1,000 plus a 30% chance of $50 plus a 10% chance of $0 is $100 + $100 + $15 + $0 = $215. Compare that to your stake to decide whether the bet is worth it.

Why do rare jackpots and risk of ruin matter so little, or so much?

A rare outcome contributes only its result times its small probability, so a 10% jackpot adds a tenth of its value to the average · less than people expect. A risk of ruin works the same way but downward: even a small chance of losing everything pulls the expected value down and, in real life, can end the game entirely.

How does difficulty work?

Easy is a two-outcome gain-vs-loss gamble. Medium adds a third outcome and a rare jackpot. Hard is a four-outcome bet with both a jackpot and a risk of ruin · the fat-tailed gambles where the arithmetic matters most.

Can I print it as a worksheet?

Yes. Expected Value supports the printable worksheet generator at /worksheets · each problem prints the table of chances and results with lettered choices and an answer key, ready for a maths or finance classroom.

Does it work offline?

Yes · Expected Value is part of the PlayMemorize Progressive Web App. Install once and play anywhere, even with no connection.

Expected Value · Ελληνικά

Estimate the probability-weighted payoff of a bet · weigh upside, downside, jackpots and the rare risk of ruin

Estimate the expected value of a bet · multiply each outcome by its chance and add them up. Multiple-choice probability game. JavaScript required.

Enable JavaScript to play.