Question 1

What is expected value?

Accepted Answer

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.

Question 2

How do I calculate it quickly?

Accepted Answer

Multiply each result by its probability (as a decimal) and sum them. For example, a 50% chance of $200 plus a 10% chance of description: 'Estimate the probability-weighted payoff of a bet · weigh upside, downside, jackpots and the rare risk of ruin.',,000 plus a 30% chance of $50 plus a 10% chance of $0 is description: 'Estimate the probability-weighted payoff of a bet · weigh upside, downside, jackpots and the rare risk of ruin.',00 + description: 'Estimate the probability-weighted payoff of a bet · weigh upside, downside, jackpots and the rare risk of ruin.',00 + description: 'Estimate the probability-weighted payoff of a bet · weigh upside, downside, jackpots and the rare risk of ruin.',5 + $0 = $215. Compare that to your stake to decide whether the bet is worth it.

Question 3

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

Accepted Answer

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.

Question 4

How does difficulty work?

Accepted Answer

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.

Question 5

Can I print it as a worksheet?

Accepted Answer

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.

Question 6

Does it work offline?

Accepted Answer

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