Expected Value

Expected Value is a fast decision-making trainer built on the single most useful idea in probability: the expected value of a bet is the average amount you would walk away with if you could play it over and over. Each round shows a description: 'Estimate the probability-weighted payoff of a bet · weigh upside, downside, jackpots and the rare risk of ruin.',00 stake and a small table of outcomes · each outcome has a chance and a dollar result · and your job is to estimate the probability-weighted average and pick the closest figure from four choices.

How expected value works. You multiply each result by its probability, then add everything up. A bet with a 50% chance of ending at $200, a 10% shot at a description: 'Estimate the probability-weighted payoff of a bet · weigh upside, downside, jackpots and the rare risk of ruin.',,000 jackpot, a 30% chance of dropping to $50, and a 10% risk of losing it all is worth 0.5 × $200 + 0.1 × description: 'Estimate the probability-weighted payoff of a bet · weigh upside, downside, jackpots and the rare risk of ruin.',,000 + 0.3 × $50 + 0.1 × $0 = $215 on average. That single number tells you whether the bet is worth taking · above your description: 'Estimate the probability-weighted payoff of a bet · weigh upside, downside, jackpots and the rare risk of ruin.',00 stake it is favourable, below it is a losing proposition.

Why the tails matter. The whole skill is learning to weight rare outcomes correctly. A jackpot that only hits 10% of the time barely moves the average · and a 10% risk of ruin quietly drags it down. Most people anchor on the headline outcome or average the results as if every branch were equally likely; the game's distractors are built from exactly those mistakes, so you learn to spot them in yourself.

Three difficulty tiers. Easy is a clean two-outcome gamble · one gain, one loss · the calculation a beginner can do in their head. Medium adds a third branch and a rare jackpot. Hard is the full four-outcome bet with both a jackpot and a risk of ruin, the fat-tailed gambles where intuition fails and the arithmetic earns its keep.

Deterministic. Every round is generated from a seed, so the same difficulty always produces reproducible bets and the printable worksheet's answer key matches the live game byte-for-byte.

Part of the PlayMemorize family of brain-training games. Runs entirely in your browser, works offline as a Progressive Web App. Prefer to just crunch your own numbers? Use the Expected Value Calculator.