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Optiver's first-round interview leans hard on fast probability and expected value: an interviewer puts simple random events in front of you — coin flips, dice rolls, card draws — quotes a payout, and watches how you decide whether the price is worth taking. This game drills that exact instinct. You're shown a board of propositions, each with a stated payout, and you take only the lines priced in your favour. You're taking prices, not quoting them — the board sets the odds, and your score is your final bankroll. The whole game reduces to two skills: pricing each line against its true probability, and declining to bet when there is no edge.
That second skill is where most candidates lose. The board is seeded so that most lines are fair or slightly against you; the people who pass sit those out, take only the genuinely mispriced ones, and stake a fraction of bankroll instead of going all-in on a 60/40. Betting every line at full size is the fastest way to a zero.
Each round deals a priced board of coin, dice, card and combined propositions where some lines are −EV, some are real overlays, and occasionally two complementary lines pay enough on both sides to lock in an arbitrage. You compute the fair odds in your head and take only the positive-EV bets. Fair probabilities are computed exactly (or by simulation for the combined legs), so every grade is checkable. (Want the helpers — fair odds, the EV of each line, recommended sizing — visible while you learn? Switch to Assisted mode; Test mode hides them, the way the real interview does.)
It is a fast probability and expected-value exercise in Optiver's first interview round (used for both quant trader and quant researcher candidates). You're given betting propositions on simple random events (coins, dice, cards) with stated payout odds, and you decide whether to take each one and how much to stake. You're scored on your final bankroll, so it rewards correct pricing and disciplined sizing, not volume of bets.
Compute the true probability p of the event, then compare to the offered profit odds b. The bet is +EV when b·p − (1 − p) > 0, i.e. when the offered odds are better than the fair odds (1 − p)/p. If the line is fair or worse, the correct play is to skip it.
The Kelly fraction: f = (bp − q)/b, where b is the profit odds, p the win probability and q = 1 − p. In practice a half-Kelly stake is safer because your probability estimates under time pressure carry error. Never bet the full bankroll on a single line.
Yes. It runs in the browser at quantvault.org with no payment required. Each round generates a fresh board with exact fair probabilities, so you can drill the find-the-edge, skip-the-rest, Kelly-size loop as many times as you want before the real assessment.