🪙 Probability Betting Game Explained

In many quantitative-trading interviews you will be asked to reason about games of chance: dice rolls, card draws, coin flips, or synthetic “bets” that mimic option pay-offs. The exercise is not meant to turn you into a gambler; it is a quick and revealing way for the interviewer to see whether you can translate an informal description of risk into formal probabilities, price that risk correctly, and decide how much capital to allocate.

The game outlined here involves two dice, two cards, three coins, plus side bets that insure or lever the whole round of bets. You must recognise how the fractional odds the house quotes correspond to implied probabilities, spot when those odds are mis-priced, size each trade with a growth-optimal rule such as the Kelly criterion, and, when the provided odds allows it, stitch several bets together into a guaranteed-profit arbitrage. Being fluent in that sequence of steps matters because the logic is the same one you will apply on a trading desk: market odds are option prices, your edge is the difference between those prices and your model’s probabilities, your position size is a risk-budgeting decision, and an arbitrage is still the purest form of alpha. Some firms make the connection explicit and will hand you exactly this sort of betting puzzle under timed conditions. Master the mechanics here and you walk into the interview already speaking the language they expect.