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Market Making

Probability Betting Game

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Market Making Game ~5 min Guided tutorial
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Play Now Access includes a guided tutorial for your first game
Overview
Probability Betting is the classic trading interview betting puzzle turned into a game. You start with a balance of 1,000 and each round the house quotes fractional odds on random events from three sources: two dice, two cards dealt from a fresh deck, and three coins. Odds like 6.50:1 are prices, and every price implies a probability. Your job is to compute the true probability of each event, compare it to what the odds imply, bet only where the house is offering more than fair, and size each stake with the Kelly criterion. Two special bets, Insurance and Boost, pay out on whether your regular bets net a loss or a profit, and pairing Insurance with a big favourable bet can lock in a guaranteed profit. It is the same logic you will apply on a trading desk: market odds are option prices, your edge is the gap between those prices and your model, and your bet size is a risk-budgeting decision.
Example: picking the mispriced bets
Every round offers a handful of events on two dice, two cards and three coins, each with the odds the house will pay. Some are priced above their true probability and some below. You work out the real odds, stake what you like on the good ones, and pass on the rest.
Fair odds on the three backed events are 1.40, 3.25 and 7.00, so the dice and cards bets are priced generously and the three-heads bet is not.
Game Phases
1
Price every event Each round shows a menu of events across dice, cards and coins, each with fractional odds. Convert the quote to an implied probability: 3:1 means the house is pricing the event at 25 percent. Then compute the true probability yourself, for example both dice even is one in four and all three coins heads is one in eight.
2
Bet only with an edge Compare your probability to the implied one. When the quoted odds pay more than fair, for example 3.78:1 on a one in four event, the bet has positive expected value. Skip everything priced at or below fair; passing on a bad bet costs nothing and protects your balance.
3
Size with the Kelly criterion With variable bets you choose every stake. The Kelly fraction is bp minus q over b, where b is the net odds, p your win probability and q equals 1 minus p. A slightly generous 7.26:1 quote on a one in eight event justifies staking about half a percent of your balance, so favourable does not mean big.
4
Use the special bets Insurance wins if your regular bets end the round at a net loss, Boost wins if they end at a net profit. When one event carries very high odds, combining it with Insurance can guarantee a profit whichever way the round resolves. Submit to roll the dice, deal the cards and flip the coins, then watch each bet settle.
More Practice

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