Evaluating a Parlay Bet on Four Sports Matches

This question looks at a simple gambling product: a parlay bet on the outcomes of several sports matches, where you only get paid if every prediction is correct. The candidate is asked to judge whether the quoted odds make the bet attractive when they have no special insight into the teams or matches. The setup mimics real bookmaker offerings, where casual bettors often underestimate how unlikely it is to get every leg of a multi-game ticket right, especially when each game is roughly a coin flip.

Answering it well requires comfort with computing probabilities of independent events, translating odds into implied probabilities, and then forming an expected value. The interviewer is watching whether the candidate naturally multiplies probabilities for the joint event, correctly interprets "X-to-1" odds as a payoff structure, and sets up the expectation cleanly rather than relying on intuition. They also look for an understanding that, in the absence of informational advantage, such constructed games are typically unfavorable, and for clear, numerate reasoning instead of hand-waving.

What it tests

The core structure here is the comparison between the true probability of a compound event and the payout odds offered. In any problem where a payout is contingent on multiple independent events all occurring, the probability of success is the product of the individual probabilities. The expected value of the bet is then the probability of success times the payout, minus the probability of failure times the loss. The key is that bookmakers set odds to ensure the expected value is negative for the bettor, unless the bettor has an informational edge. This pattern holds because, without such an edge, the law of large numbers ensures repeated bets will lose money over time if the payout does not match or exceed the inverse of the true probability.