Coin flip strategy raises game show odds to 50 percent
9 reported
A puzzle about an imaginary game show, published by The Guardian, presents a strategy that increases the chance of two contestants winning a prize from 25 percent to 50 percent. In the game, two people each flip a fair coin in separate booths, visible to the audience but not to each other. They must each guess what the other flipped, and both must guess correctly to win. The puzzle asks how a whispered strategy before the game can improve the odds. The solution, provided by Henk Tijms, Emeritus Professor of Operations Research at VU Amsterdam, is for each contestant to announce the result of their own coin flip. This strategy works because the two flips will match 50 percent of the time, and when they do, each person will have correctly predicted the other’s flip. An alternative strategy is for each to guess the opposite of their own flip, which yields the same probability. The puzzle was set on alternate Mondays since 2015 by The Guardian.
What’s reported
The game involves two people each flipping a fair coin in separate booths, visible to the audience but not to each other.
Each must guess what the other flipped; both must guess correctly to win a prize.
Without a strategy, the chance of both guessing correctly is 25 percent.
The solution strategy: each contestant announces the result of their own coin flip.
With this strategy, the probability of winning rises to 50 percent.
The four equally likely outcomes of two flips are HH, TH, HT, and TT.
The two flips will match (HH or TT) 50 percent of the time.
An alternative strategy is to guess the opposite of one’s own flip, with the same odds.
The puzzle was contributed by Henk Tijms, Emeritus Professor of Operations Research at VU Amsterdam.
Key figures
Henk Tijms, Emeritus Professor of Operations Research at VU Amsterdam, author of several books on probability.
Sources: The Guardian
