Coin flip strategy boosts game show odds to 50 percent
7 reported
A puzzle about an imaginary game show, published by The Guardian, presents a strategy that increases the probability 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 guess what the other person flipped, and both must guess correctly to win. The puzzle asks how a whispered strategy between contestants can improve their odds. The solution, credited to Henk Tijms, Emeritus Professor of Operations Research at VU Amsterdam, involves each contestant announcing 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 contestant has correctly predicted the other’s flip. An alternative strategy of guessing the opposite flip also yields the same 50 percent probability. The puzzle was set on alternate Mondays since 2015.
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 person 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: each contestant announces the result of their own coin flip, raising the probability of winning to 50 percent.
The four equally likely outcomes are HH, TH, HT, and TT; both flip the same value 50 percent of the time.
An alternative strategy of guessing the opposite flip also yields 50 percent odds.
The puzzle was provided by Henk Tijms, Emeritus Professor of Operations Research at VU Amsterdam.
Key figures
Henk Tijms, Emeritus Professor of Operations Research at VU Amsterdam
Sources: The Guardian
