The Intuitive Monty Hall Problem

Many puzzles are difficult to solve from one perspective but easy from another. A challenge on stackexchange was to find an equivalent version of the Monty Hall problem where the correct solution of switching is obvious. Joshua B. Miller has an excellent answer. To recall, in the original there is a great prize hidden behind one of three doors. You choose a door. Monty Hall then reveals a lousy prize behind one of the other two doors (it’s always a lousy prize). Do you switch doors? Most people see no reason to switch. Even Paul Erdos was a no switcher! Moreover, most of those who do switch get to that conclusion with an unintuitive Bayesian calculation.

Here’s the intuitive version.

There are three boxers. Two of the boxers are evenly matched (no draws!); the other boxer will beat either them, always.

You blindly guess that Boxer A is the best and let the other two fight.

Boxer B beats Boxer C.

Do you want to stick with Boxer A in a match-up with Boxer B, or do you want to switch?

See also Miller’s new piece in the JEP which looks at the Monty Hall problem and the Hot hand puzzle.