Monty Hall

The Monty Hall Problem, sometimes called the Monty Hall Paradox, is a fascinating demonstration of how counter-intuitive statistics can be.

As the name suggests, the scenario plays out something like a game show. Say, with thanks to Frank Stockton, an eccentric ruler has arranged for you a game a chance and wit. You must pick and open one of three doors. behind one is a fair maiden to marry, behind the others, tigers. Pick one. But before opening it to discover your fate, the ruler indicates one of the doors you didn't pick that hides a tiger and asks if you would like to change your guess now that you've seen one of the tiger doors. Switch or stay?

Intuitively, it seems that whether you stay or switch, your chance is the same. Two doors and two fates: 50/50. But in fact that's not the case.

As it happens, switching as a strategy is twice as likely to be successful. Think of it this way: the only way to lose by switching is if your initial guess was correct, 1/3. Therefore, the odds of winning by switching are 2/3.