Let's Make A Deal

Every remotely serious bridge player is aware of the Monty Hall Problem. You are on game show. There are three doors. Behind one door is a car and behind the other two are goats. You choose a door and then the host will open one door to reveal a goat. You are then offered a choice to stay with your door or switch to the other door.

Should you stay or switch?




The correct answer is to switch. This will be the correct strategy 2/3 of the time. You can work this out by brute force but the explanation I like was givent to me by a friend. We were setting up a game of poker and someone noticed that a seven was missing. I wondered, if we took out all the sevens, would this make a straight (now 98654 would be a straight) more or less likely. He just asked if you had one deck with five ranks and another with 1,000,000 ranks, which would be more likely to produce straights.

I would sum up this, which make it seem rather obvious, as follows: if you are trying to determine the direction of a function that you think is linear then uses numbers that are far apart instead of the ones presented to you.

In the Monty Hall Problem, imagine there are one million doors. When you select a door, the host opens every door but one. Would you stay or switch?