Probability which door to pick

Donovan, D. Ellis, K. Flannery, S. In Code: A Mathematical Journey. London: Profile Books, pp. Gardner, M. Gotcha: Paradoxes to Puzzle and Delight. New York: W. Freeman, Gillman, L. Monthly 99 , 3, Hoffman, P. New York: Hyperion, pp. Neuwirth, E. Selvin, S. The Power of Logical Thinking. New York: St. Martin's Press, Weisstein, Eric W. To build the suspense still further, he gives the contestant an opportunity either to stick with their original choice or to switch to the unopened door. You are the contestant.

What should you do? Almost everyone stays. So they stick with their first choice out of inertia, pride, or anticipation that their regret after an unlucky switch would be more intense than their delight after a lucky one. Vos Savant wrote that you should switch: the odds of the car being behind Door 2 are two in three, compared with one in three for Door 1.

The column drew ten thousand letters, a thousand of them from PhDs, mainly in mathematics and statistics, most of whom said she was wrong. Here are some examples:. You blew it, and you blew it big! Whether you change your selection or not, the odds are the same. I am sure you will receive many letters on this topic from high school and college students. Perhaps you should keep a few addresses for help with future columns. Maybe women look at math problems differently than men. You should switch.

There are three possibilities for where the car could have been placed. If the car is behind Door 1 top left , you win. If the car is behind Door 2 middle left , you lose. If the car is behind Door 3 bottom left , you lose.

If the car is behind Door 1, you lose. If the car is behind Door 2, Monty would have opened Door 3, so you would switch to Door 2 and win. If the car is behind Door 3, he would have opened Door 2, so you would switch to Door 3 and win. Nowadays, you can play it online. Many people insist that each of the unknown alternatives in this case, the unopened doors must have an equal probability. Does it matter? The game is really about re-evaluating your decisions as new information emerges.

Just pick door 1 or 2, or 3 and keep clicking. Click click click. Look at your percent win rate. Pick a door, Monty reveals a goat grey door , and you switch to the other. Look at your win rate. If you had a coin, how many flips would you need to convince yourself it was fair? You might get 2 heads in a row and think it was rigged.

Just play the game a few dozen times to even it out and reduce the noise. The best I can do with my original choice is 1 in 3. Instead of the regular game, imagine this variant:. Try this in the simulator game; use 10 doors instead of Your decision: Do you want a random door out of initial guess or the best door out of 99? Said another way, do you want 1 random chance or the best of 99 random chances? Filtered is better. Yes, two choices are equally likely when you know nothing about either choice.

You pick the name that sounds cooler, and is the best you can do. You know nothing about the situation. Would this change your guess?