# The Monty Hall Problem. Probability is that you will win.

The Monty Hall Problem is a very challenging and interesting problem. It basically was a game show titled,”Let’s Make a Deal” ,hosted by Monty Hall and Carol Merril. It originally ran from 1963 to 1977 on network TV.

The highlight of the show was the “Big Deal,” where contestants would trade previous winnings for the chance to choose one of three doors and take whatever was behind it–maybe a car, maybe livestock. Let’s Make a Deal inspired a probability problem that can confuse and anger the best mathematicians, even Paul Erdös.

The popular Indian show, “Khul Jaa Sim Sim”, was an Indian version of this reality show. Now a very simple yet technical concept goes into winning this game. It is also explained in the movie “21” which is based on a true story of card dealing.

Here goes the probability theory. There are 3 doors. Behind one is the grand prize, say a brand new Audi R8. And the other two have nothing. The game show host knows what’s behind each of the doors. Now he asks you to choose one.( assume that the car is behind door 2). Say, you chose door no. 1. He, then, opens door no. 3 to reveal that there’s nothing and asks you if you want to switch. If you switch, you win. If you don’t, you lose. Now it could be possible that the car could have been behind door 1 only. But the probability of switching the door increases your chances of winning. HOW? Let’s see

Initially, out of the three doors, choosing the winning door in the first try and not switching later is 1/3 or 33.3%. The chances of winning double when you switch.

Take the previous case only. Now, if you switch from 1 to 2 or 3 to 2, you get 2 win situations. And if you switch from 2 to 1 or 3, you lose. So out of the three cases, 2 mean win and 1 means lost. So 2/3 is 66.67% which is double of 33.3%. so with a simple concept of conditional probability, we understand, how switching can help you increase your odds of winning.  This important concept of statistics can be extended to card dealing and other such prospective activities also. So do you see how you could double your odds of winning? So next time you play such a game, SWITCH!