The Monty Hall Paradox

The Monty Hall problem is a famous game of probabilities named after a television program . It calls the paradox , because the right strategy we often seems against - intuitive. Experiments also show that even repeating several times the game , humans really hard to understand the trick , as the pigeon , he 's doing very well. From there to conclude that intellectual superiority volatile , it is only one step !





The game principle :
 The Monty Hall paradox originates in the game show Let's Make a Deal , aired in the US from 1963. The host Monty Hall are offered the following choice . A candidate is presented face 3 doors : Behind one of these doors is a gift , whereas behind each of the other two doors is an object without interest (typically a goat ) . The candidate chooses one of those three doors, but without opening ; The host ( who knows where the gift is) opens one of the two remaining doors , taking care (if necessary) to avoid the door that contains the gift ( the door opened by the host always so reveals a goat ) ; The candidate can then choose between keeping the original door, or to change to take the other remaining door. What should the candidate? Keep or change? So think 5 minutes ...



One chance in two (or three) :


By doing a quick reasoning, we can say we have a choice between two doors, and each door initially just as likely as the other to contain the gift. While the changing or that one keeps his door, we win with an even chance. In fact this argument is misleading and the real result is that the probability of winning if we change is 2/3 against 1/3 only if one retains its original door: so we always interest in changing! One can spend hours trying to convince himself of this result. Here is the most simple argument: if you stay, you win if you had originally made the right choice (which occurs in one third of cases), if you change, you win if you made the wrong choice from (which occurs 2 times 3). So you change saves in 2/3 of cases. For skeptics, the most definitive method is to count all cases, even to a numerical simulation (it is said that the mathematician Erdos had to do this simulation to be convinced of the result). For skeptics who do not like the physicist methods, the solution with Bayesian probabilities.