Three on three problems, also called Monty Hall problem, from the American television game show Let 's Make a Deal, the name of the problem from the show's host Monty Hall (Monty Hall), the question is this: the participants before three of a closed door, behind one door is a car, select a car somewhere behind that door can win the car, while the other two doors behind in possession of a goat, selected a goat behind that door can win the goat, when participants selected a door, but not to open it, in the host opens the door to the remaining two fan, the result is a goat, host then asked participants want to change to choose, choose another still closed door

, 1. If the host know car after the door (i.e., the host will opened two doors are left no cars in the door), so participants don't change and change in both cases, the statistical probability of participants selected car number (through the experiment many times, statistics is selected, and the total test times), (2) if the host does not know the car after the door (namely the host will open a door in the remaining two doors, but when the door may be a car, if it is a car, the participants can only win a goat (but this situation with the experimental requirements), if not the car, the contestants to decide whether to replace option), so participants don't change and change in both cases, the statistical probability of participants selected car, 3. If the host know the car after the door, but the contestants don't know whether the host know cars after that door, in front of the participants choose whether to replace, host contestant asked: "do you know a car behind that door?" , the host honest answer: "know," so if the answer to the host will help participants to choose,

Extension consider: 1. The host provides answers contain much information? 2. If you can calculate the host to provide the answer to the worth? 3. If you can't calculate, what information you need in order to assess the value of the message? Extension problem: if the three into four problems (three goats, a car) 1. The host opens a door in the remaining three, behind is a goat. 2. The host opened two of the three remaining, is behind the goats; Please design process simulation, gives and not in probability,