Monty Hall
The Monty Hall problem is a statistics problem that can be solved using a simulation. The problem is as follows:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, Do you want to pick door No. 2?
Is it to your advantage to switch your choice? Let's find out!
Wins
With Switch
0
Without Switch
0
Iterations
Current
0
Total
switching
no switching
Results
The simulation could not confirm the well-known probability puzzle. Most likely the simulation was not run for enough iterations. In theory:
Switching doors increases your chances of winning. Specifically, while your initial choice of a door has a 1 in 3 (or 33%) chance of being the winning door, switching after the host reveals a goat behind one of the other doors gives you a 2 in 3 (or 66%) chance.
Why does this happen? Initially, you have a 33% chance of picking the prize door and a 66% chance of picking a goat door. When the host, who knows where the prize is, reveals a goat behind one of the other doors, nothing changes about the door you initially picked. If it was a losing door (which happens 66% of the time), then the other unopened door must have the prize. This is why switching gives you a 66% chance of winning. On the other hand, if your initial choice was the prize door (33% chance), switching will make you lose.
Therefore, if you aim to maximize your odds, you should always switch doors.