Monty Hall Simulation
This is a simulation of Monty Hall Problem, named after the host of the game show Let's make a deal.
We have three doors. We have two goats and one car, each one behind a door. We have a player and a host (Monty Hall). The game steps are:
- Player chooses a door.
- Host opens another door revealing a goat behind it.
- Player choose to stay or switch doors.
The question is: what is the best strategy for the player? Stay or switch?
The answer is: switch.
We can show that the probability of winning is 2/3 if the player switchs and 1/3 otherwise. Most people (myself included) would think at first that the probability is the same, as remains two doors, one with the car and another with a goat, and that is what makes this problem so interesting (for me, at least).
The best explanation in my opinion is as follows:
- We choose a door, let's say number one.
- We have a 1/3 chance that the car is behind the door. In this case, if we switch we will loose the car.
- We have a 2/3 chance that a goat is behind the door. In this case, if we switch we win (as the other goat was revealed by the host).
- Conclusion: if we switch we win 2/3 of times.