This code runs an experimental verification of the Monty Hall brain teaser, which is rephrased below:
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, camels. 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 camel. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
The intuitive (but incorrect) answer is that it makes no difference whether you switch or not: the odds of getting a car are 50/50.
The actual answer is that you should always switch*; when you switch, you have a 2/3 chance of getting the car, and when you don't you have a 1/3 chance of getting the car.
- assuming you want a car and not a camel.
Figure 1: results of running experiment 1000 times switching and 1000 times not switching
The host is not choosing their guesses randomly, but is being informed by both your initial decision and their existing knowledge of which door has a car behind it. If you switch, you will always end up getting the opposite of what you first guessed. Since you are twice as likely to have first guessed a camel, you are twice as likely to end up with a car if you switch; see table below.
| Initial guess | Odds of getting car if you switch | Odds of getting car if you don't switch |
|---|---|---|
| Car | 0 | 1 |
| camel | 1 | 0 |
| camel | 1 | 0 |
Table 1: If you switch you have a 2/3 chance of getting the car, if you don't you have a 1/3 chance
Basically just press run MontyHall.py to reproduce the figure above. The only non standard library is matplotlib for plotting.