Here is a terminal demonstration of the monty hall problem in python with nicely colored text.
You can try it out here: https://replit.com/@CSharpIsGud/MontyHallDemo?v=1
It’s configurable so that you can change the number of doors, you won’t see a big difference if you choose the traditional 3 doors, but if you have more doors you will choose the prize door much more often if you switch.
Or if you don’t know what the monty hall problem is, you can read a screenshot of the included explanation from the demo.
Could you explain why there would be a 99% chance of winning if you switch and there are 100 doors? Is that assuming that there are things behind nearly all doors?
There would only be one prize and every other door would be empty. But even after all but 2 doors have been revealed out of 100 doors. Switching is a 99% win.
Put the door you chose in group 1.
Now put all the 99 other doors in group 2.
The chance of the prize being in group 2 is much higher than group 1, since there are many more doors in group 2.
The result is that once every door but one in group 2 is revealed to be empty, the entire probability of group 2 converges on that single door.
But what if the door they originally picked was the correct one? Then if you switch then you lose… Also, it would still be a 1/3 chance no? Because even if you choose to switch the doors, again, there is still a chance that the one you chose first was correct, so it would, in fact, be a 1/3 chance.
The monty hall problem would not exist if that were the case. That’s why the demo allows you to change the number of doors. If you set the number of doors higher you will notice the effect get very strong.
Indeed if you were plainly choosing from a set of 3 doors, it would be a 1/3 chance.
But since the host opens one of the other doors that doesn’t have the prize it’s a 2/3 chance the other remaining door has the prize instead.
You can experience this by setting the amount of doors higher, you might not notice it when it’s just a 2/3 chance but as you increase the number of doors it will start getting impossible to win if you don’t switch.
