Easy, Martini, don't get too worked up. I can throw facts and figures out there and computer simulations.
I didn't get worked up. If you can throw out computer simulations that prove your assertion to be correct, then please do it. Mine proved that my solution is the correct one. All "facts and figures" you threw out were disputed.
I think it is all irrelevant information to make a game show more entertaining. It all boils down to two doors, one with a goat, one with a car. You get to pick one. That gives you a 50% chance.
And again, according to that rationale, if it boiled down to two doors (but there were originally 100) one with a goat, one with a car. You get to pick one. That gives you a 50% chance.
I am not trying to disprove the fact that you start with a 1/3 of getting it right with your first guess. I am saying that when you eliminate a possibility, the chances of the remaining possibilities should be recalculated.
That would only be true if the host randomly eliminated a door and it happened to be a goat. I'll explain using the example with 100 doors:
You choose a door, the host randomly opens up 98 of them from the remaining 99 doors. All 98 happen to have goats behind them. Should you switch to the one he didn't open? It doesn't matter. The probability is 1/2 that you chose the door with the car behind it.
other scenario:
You choose a door, the host knows which door has the car behind it (one of the 99 or the one you chose) and purposely doesn't open it if it happens to be behind one of the 99 remaining doors. He opens up 98 doors which he knows have goats behind them. Should you switch? Yes. Switching will give you a 99/100 probability of winning a car.
For your 100 boxes example:
The chance of choosing the box correctly on the first guess is 1:100. The host takes away 98 boxes. It's a slightly different problem because the possibilities eliminated have a different combined probability than the original choice. Now if there were 99 boxes, and you got to choose 33, then the host removed 33 and you could either keep your original or take the 33 left untouched, then the probability of the winning box being in your original 33 and the untouched 33 would be the same.
But you said, "It all boils down to two doors, one with a goat, one with a car. You get to pick one. That gives you a 50% chance."
If the host reveals 33 doors which have goats behind them
on purpose, then you should switch. He only revealed what's behind the doors if they had goats behind them. That makes the other 33 doors much more special than yours. Yours were picked randomly; the other 33 remaining doors were given special protection from not having the car removed from it if it were among the 66 that you didn't choose.
