Is that (that it didn't remove your guess) a reason not to switch? Note that the computer in this case knows, as monty Hall does, what the right answer is, and always removes wrong answers.

And here's the crucial part. If the computer, who randomly opens one of the other two doors you didn't choose, reveals the car, the program terminates right there, and starts again. If on the other hand, the computer opens one of the other doors, and by chance it is a goat, the program continues and you are given a choice to switch or not.

My question is, in this simulation of the Monty Hall show, with this extra random variation where the computer doesn't "know" which door contains the goat or car, but reveals a goat in one of the other doors by chance, is the probability still 2/3 that the other unopened door contains the car? Or does the probability change because of the extra random process? — Purple Pond

As I see it, you should be indifferent to keeping or switching in the modified game. My reasoning:

If you initially correctly pick the door with the car, then the computer will continue the game. However there is a 2/3 probability that you are initially incorrect. In those games, there is a 1/2 probability that the computer will open the door with the car and the game will be terminated. Then the same logic applies to the rerun games.

So if you play a game where you are asked to keep or switch, then that is one of the non-terminated games. Out of 300 games, you will (on average) be correct on 100 games that therefore continue, incorrect on 100 games that continue, and the remaining 100 games will be terminated and replayed. Of those replayed 100 games, you will be correct on 33, incorrect on 33, and 33 will be replayed. In this way, you will approach being correct on 150 games and incorrect on 150 games.

Is that (that it didn't remove your guess) a reason not to switch? Note that the computer in this case knows, as monty Hall does, what the right answer is, and always removes wrong answers. — unenlightened

For the millionaire scenario, the computer randomly removes two wrong answers from the set of three wrong answers. That selection is statistically independent of your (secret) guess, so the remaining two answers are equally probable.

Yes. It seems fairly intuitive in this case, and the only reason i brought it up is that it illustrates another feature of Monty's knowledge that is somewhat forgotten but necessary. - that Monty knows not only where the car is, but also what your choice is and responds selectively to both.

millionaire answers, Right and Wrong.

my guess:- R_____W_____W_____W

Computer
leaves:- WWW____R______R_____R

Yes. It seems fairly intuitive in this case, and the only reason i brought it up is that it illustrates another feature of Monty's knowledge that is somewhat forgotten but necessary. - that Monty knows not only where the car is, but also what your choice is and responds selectively to both. — unenlightened

Exactly. :up: