Monty Hall Simulator

Because the host's action carries information. The host always knows where the car is and always opens a goat door — never the car, and never your door. When you first picked, you had a 1/3 chance of being right and a 2/3 chance of being wrong. If you were wrong (2/3 of the time), the host is forced to open the only other goat door, which means the remaining door is guaranteed to be the car. Switching wins whenever your first guess was wrong — which is 2/3 of the time.

Then the information changes completely, and switching would no longer have an advantage — a random reveal that happens to show a goat gives you no extra information about where the car is. The entire effect depends on the host knowing where the car is and deliberately avoiding it.

Yes — play enough rounds yourself with the same strategy and your personal win rate will settle near the theoretical value, same as the bulk simulation shows instantly over thousands of trials. A handful of rounds can easily look close to 50/50 by chance; the pattern only becomes reliable with more trials, which is exactly what the law of large numbers predicts.

No — by symmetry, every door has an equal 1/3 chance of hiding the car before you choose, so your first pick doesn't bias the outcome one way or another. What matters is only what you do after the host reveals a goat.