Thanks for clarifying a very counter intuitive problem. I always struggled with this one, not anymore :) Sometimes scaling things up is the best way to understand things. Who knew!

I don't see why the other door has 99x more probability of being correct. It's still 50/50, original door or remaining door, the other 98 don't change the odds.

Your initial pick has a 1/100 chance of being right. If you switch, and you were right, you lose. On the other hand, your initial pick has a 99/100 chance of being wrong, and if you were wrong, and you switch, you win. So switch.

Let's play a game to make this more clear. I'm thinking of a number between 1 and 1000. First, guess what it is.

2

Well, before you finalize your guess, I'll give you a hint: it's either 2, or 437. It's not any other number.

Keep in mind I made my choice before we started, and it hasn't changed.

Do you want to change your guess to 437, or stick with 2?

I've always flip-flopped on grasping the Monty Hall thing (sometimes I'd think I understand, other times not so much)... but this little guessing game really clarified it for me, once and for all. Thanks!

This is a nice reinterpretation.

the behavior of the game host as he will never reveal the door with the car this is the key bit. If the door you picked is the correct one (1% chance) the host can open any door. If you picked incorrectly (99% chance) he can open any door except the winning door so the remaining door will be the correct one 99% of the time.