Scenario 2 isn’t the Monty Hall problem, although it’s clearly psychologically what many people get hung up on.
If you came to the three doors and one was open, then, yes, you have a 50% chance of getting it right.
But that’s not what happened. When you picked a door, you blocked Monty Hall from picking that.
Monty is stuck by the rules of the game: he’s required to open a losing door, and he can’t pick your blocked door. Now, when you blocked a door at random, you’re in one of two scenarios:
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1/3 of the time you will have blocked the winning door. In this case, Monty can pick either of the remaining doors, and the other door is also a loser.
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But 2/3 of the time, Monty is required to pick the sole remaining losing door, and the other door is a winner!
So maybe if you didn’t think of it as “choosing and switching” but instead “blocking and then choosing,” this makes more sense.
What do you think? @simonize?
