A very educational variant I've heard is to up the number of doors from 3 to 10000.
Now that Monty is closing off 9998 doors, it makes the leap of logic much less difficult. Clearly the one door he didn't close off is special.
Now that Monty is closing off 9998 doors, it makes the leap of logic much less difficult. Clearly the one door he didn't close off is special.
My variant was not intended to assist explaining the original, it's a variant intended to make people think again. It often exposes non-understanding in those who will blindly and automatically say "Switch".
Here's another variant. 12 doors, I let you choose 3. I then open 4, leaving your chosen 3 and 5 others.
I let you keep your original choice, or give them up to choose only one of the others. Should you switch now?
P(3/12) = 25%
The remaining doors have 75% probability and choosing 1/5 only gives you 15% chance of winning.
Explaining that to muggles, though, is non-trivial.