>Dan
>
>Ah.
>
>It seems the basis of the "proof" is that if you choose a door with a goat, you are better off changing once Monty shows you the other goat. Since there are twice as many goats as cars, you are twice as likely to have picked a goat and are therefore twice as likely to get a car if you change.
>
>On that basis, the issue is that the "other" door will have a 100% chance of a car 66% of the time, while it will have a 0% chance of a car 33% of the time.
>
>Got it.
>
>So here's one for you.
>
>3 people arrive late at a $100/night per person hotel. They ask for rooms; there is only a room with two beds left. The night bellboy is not allowed to offer discounts so they take the room at full price, $100 each, or $300 total.
>
>In the morning the manager says to give them a $50 discount for having 3 people in a double room.
>
>The bellboy is dishonest. He gives each guest $10 back and pockets $20 himself.
>
>So: the guests ended up paying $90 each, that's $270. Add the $20 kept by the bellboy, that's $290.
>
>What happened to the other $10 they paid?

They didn't pay these $10. They paid 3*100-30=3*90. The same $300 was initially split by 3*100-50+20=270, i.e. 250+20 (the 250 they had to pay after discount plus the 20 the bellboy took).

Nice try. My students were bombing me with such examples of barroom calculus about once in two weeks. It's been a while, but I think I'm still in shape :).