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?

Regards

JR