The puzzle doesn't work without the host always revealing a booby prize.
In the example you gave it's just random chance. In the Monty Hall puzzle it works out that statistically you should swap.
In the example you gave it's just random chance. In the Monty Hall puzzle it works out that statistically you should swap.
"Monty Fall" or "Ignorant Monty": The host does not know what lies behind the doors, and opens one at random that happens not to reveal the car. Switching wins the car half of the time.
Swapping doesn't affect the outcome, it's a 50/50 whether you swap or not.