When Switching Fails

The host's intent is everything. Picture a careless host who flings open a random door without knowing what is behind it:

• Sometimes he reveals the car, and the round is spoiled
• When he happens to miss the car, the two remaining doors really are 50-50
• Switching no longer helps

That is the twist most people skip. The advantage exists only because the real host never opens the car on purpose. Remove his knowledge and the magic disappears.