Thinking about the counterintuitive Monty Hall Problem (stick or switch?), revisited in this ME question, I thought I would issue a challenge:
Give in one (perhaps long) sentence a convincing explanation of why switching is twice as likely to lead to winning as sticking.
Assume the game assumptions are pre-stated and clear.
The probabilities are not even close, so there should be a convincing explanation after all the discussion of this topic, even though "1,000 Ph.D."s got it wrong (in 1990 when it first went viral).