Three doors, one car, two goats; you pick, the host — who knows where the car is — opens a goat door and offers a switch. When Marilyn vos Savant said switching wins twice as often, ten thousand readers wrote in to disagree, PhDs included. Play until the numbers convince you, then see every possible world at once — and meet the evil twin hosts who change the answer.
Your first pick is a 1-in-3 shot, and nothing the host does can retroactively improve it — he was always going to show you a goat, whichever door you were standing on. So after his reveal your door still holds 1/3, and the remaining 2/3 has nowhere left to live but the single door he conspicuously refused to open. Switching is just collecting it.
If the fog won't lift at three doors, add ninety-seven: pick 1 of 100, watch him snap open 98 doors he knew were safe, and ask yourself whether the lone door he tiptoed around is really a coin flip against yours.