Vos Savant suggests that the solution will be more intuitive with 1,000,000 doors rather than 3. (
vos Savant 1990a) In this case there are 999,999 doors with goats behind them and one door with a prize. After the player picks a door the host opens all but 1 of the remaining doors. On average, in 999,999 times out of 1,000,000, the remaining door will contain the prize. Intuitively, the player should ask how likely is it, that given a million doors, he or she managed to pick the right one initially.