Monty Hall

Three doors. Behind one is big prize, behind the other two is nothing. You choose a door. Monty then opens one of the other two doors to show there is nothing behind it (he's not randomly choosing, he knows what's behind every door) and offers you the opportunity to either switch your choice to the third door or to stick with the door you have.

Number of games (n):
Stick   Switch

Games results: (only displays if games≤1000)
0=lost, 1=won

Number of games won:
Number of games lost:
Probabilty of winning:

Intuition: If there are one million doors, you choose one, Monty shows empty 999,998 doors.
What's more likely, you picked the one-in-a-million door or the one unopened door is the winner?

3 doors: your initial door has 1/3 chance of being the winner, same as each of the other two doors. After the empty reveal your door's chance remains 1/3; the third door's chance increases to 2/3.

Million doors: your initial door has 1/M chance of being the winner, same as all of the other 999,999 doors. After the 999,998 empty reveals your door's chance remains 1/M; the third door's chance increases to 999,999/M.