The variant works like this: A player picks a door, and Monty picks a door, and whoever gets the right door gets the prize. Monty knows what is behind every doo

The variant works like this: A player picks a door, and Monty picks a door, and whoever gets the right door gets the prize. Monty knows what is behind every door, so the prize is either behind the player's door or Monty's. So now, suppose you get to bet on who will win. Its clear that the chance of the player winning is 1/3. Thus the chance of Monty winning is 2/3. So bet on Monty. To change it back to the original problem, you are also the player in the game. So now, do you bet on yourself or on Monty?