Alternate reality rules of the game are: nobody speaks, you pick any two doors you like, and you win the prize behind both of them. The odds of wining this game

Alternate reality rules of the game are: nobody speaks, you pick any two doors you like, and you win the prize behind both of them. The odds of wining this game is obviously 2/3. Monty will gesture at you to point to a door. You point at the one you don't like. Monty will then show you one of your prizes behind one of your two chosen doors. Monty will then gesture for you to point to a door. You point at the remaining one you liked. Monty then gives you your second prize behind that door. Notice that all of the externally visible actions are identical to the original game.