The Monty Hall problem illustrates a simple setting where intuition often leads to a solution different from formal reasoning. The situation is based on the game show Let’s Make a Deal. First, Monty puts a prize behind one of three doors. Then the player chooses a door. Next, (without moving the pize) Monty opens an unselected door, revealing that the prize is not behind it. The player may

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**Tags:** looping, Monty Hall problem, multinomial observations, pseudo-random numbers, R function, simulation studies