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I'm sorry, I understand the difference you're implying, but can't figure out how it matters in practice. How can I even differentiate if Monty opens the door to

• dllthomas 6y ago
  It depends on the context. If it's a riddle, you could see if it's made clear by the wording, interrogate the person asking the riddle, or state the assumption you're making in your answer. If you find yourself actually in the situation, you need to make your best guess from what information is available. As for simulation, write a function that handles a single play through of the game and returns the outcome if you switch. Make Monty's strategy a parameter. Remember that "Monty revealed the car" is a separate outcome from "win" or "lose". Run that function a whole bunch of times, counting the outcomes. Compare the ratio between wins and losses, at various choices of strategy. To really drive home the point that strategy can matter, consider another possibility: maybe this season the studio executives have decided that cutting costs is more important than having an interesting game show, and Monty's strategy is now "reveal the car if you haven't already chosen it". Monty has revealed a goat. Is there still a 2/3 chance that you didn't pick the car?