Does Monty Hall logic apply to this real world situation?

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I recently posted a tweet claiming I had encountered a real life Monty Hall dilemma. Based on the resulting discussion, I’m not sure I have.

The Scenario

  • I have 3 tacos (A,B,C) where tacos A and C are filled with beans, and taco B is filled with steak.

  • I have no foreknowledge of the filling of any tacos.

  • My wife only knows that taco C is filled with beans.

  • My wife and I both know that I want steak.

  • After I pick taco A, my wife informs me taco C is filled with beans.

  • I switch my pick from taco A to taco B, thinking the logic behind the Monty Hall problem is relevant to my choice.

Edit for clarity

  • Timing: The contents of taco C were not revealed to me until after I had made my selection of taco A.

  • My knowledge of what my wife knew: When she told me the contents of taco C, I knew that she had previously opened taco C. I also knew that she had no other knowledge of the contents of the other tacos.

Questions

  1. Even though my wife does not know the fillings of all the tacos, does her revealing that taco C is definitively not the taco I want after I’ve made my initial selection satisfy the logic for me switching (from A to B) if I thought it would give me a 66.6% chance of getting the steak taco?
  2. If this is not a Monty Hall situation, is there any benefit in me switching?

Answer

No, this is not a Monty Hall problem. If your wife only knew the contents of #3, and was going to reveal it regardless, then the odds were always 50/50/0. The information never changed. It was just delayed until after your original choice. Essentially, you NEVER had the chance to pick #3, as she would have immediately told you it was wrong. (In this case, she is on your team, and essentially part of the player). #3 would be eliminated regardless: “No, not that one!”

Imagine you had picked #3. Monty Hall never said, “You picked a goat. Want to switch?”

If he did, the odds would immediately become 50/50, which is what we have here.

Monty always reveals the worst half of the 2/3 you didn’t select, leaving the player at 33/67/0.

Attribution
Source : Link , Question Author : Will Cole , Answer Author : GAEfan

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