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.
- 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?
- If this is not a Monty Hall situation, is there any benefit in me switching?
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.