[Question] When should I close the fridge?

Say an open fridge door loses 1 Joule’s worth of cool air every second. Opening or closing the door blows a lot of air so you lose 10J.

If I’m just pouring milk in my coffee I can usually do that in 5 seconds so I should keep the fridge open because 10+5+10 < 10+1+10 + 10+1+10 (if it takes 1 second to get milk).

If I am making a sandwich then I should definitely grab everything (12 seconds), close the door, make a sandwich (3 minutes), then put everything back because 10+12+10 + 10+12+10 < 10 + 180 + 10.

Say it takes seconds to grab or return something and seconds to grab it and use it and return it. Then we should close the fridge if .

What if I’m not sure how long something will take?

Suppose the time to pour my coffee is drawn from a nearly normal distribution with mean 8 seconds and s.d. 2 seconds. I’m better off on average leaving the door open. Even if it’s already been 10 seconds, I expect to be done very soon. So I should always leave the door open.

(Scaled) geometric distribution: Half the time, when I would be done, another thing comes up (milk is sealed, spoon not in drawer) that takes another 4 seconds. I always expect to be done 8 seconds later, so I should still always keep the door open I think.

What if I have no idea how long something will take? The door is open and I’m waiting and waiting for the toddler to give back the iced mocha latte and it’s sure been a while. Must I take some prior? Is there a mystery here or is this just standard bayesian stuff?