Before you stands a building with N-floors. On each floor there is an open window. You have two identical glass balls. If you were to drop a ball out the window onto the ground below, it might or might not break.
Your goal is to determine the highest floor for which dropping a ball out the window results in the ball not breaking. You can continue dropping the balls out the window as long as at least one of the balls remains intact.
Example: You go to floor 1 and drop a ball. It doesn't break so you go to floor 2 and try again. This time it breaks so you can no longer use that ball. But you still have 1 ball left so you continue until that ball is broken. By the time the second ball breaks, you should know the answer (if not then the strategy is invalid).
The question: What is the most efficient strategy for determining said highest floor? For this question, the most efficient strategy is the one which yields the smallest average number of total drops over all possible highest floors for the building.
Example continued: If the building has 100 floors, the strategy described would require X + 1 drops where X = the highest floor's number. Summing over all possible X we would get 5050 so the average is 50.5 drops.
Note: It is possible that a drop from floor 1 results in a broken ball. It is also possible that a drop from the top floor results in an unbroken ball.
An answer will only get a green check if it is both correct and clearly explained.
Special aside: This is my first time posting a puzzle here. I tried to be clear and concise but please let me know about anything I need to clarify.
Is this question a duplicate? There are certainly similarities between this and the puzzle proposed here: Dinosaur egg drop. However, that puzzle specifies the number of floors and total number of drops. My question asks to generalize the number of floors and does not specify the number of drops, only that you can continue as long as at least one glass ball is intact. Additionally, I do not see the correct answer to this puzzle on that puzzle. Some of the answers and reasoning there are definitely similar to what I am looking for but none of those would get the green check from me on this puzzle.