Egg dropping puzzle - clarification of problem statement
Imagine this as a game of two players: the experimenter vs. nature.

The egg breaking limit is not chosen in advance.
Instead, the players together form statements about its possible values, all the way until only one value remains.

On each turn, the experimenter chooses the floor from which to drop the egg.
After that, the nature chooses whether the egg actually breaks or not.

Of course, with some moves of the experimenter, nature can't choose because the previous statements already determine the outcome.
However, note that a good strategy for the experimenter does not make such redundant moves.

With such formulation, the "worst case" here is equivalent to the game-theoretic "if nature plays optimally", and "minimizing the number of moves in the worst case" to "if both play optimally".