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    $\begingroup$ @z100 FYI I've posted a simple python implementation. It very consistently (almost suspiciously so) comes out at 1006 or 1007 questions. $\endgroup$
    – loopy walt
    Commented Jul 28, 2023 at 1:31
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    $\begingroup$ Very similar to isaacg idea, but does something specific with the E part instead of just trying to bisect I all the time. Doesn't look suspicious to me. :+1: $\endgroup$
    – justhalf
    Commented Jul 28, 2023 at 2:35
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    $\begingroup$ @JaapScherphuis I have now, see updated post. Thanks for the suggestion. $\endgroup$
    – loopy walt
    Commented Jul 28, 2023 at 16:03
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    $\begingroup$ Great solution! About finite size issues, here's a way of thinking I've found helpful in problems like this. Imagine a continuous variant of the game, where the players' numbers and your guesses are real numbers in the range. You win if your interval shrinks below length 1. Then, a winning strategy in this game translates to the original game within the same number of guesses -- translate each question to a discrete one, and finish by guessing the unique number in the interval. This may waste a couple questions though since the interval can contain a unique integer but have length above 1. $\endgroup$
    – xnor
    Commented Jul 28, 2023 at 22:51
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    $\begingroup$ @xnor That looks like a good way to get some intuition and perhaps estimates. Thanks. Also, you have been outgolfed ;-) I'll post in a minute. (Probably just a comment.) $\endgroup$
    – loopy walt
    Commented Jul 29, 2023 at 19:05