Comments by "" (@PunmasterSTP) on "" video.

That is a good thought! I think the issue might be that your opponent can't guarantee that his or her highest preference would still be available, as you could have gotten it earlier. I think the KC algorithm only works because your opponent knows that you would never choose your least preferable city at any point. Keeping it "available" for you until the end gives your opponent leverage that they wouldn't otherwise have.
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That definitely seems to work for this example. I'm wondering if there is a certain way to figure out if and when it's fine to "switch strategies" for the rest of the game...
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I don't think it generates a complete ordering (i.e. it generates just a weak partial order), but you can still make some comparisons. For instance, someone getting their 1st, 2nd and 4th preferences is still preferable to them getting their 1st, 2nd and 5th preferences. For the problem in the video, you initially got your 1st, 3rd and 5th preferences. But you can think how your 2nd preference is better than your 3rd, and how your 3rd is better than your 5th. Therefore the set (1st, 2nd, 3rd) is strictly better than (1st, 3rd, 5th). Thinking about it another way, going from your outcome in the initial draft to the final outcome, you basically swapped out your 5th preference for your 2nd, which is something you'd want to do (assuming you're rational).
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@BinaryRhyme.JackOfArts Sorry I'm not quite sure I understand. On the opponent's last pick, there'd be only one choice left to make.
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@BinaryRhyme.JackOfArts I think that could make sense, but the situation is a bit different since William is demonstrating backwards induction. Your opponent's first pick at 7:51 occurs after your first pick at 8:05, where you select Pittsburgh.
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@BinaryRhyme.JackOfArts I think the issue is still related to the illustration of backwards induction, which moves *backwards in time*. The demonstration starts around 4:31 when William mentions that your opponent chooses a city "with the final pick." And at 8:33, William mentions that the key move was sniping Pittsburgh "with the first overall selection." I definitely think this can be confusing, and it was especially so for me because I didn't quite remember or recognize all of the cities by their landmarks.
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@BinaryRhyme.JackOfArts I think this situation was rather complex, and backwards induction can always be confusing. I've noticed that William uses backwards induction in a lot of his other puzzle videos, and for a more gentle introduction/review, I'd recommend taking a look at the "chessboard" puzzles: https://youtu.be/ZTsJvpuBCLI https://youtu.be/zUqCEsURNuI There's also this pyramid puzzle, which I think is a step up, but still easier than the backwards induction with the drafts: https://youtu.be/SbfawONvV-A
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Kohler? More like "cooler"! Thanks for another wonderful puzzle.
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