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  • Tiantian@kif.rocks
    Oct 14, 2026, 10:45 AM

    @whybird @blinry
    I think each result has to be weighted with
    (1/2)^(number of branchings on the way to it).
    Summing then gives 13/16 for flowers and 3/16 for apples, so the proportion to share should be 13:3.

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  • Mark Whybirdwhybird@aus.social
    Oct 14, 2026, 11:03 AM

    @tian @blinry Its winner takes all though, regardless of how many steps it took to get there. From our starting position, there are 10 outcomes where flower wins and 5 where apple wins.

    I think you are suggesting those outcomes are not all equally probable though? So now you have me doubting myself!

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  • Tiantian@kif.rocks
    Oct 14, 2026, 11:36 AM

    @whybird @blinry Yes, for example:
    the leftmost outcome, flower wins the next two rounds, has probability 1/4, whereas the rightmost, apple wins the next four rounds, only has prob. 1/16.

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  • Mark Whybirdwhybird@aus.social
    Oct 14, 2026, 12:11 PM

    @tian @blinry Wow, I was clearly wrong - thank you!

    The probabilities come out like this, as you described.

    🌼:🍎 = (1/4+1/8+1/16+1/32 + 1/8+1/16+1/32 + 1/16+1/32 + 1/32) : (1/32 + 1/32 + 1/32 + 1/16) = (26/32):(5/32) = 26:5

    (You got 26:6=13:3… I *think* you were off by 1? Unless I made another mistake.)

    The same tree diagram as before, but with probability fractions marked at each branching. They start at 1/2:1/2, then 1/4:1/4 etc out to the previously noted winning positions, which are circled and have the probabilities listed in the body of the post.
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  • Mark Whybirdwhybird@aus.social
    Oct 14, 2026, 12:19 PM

    @tian @blinry It occurs to me that the diagram could be modified so that the branch thickness corresponds to probability :)

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  • blinryblinry@chaos.social
    Oct 14, 2026, 1:02 PM

    @whybird @tian Ohh, I also didn't consider this correctly when I made the drawing! Thanks for catching this! :)

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  • Mark Whybirdwhybird@aus.social
    Oct 14, 2026, 10:05 PM

    @tian I actually have in my brain now a little animation of two players (in your drawing style @blinry, and one is a hedgehog… but that’s not really the point) dividing the pot, which in this case is conveniently exactly 32 $1 notes, by splitting it in half per turn and keeping scores on each possible outcome and awarding the portion of the pot to the winner at each of the possible win states… never mind that for this scenario to be reasonable, the actual game they were playing would have had to have been harder than this dividing activity, so not a coin toss I suppose :)

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