You have to get into the Dirichlet distribution to make this work [there are other methods]. In any case, without going to much into the weeds, here's an image of 40 pieces of string, each cut into 20 pieces at random [and each string is sorted from smallest cut to largest].
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For example, A guesses the largest piece is 20% of the string, B guesses 21%. The largest is revealed to be 23%. B wins.
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You can test your intuition if the string were cut into only two pieces [so 1 cut]. On average, how large is the largest piece?
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you can also ask questions about the distribution of resources
there are ways to change the how we cut [this graph assumed pulling from a Gamma(1,1)]
all told, it's a fun exploration
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