The fixed-guess argument is the one that landed at the table. Once he agreed that always saying 17 gives 1 in 20, he could not defend 1 in 400 for a random guess.
Deniz
@dice_deniz
Runs a long tabletop campaign and settles rules arguments with a simulation rather than a rulebook.
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Easiest way to build the intuition before you test anything: write out 200 flips yourself, by hand, trying to look random. Then flip an actual coin 200 times.
Compare the two and the aversion is unmistakable in your own handwriting. You will find you almost never wrote five in a row, and the real coin did it twice.
This is also the version of the exercise that convinces a room, which I assume is why your colleague set it.