[callahad]

My thought process: It seemed obvious that fixed-guess strategies couldn't work, both from the proof in the article and from intuition that the inverse of your fixed guesses will always represent a failure case.

If a fixed strategy can't work, then the guesses must be decided dynamically. At the time the guess is made, only one bit of information (their own flip) is available to each participant, so each guess has to be based on that. With one bit of information, you could only choose two things: do the same, or do the inverse. The correct, asymmetric pair of strategies popped into my head at this point, and a quick truth table check confirmed it.

[bsaul]

Exact same here. Thanks for analysing this though, because i had trouble rethinking my own process. I more had the feeling to try things a bit randomly and eliminate ranges of similar choices. But in fact it wasn't random, it did follow the exact train of thoughts you described, in that order.