example I was thinking:
each player flips 3(? 10) coins of their own. (giving them various possibilities on what they think the whole coin-space looks like) They present their 90%, 99% confidence intervals on there being more than 4 (9) heads. Round 2 repeat. (also make statements based on what they think the state of play is ++ try to get to the answer before the other person. So make statements that can be misleading maybe?)
Not sure how easy it is to tease out that information for a human. maybe a computer could solve it. but not so much a human...
"I flipped 10 coins; My 90% confidence that there are at least 7 of each heads and tails is 90%. 99% confidence is 60%."
confidence for "at least 10 heads and 6 tails" etc.
Here's how that goes. I flip 3 coins. Say I get 2 heads. My probability estimate for "there are 4+ heads total" is now 4/8 (the probability that 2 or 3 of your coins are heads). For the full set of outcomes I can have, the options are: (0H, 0/8) (1H, 1/8) (2H, 4/8) (3H, 7/8). You perform the same reasoning. Then we each share our probability estimates with the other. Say that on the first round, we each share estimates of 50%. Then we can each deduce that the other saw exactly two heads, and on the second round (and forever after) both our estima...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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