What change would you make that results in multiple rounds being required?
For example, if each player flips multiple coins, and then we share probability estimates for "all coins heads" or "majority of coins heads" or expectations for number of heads, in each case the first time I share my summary, I am sharing info that exactly tells the other player what information I have (and vice versa). So we will agree exactly from the second round onwards.
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...
&...
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