I'm looking for a good demonstration of Aumann's Agreement Theorem that I could actually conduct between two people competent in Bayesian probability. Presumably this would have a structure where each player performs some randomizing action, then they exchange information in some formal way in rounds, and eventually reach agreement.

A trivial example: each player flips a coin in secret, then they repeatedly exchange their probability estimates for a statement like "both coin flips came up heads". Unfortunately, for that case they both agree from round 2 onwards. Hal Finney has a version that seems to kinda work, but his reasoning at each step looks flawed. (As soon as I try to construct a method for generating the hints, I find that at each step when I update my estimate for my opponent's hint quality, I no longer get a bounded uniform distribution.)

So, what I'd like: a version that (with at least moderate probability) continues for multiple rounds before agreement is reached; where the information communicated is some sort of simple summary of a current estimate, not the information used to get there; where the math at each step is simple enough that the game can be played by humans with pencil and paper at a reasonable speed.

Alternate mechanisms (like players alternate communication instead of communicating current states simultaneously) are also fine.