Illano comments on Games for Rationalists - Less Wrong
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The estimation game you describe sounds a lot like the party game Wits and Wagers, though with the added challenge of predicting what the other players may predict as well.
I like the idea behind your game though. One way you may be able to help it teach to calibrate your own confidence intervals is to have everyone also guess an X% confidence range for their guess (whatever you decide is a good range). Then, each time the answer falls within that range, award the player P points, and whenever it is outside the range, penalize them P/(1-X) points (e.g. confidence of 90%, give 1 point for correct range and -10 for incorrect). To keep the ranges tight, offer another bonus to whoever had the tightest correct bounds.
I discovered that Wits and Wagers was actually discussed here: http://lesswrong.com/lw/14u/wits_and_wagers/
I tried it out and it is much easier to play than my game and thus is somewhat more fun. But it also has less insights.
My experience is as follows:
It really is optimized for playability. I think it does some calibration of (over)confidence and it builds intuition for probability and risk-trade-offs.
But - and that is my main point - it doesn't have clear concepts. The concepts are all mingled up, skewed, hidden. You may gain intuition but it will not help you toward overcoming e.g. overconfidence bias or egocentric bias.
I still think for that the concept must be sufficiently present to be able to reflect and consciously use it.
Indeed. I wasn't aware of http://en.wikipedia.org/wiki/Wits_and_Wagers. There is no German match for it (yet). I actually considered using a confidence rating but discarded it because it was too easy to game the rules for it - but that was during the first test games that were about estimating your own performance via multiple estimates (called 'strict variant' in the post). When I switched to estimating the range of the other players guesses I didn't reconsider confidence ranges. Could be an interesting variant.
The current gameplay is really simple even though it includes a min-max range. There was a earlier and more complex version that had a 90% range (or more precisely an 1-1/N range) which earned N points if it excluded exactly 1 guess, 1 if it excluded none and 0 if more than 1. That was OK but didn't gain much. The most surprises were still registered by the min-max range.