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If Alice thinks X happens with a probability of 20% while Bob thinks it's 40%, what would be a fair bet between them?
I created a Claude Artifact, which calculates a bet such that the expected value is the same for both.
In this case, Bob wins if X happens (he thinks it's more likely). If Alice bets $100, he should bet $42.86, and the EV of such bet for both players (according to their beliefs) is $14.29.
I wrote this mostly for personal purposes. I wanted to organize my thoughts about the problem while reading the paper, and publishing the notes, even if no one reads them, forces me to write more clearly and precisely.
I would like to get some feedback if there may be value in posts such as this one for other people. Please let me know! Thank you.