If I’m understanding properly, you’re trying to use the set of bets offered as evidence to infer the common beliefs of the market that’s offering them. Yet from a Bayesian perspective, it seems like you’re assigning P( X offers bet B | bet B has positive expectation ) = 0. While that’s literally the statement of the Efficient Markets Hypothesis, presumably you—as a Bayesian—don’t actually believe the probability to be literally 0.
Getting this right and generalizing a bit (presumably, you think that P( X offers B | B has expectation +epsilon ) < P( X offers B | B has expectation +BIG_E )), should make the market evidence more informative (and cases of arbitrage less divide-by-zero, break-your-math confusing).
(This comment isn’t an answer to your question.)
If I’m understanding properly, you’re trying to use the set of bets offered as evidence to infer the common beliefs of the market that’s offering them. Yet from a Bayesian perspective, it seems like you’re assigning P( X offers bet B | bet B has positive expectation ) = 0. While that’s literally the statement of the Efficient Markets Hypothesis, presumably you—as a Bayesian—don’t actually believe the probability to be literally 0.
Getting this right and generalizing a bit (presumably, you think that P( X offers B | B has expectation +epsilon ) < P( X offers B | B has expectation +BIG_E )), should make the market evidence more informative (and cases of arbitrage less divide-by-zero, break-your-math confusing).