This is one question where my odds are pretty far from being coherently Bayesian; I would bet against only up to around 100:1, but I wouldn’t bet in favor until somewhere around 8e7:1.
Why is that not Bayesian? The decision to bet is going to include a term for your counterparty’s willingness to bet, which is some evidence.
One way to overcome this in thought experiments is to frame it as a line with no spread, and no neutral option. At, say, 150k:1, which side would you bet? Then adjust to where you’d SET a line where you had to accept a wager on either side.
What happens if you ask a logical inductor whether ππππ is an integer? What’s your own subjective probability?
This is one question where my odds are pretty far from being coherently Bayesian; I would bet against only up to around 100:1, but I wouldn’t bet in favor until somewhere around 8e7:1.
Why is that not Bayesian? The decision to bet is going to include a term for your counterparty’s willingness to bet, which is some evidence.
One way to overcome this in thought experiments is to frame it as a line with no spread, and no neutral option. At, say, 150k:1, which side would you bet? Then adjust to where you’d SET a line where you had to accept a wager on either side.