I agree. This should be time-symmetrical; your actions should be the same whether you rolled first then saw market prices or vice-versa. If you observe then roll, you have gained information making 6 more probable at least a little bit, and you must trade in the direction of your information (going long 6 or short the others), which is +EV.
The real question is how much should you trade, since you cannot afford to bet indefinite amounts of money on tiny +EV opportunities. For a prediction market that is a bit tricky, since they won’t typically be on problems where you can read off the posterior distribution from a few summary prices (if it’s 50/10/10/10/10/10%, does that mean that the market is highly certain that it’s a problem which simply has those true frequencies, or could it mean that it’s a deterministic problem but that the market is currently highly uncertain? in the former case, you have almost no edge and want to bet little and in the latter you want to bet a lot), and you have to start looking at things like volatility of the prices to gauge how much information you have relative to it and so how much of an edge and how much you can afford to bet.
I agree. This should be time-symmetrical; your actions should be the same whether you rolled first then saw market prices or vice-versa. If you observe then roll, you have gained information making 6 more probable at least a little bit, and you must trade in the direction of your information (going long 6 or short the others), which is +EV.
The real question is how much should you trade, since you cannot afford to bet indefinite amounts of money on tiny +EV opportunities. For a prediction market that is a bit tricky, since they won’t typically be on problems where you can read off the posterior distribution from a few summary prices (if it’s 50/10/10/10/10/10%, does that mean that the market is highly certain that it’s a problem which simply has those true frequencies, or could it mean that it’s a deterministic problem but that the market is currently highly uncertain? in the former case, you have almost no edge and want to bet little and in the latter you want to bet a lot), and you have to start looking at things like volatility of the prices to gauge how much information you have relative to it and so how much of an edge and how much you can afford to bet.