Missing information—how many people have rolled the die how many times before participating in the market? If you don’t expect that there’s private information that the market can make public, you shouldn’t expect it to indicate truth.
Also missing—what are the actual contracts? Is this a wager on the next roll of the die? Meaning 50% is paying 1:1, 10% paying 9:1 ($100 bet on 3 pays $100, $100 bet on 6 pays $900 if it wins)?
In that case, if the market is one person who saw one roll, I bet 5 contracts on 6, and one on each of 1,2,4,5. If the market is hundreds of people, even if they’ve each only seen it once (independently; hundreds of rolls with one observer each, not 100s of observers of one roll), then the market has likely already worked out the correct odds, so my observation doesn’t add much.
Note: if the market is hundreds of people, and it’s a market on which face comes up 50% of the time (not on which face will come up on a specific roll), and it only gets 50% odds on that being a particular number, then something unusual is happening. An efficient market under these circumstances should be very confident.
(I haven’t done any explicit calculations, but I’m reasonably confident.)
Missing information—how many people have rolled the die how many times before participating in the market? If you don’t expect that there’s private information that the market can make public, you shouldn’t expect it to indicate truth.
Also missing—what are the actual contracts? Is this a wager on the next roll of the die? Meaning 50% is paying 1:1, 10% paying 9:1 ($100 bet on 3 pays $100, $100 bet on 6 pays $900 if it wins)?
In that case, if the market is one person who saw one roll, I bet 5 contracts on 6, and one on each of 1,2,4,5. If the market is hundreds of people, even if they’ve each only seen it once (independently; hundreds of rolls with one observer each, not 100s of observers of one roll), then the market has likely already worked out the correct odds, so my observation doesn’t add much.
Note: if the market is hundreds of people, and it’s a market on which face comes up 50% of the time (not on which face will come up on a specific roll), and it only gets 50% odds on that being a particular number, then something unusual is happening. An efficient market under these circumstances should be very confident.
(I haven’t done any explicit calculations, but I’m reasonably confident.)
Unless only one roll of the die was seen by the hundreds of people, and it came up “3”.
Ah, sure. It would have been better of me to say “if the market has collectively observed hundreds of rolls”.