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Behemouth, i'm not sure the coin flip example is completely wrong, perhaps the fair thing to say would be that its open to interpretation, but Elizer can clarify his thinking for us.

Elizer seems to be saying that the market price will be around 50%, fair value is 91%, and you should bet heads on that basis, and should expect to capture an edge of 41%.

Another alternative is that the market price could be above 91%, say 95%, and in that instance you should bet on tails, and expect to capture only a 4% edge.

We could informally test this ... we could ask/email 20 people if given they know a coin is baised and given that it just landed heads 9 times in a row, how many heads in 100 tosses will the coin produce. Their responses could become the market price, if that number averages out to say 90 heads, then the market price is 90% for example, and then we could see if a bet on heads or tails would be more appropriate. I am not sure of the final answer, but I think its unlikely that the market price will be near 50/50.

Elizer, I accept your general point, but in your coin flipping example, it was unclear to me what your trade would be. Would you bet on heads or tails and in what circumstances? In a real world scenario I suspect its more likely to be the opposite of what I think you suggested but that is not entirely clear to me.

It all depends on where the market price is. There is a theory formed by a relatively respected speculator called "reflexivity," basically that markets tend to perpetuate trends and overshoot fair values And there is some other evidence of this in books such as Bob Schiller’s Irrational Exuberance about information cascades etc. So given there have been 9 heads in a row, maybe your average bear would think its more likely to come up heads than it’s genuine expected value, so I would argue that the market would probably overvalue the true likelihood (which according to you is 10/11ths), and so they would bet on heads and you would want to be short (bet on tails) if their expectation/price is greater than 10/11ths. The difference between their price and your price is called the edge, and you would capture that edge by betting on tails. So it would be a relatively modest profit opportunity. Not the other way round as I think you described, where you seem to be saying that the market would be pricing it at 50/50 and fair value is 10/11ths and you should bet on heads. It all depends on where the market would trade, above fair value or below fair value, I say above, in which scnenario one should bet on tails, and there is a minor profit opportunity, you seem to be saying below, bet on heads, and there is a major profit opportunity. A related question is how much should you actually bet?

Anyway, maybe just a case of my misunderstanding things. Another, perhaps, simpler way to think of markets are as beauty contests, where you are trying to pick the winner of the contest, which is not the girl you think is most beautiful, but the girl that everybody else thinks is the most beautiful: