>> I'd argue that your chance of winning the bracket (or, at least, a valuation of it) is much higher than that given your ability to predict all of the matches prior.

I believe the chance to win given you win all but three are higher than 12.5%. But MUCH higher? I am not quite sure. There are too many games this year can go either way, and predicting these games right is more on luck than technique analysis. Though winning all these previous prediction did gave you the credit in your expertise, but I am not quite sure about MUCH higher statement.

Like I have said "Of course the reality is how much you would sell it very much depend on your conviction of how likely your guesses on final 3 games may be correct.". As tournaments goes on, your feeling about we will win it all will change. Say Louisville will all the team 100-0 in previous game, yet you predicted them to lose at final four, you are more likely to sell your stake at a cheaper price than not.