Make a market on the true bias of a coin you have sampled: 6 points wide and traded blind, or 12 wide and traded by someone who sees the truth. Where do you centre it?

In a game with ten coins, one is fair and each of the other nine has a heads probability drawn from a roughly normal distribution centred on 0.5 and confined to between 0 and 1. You have used 100 flips on coins of your choice. Now you must make a market on the true heads probability of each of the nine unknown coins, and for each coin you choose the width. If you quote 6 percentage points wide, the interviewer trades with you without looking at the true value. If you quote 12 points wide, the interviewer looks at the true value first and then trades. Where do you centre the market, and how wide do you make it, for a coin you flipped dozens of times with 70% heads? For a coin you flipped three times with two heads and one tail?