How does he reveal which characters are trustworthy and reliable, and which ones may not be

From the begininng we know Mr. White to be a bit of a risk taker. He does, after all, cheat at chess. Other than Mr. White's obvious compulsion to get what he wants, even to the point of grabbing the paw from the fire, no one else seems to be the least bit unreliable or untrustworthy.