Smullyan's conundrum

I've always loved logical puzzles. The books of mathematician and philosopher Raymond Smullyan have afforded me many enjoyable hours indulging this hobby. Sometimes, puzzles defy logic, as Smullyan was able to demonstrate simply by his choice of a title for one of his books - "What is the Name of this Book?". One family anecdote he included in the preface to one of his books has stuck in my mind since the time I first read it. When he was a young boy, his older brother promised him he'd get a real April Fool's Day surprise that year. He waited all day for the surprise, but it never came. When he accused his brother of not surprising him, the brother informed him that that had been the actual surprise. Smullyan puzzled and puzzled over this, but could never decide whether he'd been fooled or not.

This conundrum came to mind as I was thinking about last night's session. Based on his play, and what I'd gotten to see of his holdings at showdowns, I'd come to the conclusion that one of my opponents was a bad player. He was playing too riskily; I came to believe that any big move he made at a pot had high bluff potential. When he went all in on the turn in a hand where I'd flopped a stealth two pair, I thought he was bluffing. The trouble was, he wasn't; the turn card had paired the board, and he'd made trips. In my postmortem analysis, I caught myself thinking, "He's so bad, I'll never know what he's holding." Looked at another way, you can be considered a very good player if other players can't guess what you're holding. So my conundrum was trying to figure out if he was a bad player or not. Just like Smullyan's conundrum, mine has no real answer.

During current Hold'em session you were dealt 105 hands and saw flop:
 - 9 out of 15 times while in big blind (60%)
 - 4 out of 14 times while in small blind (28%)
 - 43 out of 76 times in other positions (56%)
 - a total of 56 out of 105 (53%)
 Pots won at showdown - 8 of 14 (57%)
 Pots won without showdown - 4

delta: $-40,000
cash game no limit hold'em balance: $3,949,306
balance: $6,398,714