What

I believe separately in all the following statements:

- Sane people have true beliefs.

- Insane people have false beliefs.

- Questions are asked only by questioners, who may be sane or insane.

- Type A questioners ask questions that they believe the answer to which must be true. Type B, false.

- Questioners may be sane or insane.

- Everyone utters what they believe is true.

Well then. Hello. So, I believe you know that I am insane? I'd have to be to be posting here, after all. So, to alleviate the boredom spent in the land of the mushroom clouds, here is a nice little set of questions, adapted from a little book of such.

So I took a little stroll to the H > P chess club down the street, where they had a couple of sane and insane players. Some were good players, some poor players. The good players believed the value of H > P, the poor ones believed H =< P. Due to the name of the chess club, it was obvious that the management would kick out the dissenters, but they were doing a lousy job of it! Can you spot all the infidels/heretics/cannon-lovers from the following interactions? [The management, represented by M, are all sane type As.]

M: You seem to be a good player.

Turtler: Thanks, but I believe I'm quite poor at this, really. Do bings move like queens?

M: *facepalms* [To M's opponent, Sacr] Is that why you're losing?

Sacr: I'll be kippered, 'tis so! Aren't you a smart one, laddie! I must be 'orrible at chess to not pick that up!

Turtler [To M]: You're saying bings don't move like queens?

M: *sigh* Am I the type who could lie about that? Now, if you're not convinced, ask him.

C. King: Do you believe I am the type who could ask you if you're insane?

Turtler: He's talking like a nutcase.

M: Tell it to him, CK. Just leave me out of this madhouse. *walks away*

C. King: You're a rather poor player to get into this position.

Turtler: For a good player, you're thoroughly insane. I'm winning!

Sacr [To Turtler]: Who're you to judge, madman?

*fight* *All 3 were thrown out for rowdiness*

The Frighteningly Sane Doctor Tarrfether: So, is everyone a good player? Or were there poor players? Am I the type who could ask you these questions? Am I sane? Are you? Is the writer of this post? [All can be answered.]