> People bluff but you generally have to be prepared to walk if your bluff is called.

Then you aren't bluffing.

Fair enough. And maybe the lesson is don't bluff in situations where you aren't prepared to deal with the consequences if the other party calls your bluff.

How do you figure that? If I hold 27 off suit then I still have to be prepared to show my hand if you call me. Doesn't mean my all-in raise wasn't bluffing.

But presumably you understand that your opponent may call you. The relevant MW definition is "a false threat or claim intended to deter or deceive someone." So in this context, it's a claim you won't really leave if you don't get your way. But the other party may decide to get rid of you anyway based on the bluff. (Thinking about it, it's probably reasonable to call it a bluff but that doesn't mean there aren't consequences if the other party calls you on it.)

I suppose there is an ambiguity regarding whether the "bluff" was that she wasn't actually prepared to leave or whether it was that she actually was.

Yep. You don't really know the ranking of stay with conditions granted, leave without conditions granted, and leave without conditions granted rank. (Well #1 is obvious but the others less so.)

Yeah, but your all-in raise is you saying that you have two aces. You're bluffing because you don't actually have the hand you're pretending to have.

If I find myself in a situation where, if I don't get X, I prefer to leave, then an ultimatum is an obvious course: "give me X or I will leave."

It can be to my benefit in negotiation for the other party to think that I am in such a situation, and so I may still say "give me X or I will leave."

If I do not intend to follow through, I am clearly bluffing.

If I intend to follow through, but absent this gambit I have preferred to stay even in the absence of X, I think we can still call it a bluff in a weaker sense - I am not misleading about my future actions, but I am misleading about the strength of my preferences.