Interpreting the Fundamental Theorem

[Siegmund]

Quoting as closely as I can recall it without the book in front of me, it says something like: "You make a mistake anytime you play differently than you would have if you could see your opponents' cards. Your opponent makes a mistake anytime he plays differently than if he could see your cards [and his other opponents'.]"

Consider the alternative statement "A player makes a mistake when he plays differently than he would if everyone knew everyone else's cards."

Also consider the usual notion of 'regretting your choice' used to assess whether Nash equilibrium has been achieved: if you chose a different strategy than you would have if your opponents' strategies had been fully disclosed before you made your choice. (That is, knowing the exact range of hands your opponent might hold given his betting, but not knowing until the end which one of them he actually did hold.)

Two quick questions.

1) Is the alternative statement simply a rephrasing of the FT as it was originally intended, or was the FT deliberately worded as it was to ask each player to imagine what he would do if he could see his opponents' hands but they could not see his?

2) Neither the FT nor the alternative statement is logically equivalent to 'regretting your choice' in the Nash sense. Which do you regard as "closer" to it?