I'm trying to understand why it is valid to use "ex-showdown value" to determine the value of various strategies, as used in MOP.  In other words, why are we justified in ignoring the situations where no betting takes place?

Could somebody confirm (or deny) the following thoughts on the topic:

I see that the idea is not to show equality between various methods of calculating values, but "game theoretic"
equivalence (i.e. two values are equal to within a constant that is
independent of strategic variables so that unilaterally improving one of
the values does so for the other).



Would it be that the value of game situations where no betting takes
place is somehow a constant that is independent of strategic variables?



On the one hand, I don't see how this is true, since the strategic
variable of betting frequencies, for example, determine how often we
have a situation where no betting takes place (but on the other hand,
they do not influence the value).



If it was true that we could somehow treat "non-bet" situations as a constant, then we would have:



Value of game (for one player) = Value of game situations where betting
takes place + Value of game situations where no betting takes place



==>



Value of game ~ Value of game situations where betting takes place



Where ~ denotes game theoretic equivalence (i.e. if we can unilaterally
improve the right side with a different strategy, then we can
unilaterally improve the right side)

Am I on the track and just wrong about not being able to treat situations where no betting takes a place as a game-theoretical constant?