Theorem of expected stack sizes

[PrayingMantis]

Given a player with a stack size of S1 or S2, seated at a table with certain same conditions for both cases(1), there is no single identical hand that is played by him in both cases to maximize profit(2) and that will yield expected stack sizes of S1' or S2'(3) respectively, for which S1>S2 AND S1'<S2'.

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(1) i.e, same players, stacks, positions and "reads".
(2) or minimze loss, which is the same.
(3) i.e, stack sizes when the relevant hand is over.


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Note that this theorem isn't based upon any kind of assumed model, and as such it is simply a logical structure (that could probably be dismissed as trivial by some). Moreover, it shouldn't be very hard to refute, since all we need is to think of and describe just one "counter example hand". However, until this example if found, there is no "red zone" theory that can stand to reason.

Comments? refutations? flames?