[rzk]

[ QUOTE ]
there is a chance im wrong, I havent looked at it mathematically... just makes sense to me intuitivly.

please give me mathematical proof.

[/ QUOTE ]

ok, the formal proof is rather long. but it's based on a simple intuitive observation that you cannot get a better EV playing against a perfectly adjusting opponent than playing against an unobservant opponent.

ok then, suppose your current range is, for example, range1={AJ+, 88+}. let's call your postflop strategy with this range X1. your perfectly adjusting opponent plays the optimal counterstrategy, which we'll call A1. we will assume that you cannot come up with a better strategy than X1 against A1 (otherwise you would certainly adjust). let's call your EV with this range and this strategy EVbest(range1 vs A1). suppose AT is a -EV hand against A1, which means even when you play it the best possible way against A1 your EVbest(AT vs A1) is less than 0.

i will now assume that there exists a strategy X2 for range2={AJ+,88+,AT} such that when your opponent plays optimal counterstrategy A2 your EVbest(range2 vs A2) is greater than EVbest(range1 vs A1)+EVbest(AT vs A1). i will now show that this leads to a contradiction.

since A2 is an optimal counterstrategy against X2, X2 vs A2 has a lower EV for us than X2 vs A1. then we have:

EV(X2 vs A1)>EV(X2 vs A2)=EVbest(range2 vs A2)>EVbest(range1 vs A1)+EVbest(AT vs A1)

now, strategy X2 consists of two substrategies:

substrategy X2' : how to play range1={AJ+, 88+} postflop,
substrategy X2" : how to play AT postflop.

then we have:

EV(X2' vs A1)+EV(X2" vs A1) > EVbest(range1 vs A1)+ EVbest(AT vs A1)

but clearly,

EV(X2" vs A1)<EVbest(AT vs A1) by definition of EVbest.

therefore,

EV(X2' vs A1) > EVbest(range1 vs A1)=EV(X1 vs A1).

but this contradicts the statement that X1 was the best strategy you could come up with against A1, so there we go.

cliffnotes: if it were possible for you to increase your winrate by adding a -EV hand to your range, you would do even better if you just change the way you play your original range.