overcards v. two pair

[bobman0330]

So, I've been pondering the question of who has a playing advantage in a HU situation, two overcards, or a medium-small PP. Obviously, this question varies a lot depending on limit or big-bet, position, etc. the PP wins a small amount from set value, which I'm more or less discounting for the moment.

Anyways, here's the hypo:

One blind limit holdem. Folded to the button, who raises. Both players are aware of the other's general holding (if i'm the button holding 66, i know the opponents has 87 or better. If the opponent has 87, he knows I have 66 or worse). Now, suppose the blind can pay X amount of money to have no future betting on the hand. What would that amount be in various situations, when would it be 0, etc.? Assume variance isn't an issue. I chose limit because it's simpler to analyze, and i think it's a closer issue, due to the greater availability of the call-down as a play.

In any case, I have no idea of any of the answers to this question. Thoughts?