[The Armchair]

Just to clarify:

Pre-Flop: Normal
Flop: Each person, starting at UTG (why not SB, btw?) can muck one card, leaving them w/a one card hand. If a person does so, they get n% of their pre-flop bet back. After that, play continues as normal.

If that's the case, then there are a few reasons to "reverse buy-back" (neato name, huh?):

1) You've made junk, and intend to fold. Therefore, you'd RBB for n>0.
2) You've made a nut draw but only need one card from your hand (i.e. Ac2s on a three-club board or on a board with QJT rainbow). Your incentive to RBB is rather high, and approaches n>0.
3) You have the third to a pair on the board, but your kicker isn't all that good (i.e. 98x on a board of 992). At that point, you have to assume you're ahead, so n>0 is fine. (If you're behind, you're very behind, but note that A9 has incentive to pitch the A as well.)
4) TPNK. In that case, n is hard to measure, b/c you don't know where you stand. The higher n, the more likely you'd pitch, but that's directly proportional to the size of the kicker.
5) A made four-card hand, which is exceptionally rare -- it'd have to be quads. In that case, one could argue that you'd not pitch, as you have a near-lock on the hand.

Given that #4 is the only violently variable situation (can anyone else provide others?), let's focus on that. Take the following board:

A[img]/images/graemlins/diamond.gif[/img] Q[img]/images/graemlins/club.gif[/img] 6[img]/images/graemlins/heart.gif[/img]

Looking only at Ax hands, AA, AQ, and A6 are not going to toss the undercard, even if n=100. (Remember that they have no reason, giving your hypo, to think they are in anything other than the lead right now.) AK would probably need a very high n -- perhaps even n=100 -- but in that case, note that AK is about as valuable as A-rag.

Any rag 2 through 5 is going to pitch for n>20 or so, and it's not hard to compute. Put them against an A w/a higher kicker. Assume the kicker is going to keep its undercard. They have 3 outs to make their two pair, discounted some for the situation where they are already up against a better two pair. Figure out their EV, and find the break-even point, keeping in mind the possibility that they have the only ace. In any event, n could be as high as 100, but my gut says its closer to 20.

For rags 7 through J, you have a real problem. There simply isn't enough information out there. Obviously, as rag gets higher, there's more incentive to hold on. But you can math it out.