Cutting Off Set Equity

[JOHNY CA$H]

Hey guys, I'm crunching some numbers tonight, and have hit a wall. This SHOULD be simple math, but for some reason my brain just can't wrap my head around this after 30 minutes of thought. I'm sure you guys can clear it up real quick.


My question involves cutting off set equity- how big a 3 bet must be pre flop that a smaller pocket pair is -EV to call even if they KNEW you'd stack off every time they hit a set. I'm coming to two figures, one which seems to make sense mathematically, and one that seems to make sense intuitively. Can ignore any set over sets or spiking a set on turn or river, if that makes it easier. Assume $200 stacks, 1/2 NL with neither player A or B in the blinds.

Which line is correct?

Player A raises to $8 with a small pocket pair. Player B has AA on the button. He wishes to raise an amount that makes player B neutral EV to call (ie the amount he wins when he hits exactly matches the amount he loses the 7.1 or so times he misses). Does player A:

1) Raise exactly 1/8.1 the effective stack Player B can win ($200 + $3 blinds), ie $25.06?

OR

2) Since Player B's implied odds decision begins once Player A re-raises, Player A must raise

211 = (x-8) 7.1
211= 7.1x-56.8
267.8=7.1x

x= $37.72?

This feels like it should be straight forward, but my brain is on vacation tonight. Thanks for any and all help.