You have a 5% edge!
Stephen.C,
I ran a sim for a ENHC game and found that, with B.S., the player wins 46.47% of the non-tied rounds, and loses 53.53% of them. Since the player's Initial Bet Advantage is about -0.3% (thus, the house edge is about 0.3%), this means that, on average, each winning hand pays you about 14.5% more than you lose on each losing hand:
1.145*(46.47%) - 53.53% = -0.3%
Now, here's how you crush this opportunity!
1. Bet $3,000,000. Play the hand with B.S.
2. If you tie, keep playing.
3. If you win or lose, "call for check out" (as you phrased it). If you won, your rebate will be zero; if you lost, it'll be 10% of whatever you lost: $300,000 if you didn't split or DD; more if you did.
4. Go back to step 1.
On average, then, you'll get the normal amounts on wins, but you'll get a 10% rebate on all losses, so you'll only have to "pay" 90% of each loss. Thus, your overall edge will be:
1.145*(46.47%) - 53.53%*0.9 = 5.0%
Note that you'll need a large bankroll to afford a Kelly bet of $3MM:
BR = bet*var/edge = $3,000,000*1.15/0.05 = $69,000,000.
Hope this helps!
Dog Hand
P.S. If for some reason you cannot bet $3,000,000 per hand, you might consider buying Grosjean's new book, "Exhibit CAA", which has much more information on such an offer.