2010-06-13 3-3 Answer

The best way for Red to have a reasonable game here is by making White's 3 point.  So White should switch and not let that happen.  The problem is, giving up your 6 point often looks and feels "unnatural" and after years of playing "naturally," my partners in the chouette could not bring themselves to make this play even with some begging, betting, and badgering from me. 

Fortunately, I was rewarded by losing the game after our opponent made our 3 point and hit us to win.  I was further rewarded by being able to put the position into extremeGammon and showing my friends that my play was right.  But I still had to pay!