Match Play Answer

At this score, White needs to "go for the throat."  The value of gammons is very high (1.0).  In this situation, at this score, White must hit.  Hitting is his best chance for a gammon.  At just about any score White needs to hit the checker on his 5 point...not hitting gives Red his full roll and he if he makes White's 5 point you can pretty much say goodbye to White's gammon chances. 

So once you decide to hit the checker on the 5 point with the 3, then the question is, where is your best 5?  Hitting off the ace point greatly decreases Red's odds of hitting you back off your 5 fact, only a 5 hits back (11/36).  Of course, Red could roll a 1, and that makes it harder for White to make the 5 point, but keep in mind that Red only has one point made in his inner board, so even if you are hit, you will often be able to come back in and make the 5 point.

ExtremeGammon Rollout