What are the best ways to play the opening rolls?

It is quite true that rollout results from three backgammon playing computer programs (Expert Backgammon, TD-Gammon, and Jellyfish) have given us new insights into opening rolls and other phases of the game. Before taking any of these as gospel, there are several things to keep in mind:

1) The strengths and weakness of the programs. For example, a program which is weak in backgame play might downgrade early slotting plays in its rollouts since these plays will probably lead to backgames more often when the slotted blots are hit.

2) The rollouts do not take into account access to the cube, which might make a difference.

3) There can be quite a bit of variance in the rollouts due to luck, even with large sample sizes.

4) The rollouts do not take into account individual personalities of players playing. A player may well do better with an "inferior" opening play if it suits his personal style.

5) If playing a match, the match score may affect the value of different plays.

Now, on the what I believe is an accurate synopsis of the 15 possible opening rolls:

2-1: The slotting play 13/11, 6/5 and the splitting play 24/23, 13/11, the two most common plays, seem to be about equal. Nothing else is a serious contender.

3-1: 8/5, 6/5 is obviously the only play.

4-1: The splitting play 24/23, 13/9 has come out clearly superior to the slotting play 13/9, 6/5. Probably the reason is that with the builder on the 9 point there are so many good pointing numbers next turn anyway that you don't need the 5 point slotted.

5-1: The splitting play 24/23, 13/8 has come out a bit better than the slotting play 13/8, 6/5. A third less common alternative, 24/18, came out clearly worse.

6-1: The obvious 13/7, 8/7 is correct. Magriel's experiment of 13/7, 6/5 is awful.

3-2: The splitting play 24/21, 13/11 came out a bit better than building with 13/10, 13/11.

4-2: 8/4, 6/4 of course.

5-2: The normal play for years has been 13/11, 13/8. However the newer splitting play, 24/22, 13/8, (shunned because of the crushing 5-5 threat) has come out a bit better. The slotting play of 13/8, 6/4 (which used to be my choice) did not survive the rollouts -- it was clearly inferior.

6-2: The splitting play of 24/18, 13/11 comes out fairly clearly superior. Running with 24/16 is 2nd, but the run isn't far enough. Slotting with 13/5 (a common choice several years ago) was definitely in third place.

4-3: The building play of 13/10, 13/9 and the common splitting play of 24/20, 13/10 were just about tied. The alternative split of 24/21, 13/9 was only a little behind.

5-3: The simple 8/3, 6/3 is clearly best. The once common 13/10, 13/8 has been found vastly inferior.

6-3: The splitting 24/18, 13/10 comes out best, but the running play of 24/15 is not too far behind.

5-4: Splitting with 24/20, 13/8 and building with 13/9, 13/8 come out quite close (that builder on the 9 point is powerful), with the split generally a tiny bit better. 24/15 is weaker still.

6-4: Both running with 24/14 and splitting with 24/18, 13/9 are about equal. However the once laughed at 8/2, 6/2 has reared its head as a serious contender and comes out about equal with the other choices -- nice play to try if you get familiar with it, since your opponent probably won't be.

6-5: The simple 24/13 is clearly better than any other possibilities.