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All opening replies here are analysed using Gnu Backgammon (version 0.15-3) 4-ply. This is the same as a (hypothetical) Snowie 5-ply. For rollouts go to Tom Keith’s famous Backgammon Galore, Stick’s or Hardy’s webpage (work in progress).

Legend:

• GG = Gammon Go
• GS = Gammon Save
• DMP = Double match point

Doubles

66: Always make both barpoints if you can. If your opponent splits with 6X make your acepoint at GG. In case of opponents 61 play 4 checkers down.

55: 13/3(2) if your opponent doesn’t split. If he splits, make two homeboard points. At GS play 13/8(2), 6/1*(2) if he splits with 21, 41 or 51.

44: Usually 24/20(2), 13/9(2). If you can hit a checker on your 5-point play 13/5*(2), if you can hit a checker on the 16-point play 24-16*(2), 13/9(2). In case you can hit two checkers and make a point then hit both.

33: The most difficult answer?! In general 24/21(2), 13/10(2) is probably the best reply. If your opponent splits to your barpoint point on him, if he splits to your 5- or 3-point making two homeboard points is the best play.

22: In general play 13/11(2), 6/4(2). At GS mostly 24/20(2) is correct.

11: If you don’t leave a direct shot play 8/7(2), 6/5(2) otherwise 24/22, 6/5(2). Only hit on your opponents 5-point if he has an additional builder aiming to the slot. If he splits to your 4-point, play 6/4*(2).

Making Points

31: Always make your 5-point. Only when your opponent slots his 5-point or runs with 63 and 54 hit him there and split your back checkers.

42: If your opponent splits with 64, 63, 62 hit. If he runs with 64, 62 hit him and split your back checkers. If he slots his 5-point hit him also and play the 2 from the midpoint.. Otherwise make your own 4-point.

53: Usually making the 3-point is correct. If your opponent leaves a blot at your 5 or 10-point or his 9-point hit him. At GS it’s sometimes better to split with 24/21, 13/8.

61: Usually making the barpoint is correct. In case your opponent splits to your 5-point hit him and split your own back checkers.

Hits

Opponents side of the board: If you can hit a slot in your opponets homeboard or a builder in his outer board you should do this.

Your side of the board: If he splits to your 4- or 5-point and you are able to hit him, play the second checker from your midpoint (only in case it’s not a 6).

Double hits: Not clear. Very often hitting two checkers is correct. In case of 1. 43 24/20, 13/9  -  41 it’s better to hit and split your back checkers.

Gammon Save

In general: Mostly splitting your back checkers for getting an advanced anchor is the correct play. With 22 you tend to play 24/20(2), with 53 24/21, 13/8 very often beats making your own 3-point. Splitting beats slotting.

Gammon Go

In general: If you can’t make point or hit your opponent it’s mostly correct to play two checkers down from your midpoint. Even with 65 this is very often the right play. Slotting beats splitting.

 No breaking news regarding the opening rolls. Eveything is well known by experience and rollouts. There are still some rolls which are discussable, depend on certain match situations or which are simply a matter of style.

If you want some other published rollouts go to Tom Keith’s famous Backgammon Galore or Stick’s bgonline.

Group I: 31, 42, 61, 53, 65

This is probably the "no doubt" group. With 31 make the 5-point, with 42 the 4-point, with 61 the bar point, with 53 the 3-point, use 65 to run from the back. No matter whether you play money game or match.

Group II: 64, 63, 62

The "split or run group": The modern approach is to split with the 6 and play one checker down from the midpoint. However, with 64 in a gammon go situation you may also make the 2-point. At double match point and gammon save running with 64 might be the best. 

Group III: 54, 52, 43, 32

The "either split or both down" group: In neutral and gammon save situations most players split and play one checker down from the midpoint (54 24/20, 13/8 – 52 24/22, 13/8 – 43 24/20, 13/10 – 32 24/21, 13/11). For gammon go they play two checkers down from the midpoint.

Mostly underrated and seldom played with 43 are 24/20, 24/21 or the minor split 24/21, 13/9.Nonetheless no one did prove yet that these plays are inferior.

Group IV : 51, 41, 21

This is the "either split or slot with an ace" group. In a gammon save or neutral situation most players prefer to split with the ace and put one checker down from the midpoint.

In a gammon go situation play one checker down from the midpoint and slot the 5point with the ace. Some players always slot with 21.