6-5, 4-1, 3-2 and 2-1 make defensive anchors. Among these 6-5, which anchors on the opposing bar-point is best. The 20-point is the most advanced available point in the opponents's home board, but the anchor on the 18-point better connects the position and virtually eliminates the possibility of getting primed.

DMP 194 194	Blue has played 24/18 23/18 194 183

The anchoring with 6-5 is a better roll in equity than making home-board point with 4-2.

Second best among the anchors is the 20-point, which can be made with an opening 4-3. This point has the distinct virtue of sitting flush against a stack of four checkers on opponent's 6-point.

The other anchoring plays are best thought of as preliminary developing steps. They are safe ways to move the back men along the road to a better future, leading to escape or more advanced points.

Blue has played 4-3: 24/20 23/20 194 187
Blue has played 3-2: 24/21 23/21 194 189	Blue has played 2-1: 24/22 23/22 194 191

Equities:
6-5: 24/18 23/18    .072
4-3: 24/20 23/20    .059
3-2: 24/21 23/21    .023
2-1: 24/22 23/22    .004

Some of the remaining rolls give the opener the option of turning his two back points into four blots.

All of these "quadruple split" plays are very reasonable and none is hopelessly bad. But experience suggests that most of them are slightly inferior to more mundane alternatives.

DMP 194 194	Blue has played 24/20 23/18 194 185

The downside to Blue's position after the Quad Split (24/20 23/18) is not just that White might roll 1-1 or 3-3, but that White has a number of rolls that let him hit two blots on points that he wants to make. Not all opponents will realize that with 6-1, for example, the double-hit with 13/7* 6/5* is so strong that they should pass up the chance to make the bar-point, but in fact it is. White is likely to come out of it with either the bar or 5-point, and If he gets them both, the four-prime with four men behind it is a huge advantage.

Blue has played 5-4: 24/20 13/8

194
185

The opener shold pass up the Quad Split with 5-4 and 5-3, playing the 5 safely 13/8 in each case.

The best 5-4 is 24/20 13/8 and the best 5-3 is 23/20 13/8.

#		Ply	Move	Equity
	1	R	24/20 23/18	0.004
			0.8%  13.9%  50.2%    49.8%  14.3%   0.8%
			95% confidence interval: - money cubeless eq.: -0.001 �0.007. Rollout settings: Full rollout, 360 games (equiv. 149533 games), played 3-ply (fast), random seed, with race database.
	2	R	24/15	0.002 (-0.002)
			0.8%  14.2%  50.1%    49.9%  14.6%   0.8%
			95% confidence interval: - money cubeless eq.: -0.001 �0.009. Rollout settings: Full rollout, 360 games (equiv. 108120 games), played 3-ply (fast), random seed, with race database.
	3	R	24/20 13/8	-0.001 (-0.005)
			0.9%  15.1%  50.0%    50.0%  13.9%   0.8%
			95% confidence interval: - money cubeless eq.: 0.012 �0.008. Rollout settings: Full rollout, 360 games (equiv. 123380 games), played 3-ply (fast), random seed, with race database.
	4	R	23/14	-0.006 (-0.010)
			0.8%  13.9%  49.7%    50.3%  14.8%   0.8%
			95% confidence interval: - money cubeless eq.: -0.016 �0.011. Rollout settings: Full rollout, 180 games (equiv. 62478 games), played 3-ply (fast), random seed, with race database.
	5	R	23/18 13/9	-0.018 (-0.022)
			0.9%  14.3%  49.1%    50.9%  15.2%   1.0%
			95% confidence interval: - money cubeless eq.: -0.028 �0.012. Rollout settings: Full rollout, 180 games (equiv. 48913 games), played 3-ply (fast), random seed, with race database.

Blue has played 5-3: 23/20 13/8

194
186

Note that with 5-3 we do not make the home-board 3-point with 8/3 6/3, which would be the prefered play in Backgammon. In Nackgammon, attacking play doesn't work as well as in Backgammon, while priming play works better.

The 3-point doesn't develop into a prime very easily and when we are not likely to attack, an overly deep home-board point is not likely to be helpful. But the main reason is that activating the back men takes a priority.

Blue has played 5-3: 8/3 6/3

194
186

#		Ply	Move	Equity
	1	R	23/20 13/8	0.005
			0.9%  14.9%  50.2%    49.8%  13.5%   0.8%
			95% confidence interval: - money cubeless eq.: 0.020 �0.007. Rollout settings: Full rollout, 360 games (equiv. 128767 games), played 3-ply (fast), random seed, with race database.
	2	R	24/21 23/18	0.001 (-0.003)
			0.8%  13.9%  50.1%    49.9%  14.6%   0.8%
			95% confidence interval: - money cubeless eq.: -0.006 �0.007. Rollout settings: Full rollout, 360 games (equiv. 141848 games), played 3-ply (fast), random seed, with race database.
	3	R	24/21 13/8	0.001 (-0.004)
			0.8%  14.9%  50.0%    50.0%  13.8%   0.8%
			95% confidence interval: - money cubeless eq.: 0.012 �0.007. Rollout settings: Full rollout, 360 games (equiv. 132156 games), played 3-ply (fast), random seed, with race database.
	4	R	23/15	-0.003 (-0.008)
			0.8%  14.1%  49.8%    50.2%  14.7%   0.8%
			95% confidence interval: - money cubeless eq.: -0.010 �0.007. Rollout settings: Full rollout, 360 games (equiv. 163508 games), played 3-ply (fast), random seed, with race database.
	5	R	8/3 6/3	-0.005 (-0.010)
			0.9%  15.4%  49.7%    50.3%  14.5%   0.9%
			95% confidence interval: - money cubeless eq.: 0.003 �0.012. Rollout settings: Full rollout, 180 games (equiv. 54787 games), played 3-ply (fast), random seed, with race database.

With a 5-2 roll the split is less risky, and the best play is 24/22 23/18. The difference is that it hurts less to get hit on the 22-point than on the 21 or 20-point.

White will still hit twice happily with 6-3, mainly hoping to make his bar-point but the second hit on the 3-point is as much a sacrifice for tempo as an attempt to make the point.

Blue has played 5-2: 24/22 23/18

194
187

#		Ply	Move	Equity
	1	R	24/22 23/18	0.006
			0.8%  13.9%  50.3%    49.7%  14.4%   0.8%
			95% confidence interval: - money cubeless eq.: 0.002 �0.010. Rollout settings: Full rollout, 180 games (equiv. 75022 games), played 3-ply (fast), random seed, with race database.
	2	R	23/18 13/11	-0.004 (-0.010)
			0.9%  14.5%  49.8%    50.2%  14.5%   0.8%
			95% confidence interval: - money cubeless eq.: -0.003 �0.011. Rollout settings: Full rollout, 180 games (equiv. 60011 games), played 3-ply (fast), random seed, with race database.

5-1 is a roll that doesn't even give you the choice of making four blots. Here one can play the safe 23/22 13/8, but my personal preference is 24/18, which leads to more blot-hittng action and produces more complex positions.

Blue has played 5-1: 24/18

194
188

Blue has played 5-1: 23/18 23/22 194 188	Blue has played 5-1: 23/22 13/8 194 188

#		Ply	Move	Equity
	1	R	24/18	-0.002
			0.8%  13.9%  49.9%    50.1%  14.4%   0.8%
			95% confidence interval: - money cubeless eq.: -0.008 �0.010. Rollout settings: Full rollout, 180 games (equiv. 79004 games), played 3-ply (fast), random seed, with race database.
	2	R	23/18 23/22	-0.007 (-0.005)
			0.8%  13.7%  49.6%    50.4%  14.5%   0.8%
			95% confidence interval: - money cubeless eq.: -0.016 �0.011. Rollout settings: Full rollout, 180 games (equiv. 67810 games), played 3-ply (fast), random seed, with race database.
	3	R	23/22 13/8	-0.009 (-0.007)
			0.8%  14.0%  49.5%    50.5%  14.2%   0.8%
			95% confidence interval: - money cubeless eq.: -0.012 �0.011. Rollout settings: Full rollout, 180 games (equiv. 73718 games), played 3-ply (fast), random seed, with race database.

4-1 is the best roll for the Quad Split. There is less to fear from a double-hit, since all of the blots are in the opponent's home-board. In fact I believe the only roll that White should use for a loose double-hit is 2-1. The only reasonable alternative 4-1 play would be 23/18, but there is no need for the opener to accept less flexibility than what he gets from the four blots.

Blue has played 4-1: 24/20 23/22 194 189	Blue has played 4-1: 23/18 194 189

#		Ply	Move	Equity
	1	R	23/18	-0.000
			0.8%  13.8%  50.0%    50.0%  14.2%   0.8%
			95% confidence interval: - money cubeless eq.: -0.005 �0.009. Rollout settings: Full rollout, 360 games (equiv. 110342 games), played 3-ply (fast), random seed, with race database.
	2	R	24/20 23/22	-0.001 (-0.001)
			0.8%  14.1%  49.9%    50.1%  14.1%   0.8%
			95% confidence interval: - money cubeless eq.: -0.002 �0.007. Rollout settings: Full rollout, 360 games (equiv. 136350 games), played 3-ply (fast), random seed, with race database.

With 6-2, another rather weak roll, the split with 24/18 23/21, though dangerous, is probably correct at DMP. A running play - 23/15 - may be just slightly better in a money game or at a match score where the cube is alive and gammons matter.

Blue has played 6-2: 24/18 23/21 194 186	Blue has played 6-2: 23/15 194 186

#		Ply	Move	Equity
	1	R	23/15	-0.002
			0.8%  14.1%  49.9%    50.1%  14.5%   0.8%
			95% confidence interval: - money cubeless eq.: -0.007 �0.007. Rollout settings: Full rollout, 360 games (equiv. 118267 games), played 3-ply (fast), random seed, with race database.
	2	R	24/18 13/11	-0.004 (-0.002)
			0.9%  14.7%  49.8%    50.2%  14.8%   0.9%
			95% confidence interval: - money cubeless eq.: -0.005 �0.007. Rollout settings: Full rollout, 360 games (equiv. 129875 games), played 3-ply (fast), random seed, with race database.
	3	R	24/18 23/21	-0.006 (-0.003)
			0.8%  13.9%  49.7%    50.3%  14.9%   0.8%
			95% confidence interval: - money cubeless eq.: -0.016 �0.007. Rollout settings: Full rollout, 360 games (equiv. 159511 games), played 3-ply (fast), random seed, with race database.

With 6-3 and 6-4 the best available play is to run one back checker from the 24-point: 24/15 with 6-3 and 24/14 with 6-4. In Backgammon it is common to play these rolls by splitting to the 18-point and bringing a man down from the mid-point with the other number, but these outfield builder plays just leave too many shots in Nackgammon, with the opponent holding two points in your home-board.

Blue has played 6-3: 24/15 194 185	Blue has played 6-3: 24/18 23/20 194 185

Blue has played 6-3: 23/14 194 185	Blue has played 6-3: 24/18 13/10 194 185

#		Ply	Move	Equity
	1	R	24/18 23/20	0.003
			0.9%  14.2%  50.2%    49.8%  14.6%   0.9%
			95% confidence interval: - money cubeless eq.: 0.000 �0.007. Rollout settings: Full rollout, 360 games (equiv. 128475 games), played 3-ply (fast), random seed, with race database.
	2	R	24/15	-0.001 (-0.004)
			0.9%  14.2%  50.0%    50.0%  14.7%   0.8%
			95% confidence interval: - money cubeless eq.: -0.005 �0.007. Rollout settings: Full rollout, 360 games (equiv. 164174 games), played 3-ply (fast), random seed, with race database.
	3	R	23/14	-0.008 (-0.012)
			0.8%  14.1%  49.6%    50.4%  14.6%   0.9%
			95% confidence interval: - money cubeless eq.: -0.015 �0.009. Rollout settings: Full rollout, 180 games (equiv. 70993 games), played 3-ply (fast), random seed, with race database.
	4	R	24/18 13/10	-0.018 (-0.021)
			0.8%  14.3%  49.1%    50.9%  15.0%   0.9%
			95% confidence interval: - money cubeless eq.: -0.026 �0.011. Rollout settings: Full rollout, 180 games (equiv. 64522 games), played 3-ply (fast), random seed, with race database.

Blue has played 6-4: 24/14 194 184	Blue has played 6-4: 24/18 13/9 194 184

#		Ply	Move	Equity
	1	R	24/18 13/9	-0.010
			0.9%  14.7%  49.5%    50.5%  14.8%   0.9%
			95% confidence interval: - money cubeless eq.: -0.011 �0.007. Rollout settings: Full rollout, 360 games (equiv. 142244 games), played 3-ply (fast), random seed, with race database.
	2	R	24/14	-0.011 (-0.001)
			0.8%  13.8%  49.5%    50.5%  14.3%   0.8%
			95% confidence interval: - money cubeless eq.: -0.016 �0.008. Rollout settings: Full rollout, 360 games (equiv. 129597 games), played 3-ply (fast), random seed, with race database.
	3	R	24/18 24/20	-0.024 (-0.014)
			0.8%  13.7%  48.8%    51.2%  15.2%   0.9%
			95% confidence interval: - money cubeless eq.: -0.040 �0.008. Rollout settings: Full rollout, 360 games (equiv. 129913 games), played 3-ply (fast), random seed, with race database.

Knowledge of the opening plays and the ideas behind them is often enough to take you through several rolls of a Nackgammon game. The basic setup changes slowly at first and by the time the opening is over you may be playing a game that might have come out of the regular setup. Let's look at the start of a typical Nack game.

Blue rolls 2-1 and plays 24/22 23/22 (the forward anchor play).

White rolls 4-1 and responds with 24/20 23/22.

White makes the quadruple split, just as he would with an opening roll. Blue's 2-1 opening does not affect his decision.

189
191

Blue rolls 5-5 and plays it 23/18 13/3* 8/3.

Blue could now make the blitzing play 8/3*(2) 6/1*(2), but it would be a serious error. White anchors with any 5 or 2, and Blue is left with two checkers out of play on his ace point, a badly timed position, and undeveloped back men.

The better 5-5 play is 13/3* 8/3 23/18. Blue still points on a White blot, gaining a bit of initiative and adding to the racing lead that the big doubles roll gives him, but at the same time he activates a back checker (hoping to make the bar-point anchor), retains the valuable 8 point, and avoids an unnecessary blot on his own side of the board.

192
171

White rolls 4-3 and plays Bar/21 23/20

Almost forced. White makes the best available anchor.

185
171

Blue now rolls 4-3 and plays 22/18, 24/21

Blue, still playing with his back men, upgrades his anchor to the 18. The 18-point was the best possible anchor at the start of the game and it still is.

185
164

White plays the 5-4: 21/16, 20/16

Finally we come to a play that is not right out of the opening book. White now abandons his home-board anchor in favour of an outfield point. This is very common in Nackgammon, much less so in Backgammon. White's objective is to connect his position. The 16 point bridges the back men to the midpoint. White is not concerned much about getting attacked, since Blue still has four back, and the 16 alleviates much of his concern about getting primed. The last two back men should be able to hop out to the 16 or beyond without much difficulty.

A couple of alternative plays are not much weaker. (Nackgammon tends to produce a lot of non-volatile positions in the opening.) 24/20, 21/16 is safe and sound, almost as good as the outfield point-making play, but it is a little less flexible and the 20-point is an inferior anchor point. 13/4* is a normal backgammonish loose hit - not hopeless here, just not as good as it would probably be in the regular game. With less volatility there is less to gain from a tempo-hit, and chances of starting a successful attack are pretty remote, so the two main motives for the play are greatly diminished.

After 24/20 21/16 176 164	After 13/4* 176 168

Blue now rolls 5-2 and plays 21/16 18/16.

DMP 176 164	Blue has played 21/16 18/16 176 157

Blue emulates his opponent, with virtually the same play. Again it is a play that is easy for an experienced Backgammon player to overlook. We tend to think of anchors as relatively fixed features of the landscape, but with four checkers back there are many more opportunities to shift from one point to another and the escape process often involves several point shifts.

After 22/20 13/8 176 157	After 21/14 176 157

There are a couple of points worth noting about this position. Blue's play leaves him exposed to various double hits, but he is off the dangerous 5 and 4 points. He would actually be more dangerously exposed to attacking hits after 13/8, 22/20. It is riskier to rest blots on points that your opponent wants to make. Secondly, one reason Blue wants an outfield point like the 16-point is that the outfield is a more dangerous place than usual. 21/14 is a normal-looking running play, but here a blot on the 14-point would be exposed to a double direct shot plus an extra 6-3 from the 20-point. With a lot of hostile territory that is hard to fly over, a safe landing pad is very helpful.

We are now almost out of the opening, but we have made quite a bit of progress using nothing but 'opening roll' plays and the point-shift. Next month we'll take up more advanced Nackgammon checker play.