5-Point or 4-Point?

IMG_4632by Gerry Tansey

Prior to reaching the position below, both players had played a 52 by splitting the back checkers and bringing down a man from the midpoint.  How should White play a roll of 31?  What about a roll of 42?

 

5-2

In each case, White must decide whether to make an offensive point or a defensive anchor.  Good arguments can be made for each play.  If White makes an offensive point, White unstacks her heavy 8- and 6-points, starts to build her board, and puts pressure on Black’s back checkers.  If White makes a defensive anchor, she shuts down Black’s ability to score a quick knockout offensively, and the security of the advanced anchor allows White to play more freely up front.

Let’s see what XG thinks:

3-1

1. Rollout1 8/5 6/5 eq: +0.238
Player:
Opponent:
55.71% (G:15.57% B:0.57%)
44.29% (G:11.03% B:0.41%)
2. Rollout1 24/21 22/21 eq: +0.092 (-0.146)
Player:
Opponent:
51.72% (G:12.01% B:0.44%)
48.28% (G:9.02% B:0.32%)

 

 

4-2

1. Rollout1 24/20 22/20 eq: +0.200
Player:
Opponent:
54.55% (G:10.74% B:0.30%)
45.45% (G:7.09% B:0.25%)
2. Rollout1 8/4 6/4 eq: +0.167 (-0.033)
Player:
Opponent:
54.18% (G:15.08% B:0.58%)
45.82% (G:11.53% B:0.45%)

In each case, XG says, “Make the 5-point!”  If White rolls 31, she should make her own 5-point, and it is a big blunder to do anything else.  If she rolls 42, she should make Black’s 5-point (her own 20-point), although the plays are much closer in this case.  The reason for the size difference between the errors has to do with the heavily stacked 8- and 6-points.  If White makes her 4-point with 42, at least she is unstacking the heavy points.  By contrast, if she makes the anchor with 31, she is both making an inferior point and refusing to unstack the big towers, so this should be a much bigger error.

These two positions illustrate a principle articulated by Nack Ballard: “Either 5-point is better than either 4-point.”

There is one wrinkle I’d like to point out, however.  Both of these rollouts are money game rollouts.  In match play, if White is at a score in which a gammon is useful to her but not to her opponent (2-away / 1-away Crawford, for example), she should make her offensive 4-point with the 42.  In doing this, she gives up very few wins in exchange for a much more gammonish position.

Here’s a position that arose in the chouette the other night.  The rollout results immediately follow, so scroll slowly if you don’t want to see them right away.

chouette

 

1. Rollout1 24/20 22/20 eq: +0.203
Player:
Opponent:
53.73% (G:15.19% B:0.59%)
46.27% (G:7.93% B:0.31%)
2. Rollout1 8/4 6/4 eq: +0.135 (-0.068)
Player:
Opponent:
52.21% (G:18.40% B:1.41%)
47.79% (G:12.87% B:0.67%)

White failed to cover the blot on his 5-point, but he did roll a pretty good 42 nonetheless.  Even though making the offensive 4-point unstacks two heavy points, it is right to make the 20-point anchor in this position, and by an even larger margin than it was with the 42 earlier.  Here, Black already has a two-point board, so if White makes his own 4-point, he is only drawing even in development with Black while leaving a blot in his board and split back checkers.  By making the 20-point, White shuts down Black’s ability to create quick offense.  Even if Black is able to hit White’s 5-point blot, it is not even close to enough to decide the game.  And of course, “either 5-point is better than either 4-point.”

This next position was posted recently at the bgonline forum by Backgammon Giant John O’Hagan:

4-3

1. Rollout1 Bar/21 8/5 eq: -0.179
Player:
Opponent:
45.99% (G:13.38% B:0.61%)
54.01% (G:16.88% B:1.17%)
2. Rollout1 Bar/21 24/21 eq: -0.200 (-0.021)
Player:
Opponent:
45.25% (G:11.56% B:0.44%)
54.75% (G:14.91% B:0.66%)
3. Rollout1 Bar/22 13/9* eq: -0.212 (-0.033)
Player:
Opponent:
46.52% (G:12.83% B:0.72%)
53.48% (G:20.40% B:2.10%)

I must confess that I would have quickly made the advanced anchor by playing Bar/21 24/21.  Although making the 5-point with the 3 has some appeal, I would have been too afraid of Black’s four builders aiming at my 21-point blot to make that play.  And yet, XG has a small but clear preference for making the 5-point.  Black does not always point on White’s head next turn, and with the 5-point made, it is not always the end of the world when it happens.  Sometimes Black rolls a number like 41, which Black should use to make his 5-point.  But if he does this, he leaves White many shots to hit back.  Further, if White makes the anchor rather than his own 5-point, he leaves Black with a direct shot to send a fourth checker back.  While it is not a disaster if this checker is hit, it does mean that White will have difficulty winning the game going forward.  It is too early for White to give up going forward when he has the option of taking the lead in home board points by making his own 5-point.  While making the 5-point leads to more gammon wins for both sides, these extra gammons roughly cancel out, and making the 5-point simply wins more games.  Yet again, we have confirmation that “either 5-point is better than either 4-point.”

To me, the craziest thing about this position is the fact that the third-best play, Bar/22 13/9*, is not that far behind.  In fact, it seems to be the play that wins the most games.  It loses too many gammons to be the right play for money, but it is almost certainly right at DMP.  And there is no way I would have even considered it over the board.  Here we see the power of yet another backgammon adage: “When in doubt, hit.”

 

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