Advanced-Level Backgammon: An Outsider's Guide

Problem #3

Black opened with 65 and escaped a back man, and White responded by using their 43 to split their own back men and bring down a builder to their 10-point (shown as the 15-point). Black's now rolled the respectable 55, but how to play it?

Candidate Moves

The candidate moves include:

13/3 8/3 6/1*, closing an inner board point and hitting loose on the ace-point.
13/3(2), making the 3-point with two checkers from the midpoint.
8/3(2) 6/1*(2), closing two inner board points and pointing on White's head in the process.
13/8(2) 6/1*(2), pointing on White's back man and unstacking the midpoint.

13/3 8/3 6/1*

13/3 8/3 6/1* seems like a reasonable move: Black only hits White with a single checker and thus avoids burying two men on the ace-point, while also closing a second inner board point to increase the effectiveness of the attack. Because Black has escaped one of their back men, however, they have a lot more to lose by being hit, so the danger of White hitting with a return shot (11 rolls hit: 61, 51, 41, 31, 21, 11; 30.6% chance of hitting) is too great to justify leaving a blot. In more material terms, after this roll, Black will be leading by a solid 25 pips in the race; but if White hits this expensive blot, Black will suffer a loss of 24 pips, completely nullifying Black's advantage.

Moreover, this play leaves the 8-point stripped, and with one of White's back men sitting on the 5-point, Black can't safely break this point or bring down any builders without inviting a barrage of shots—nor can Black expect to be able to hit White's blot off of the 5-point safely without covering the blot on the ace-point. Clearly, this move leaves a lot to be desired.

13/3(2)

13/3(2) is considered a standard play for an early-game 55, but is it appropriate here? It certainly carries less risk than the previous candidate, not leaving any blots beyond Black's back runner, and it accomplishes the important tasks of unstacking the very heavy midpoint and making a new inner board point. Indeed, the main weakness of this play is that it's too passive, but why is that an issue?

Notice how White has slotted on Black's 5-point, and additionally has a builder at the ready on the 15-point. If White is allowed to use their full roll next turn, they're likely to consolidate into a strong position—and since Black opened with a running play, they're currently behind in development, so this consolidation would give White a powerful advantage. Black would like to avoid that if at all possible, so another move is called for (barring match play situations that call for an abundance of caution, such as DMP).

8/3(2) 6/1*(2)

8/3(2) 6/1*(2) is the favorite of the older theory, touted as the go-to play whenever one player rolls 55 in the opening after the other player has split their back men. The main argument presented for this play is that, should White dance (9 rolls fail to enter: 66, 63, 61, 33, 31, 11; 25% chance of staying out), Black can give a strong double on the next roll, forcing White to drop in many cases. There's merit to this argument, and the play is indeed a strong one, but it's worth examining how this position looks in the cases where White immediately re-enters after the hit:

White has many rolls that will either let them anchor on the Golden Point (15 rolls let White anchor: 56, 55, 54, 53, 52, 51, 41, 32; 41.7% chance to anchor) or hit Black's outer board blot (7 rolls hit: 53, 44, 43, 32; 19.4% chance to hit), for a total of 17 good rolls (47.2% chance). Remember: Black's racing lead will be demolished should White hit Black even once on Black's side of the board!
Black, having closed two deep inner board points, is committed to playing an attacking game, but they currently only have 8 checkers on their side of the board, leaving them short on ammunition for the attack. Thus, Black will have to scramble to bring down builders in the next few turns, all the while being threatened by White's back man (or anchor, in many cases!) sitting on Black's 5-point. That's saying nothing, of course, of how Black's attacking prospects will be largely thwarted if White succeeds in anchoring.
This attack does nothing whatsoever to manage or redistribute the massive stack of checkers on Black's midpoint. Having 5 checkers on a single point is already undesirable (it's a third of your men all crammed unproductively into a single spot), so 6 or more on the same point is a serious weakness, doubly so now that Black no longer has any outer board points with which to unstack safely.

Despite these drawbacks, the advantages of this move—giving Black a three-point board, arresting White's development with a hit, and threatening a strong double next turn—are potent enough to make this move a strong pick nonetheless.[1]

13/8(2) 6/1*(2)

13/8(2) 6/1*(2) starts an attacking game for Black in earnest, pointing on White's head on the ace-point while also bringing down two more checkers for a total of 10 in the zone. This lets Black seize the initiative and put a crimp in White's plans for development, since even if White re-enters immediately (88.9% chance)[2], they can't hope to use their builder constructively with only one of their numbers.

This move also allows Black to maintain their lead in the race without risk, as well as marginally improving their checker distribution: Stacking up 5 checkers on the 8-point is less than ideal, to be sure, but it's far better than leaving 6 piled up on the midpoint. Similarly, while making the ace-point is never especially desirable, the benefits reaped by throwing White off-balance for a turn and kicking off an attacking game outweigh the drawbacks here—and all of the inner board points are useful in an attacking game!

Although Black's position is still a bit stiff even after this move, it's the most well-rounded and promising choice, with all other factors taken into consideration.

Answer

13/8(2) 6/1*(2) is the best move overall, though 8/3(2) 6/1*(2) is just barely acceptable.
13/8(2) 6/1*(2) is the best move if Black is well ahead in the match, though 13/3(2) is just barely acceptable.
13/8(2) 6/1*(2) is the best move if White is well ahead in the match.
13/8(2) 6/1*(2) is the best move at DMP, though 13/3(2) is also acceptable.

Key points

Stacks of 5+ checkers are a liability.
Don't play passively during the opening.
Be wary of blotting when you're ahead in the race.
9+ checkers in the zone is a strong attacking force.
Builders turn into blots without a full roll to use them.
Making deep inner points means committing to an attacking game.

Rollouts

(click for larger images)

Money game rollout equity table — Rollout, money game

Basic match rollout equity table — Rollout, 7-point match, score 0-0

Black-leading match rollout equity table — Rollout, 7-point match, score 5-0 (Black leading)

White-leading match rollout equity table — Rollout, 7-point match, score 0-5 (White leading)

Double match point rollout equity table — Rollout, 7-point match, score 6-6 (DMP)

Footnotes

[1] In fact, if Black still had both of their back men on points 1-4 in White's inner board in this position, 8/3(2) 6/1*(2) would be the best move for Black! That's how much of a difference escaping a back man makes.

[2] Incidentally, in the unlikely case that White fails to re-enter after Black plays 13/8(2) 6/1*(2), the recommended cube action (in money games, at least) is for Black to double and White to take.

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