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Bill Robertie welcomes the opportunity to share his knowledge of backgammon with experienced players and beginners alike.

On his blog, Robertie publishes set and equipment reviews, creates quiz contests and provides free lessons. He would be remiss not to include his Robertie’s Rules! He also educates readers of the Gammon Press blog on the history of the game, offers backgammon instruction and more.

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Priming Games: Escape or Build Structure?

Dec 1, 2022 |

Cash game. Center cube. White on move.

(A) White to play 6-1.

(B) White to play 6-1.

One of the most difficult choices in the early and middle stages of a backgammon game is the choice between creating structure (a blocking prime) and attending to issues on the other side of the board. Those issues vary: you might be able to hit a checker, or make a defensive anchor, or escape one of your back men. In some cases, making structure is correct. In other cases, playing on the other side of the board is correct. Let’s take a look at a couple of examples, to see the ideas that have to guide us in these decisions.

Let’s start with Position (A). It’s not a tough problem. White can hit a blot with 24/17* or build some structure with 13/7 8/7. The structural play has two problems: the structure isn’t that impressive, and it gives Black a direct shot at White’s blot on the 14-point. For structure to trump hitting, you want structure which is solid and imposing.

24/17* might look loose, but it accomplishes two great things: hitting an important blot, and escaping a rear checker. True, Black may hit back. He has a total of 16 return hits (all twos except 2-6, and all fives except 5-6). But that leaves 20 rolls that don’t hit, and those are great rolls for White – he’s ahead in the race and his rear checkers are out. Potentially getting all your back checkers out is a great result, and 24/17* puts White within striking distance of that goal.

Problem (B) occurs much later in the game. White has two choices: he can block in Black’s two rear checkers with 13/7 8/7, or he can escape his own last checker with 24/17. Running out is more volatile – if White gets away with it, he’s close to a double, but if Black hits, White is an immediate underdog. Making the 7-point, on the other hand, leaves White a solid but unspectacular favorite in most variations.

What’s right? White should go ahead and make his 7-point. There are two reasons:

(1) With an advantage and a centered cube, you’re not looking to make big swing plays. You’re more interested in plays that preserve your advantage and creep closer to an eventual good double. When in doubt between the merits of two plays, lean to the more conservative choice.

(2) Trapping two men will increase your gammon chances dramatically. There’s actually not much difference in raw winning chances between the two plays, but locking in Black’s two back checkers will win many more gammons.

The basic idea in these positions is a simple one: the quality of the structure you build is crucial. Turning a very weak structure into a slightly better structure, as in Position (A), isn’t worth that much. Turning a broken structure into a 5-point prime, as in Position (B), is huge, even when the alternative is escaping the last checker from behind a 5-prime! The lesson to be learned is that creating a 5-prime or even a 4-prime may outweigh making progress on the other side of the board, but just building a blocking point or a 3-prime is probably not enough.

 

Holding Game Doubles

Nov 15, 2022 |

Cash game. Center cube. White on move.

Should White double? If he doubles, should Black take or drop?

Here’s an interesting cube position. Black has an anchor on White’s 5-point. White’s ahead in the race by 21 pips, 117-138. White also has a pretty good 4-point board. Black’s remaining checkers are in play and his board is in the process of forming.

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Two Middle Game Doubles

Nov 1, 2022 |

Cash game. Center cube. White on move.

(a) Should White double? If he doubles, should Black take or drop?

(b) Should White double? If he doubles, should Black take or drop?

These two positions show a couple of very typical middle game doubles. In each case we’re six to eight moves into the game, one side has finally grabbed a noticeable advantage, and now they’re thinking about turning the cube. Double? Take? What’s right?

Let’s start with the doubling question. The best general guide to early/middle game doubles of this sort came years ago from Joe Sylvester. (Joe was one of the titans of backgammon in the 1980s and 1990s, and he won the first World Cup in 1988. Today he’s somewhat inactive.) Joe recommended looking at three features of the position: the race, the structure, and threats. His rule was the following: if you have an edge in at least two of these three, then you have a double.

With this idea in mind, how’s White doing in Position (a)?

> White leads in the race, 133 to 149, a 16-pip lead.

> White has a better structure, with a 4-point block, his 4, 5, and 6-points already made, and good distribution. Black lacks his 4-point and 5-point and has a big stack on his 6-point.

> White has plenty of immediate threats. Twos hit the blot in Black’s board, 6-1, 6-3, and 3-1 make a 5-point prime, and 6-4 points on the 2-point. White’s edge is threatening to get much bigger next turn.

With an edge in every department, Sylvester’s rule suggests White should have a strong double in Position (a), and in fact he does.

Now let’s look at Position (b).

> White leads in the race, 134 to 162, a 28-pip lead.

> White has a better structure, with four points made in front of Black’s anchor. In addition, Black has three men back on his 23-point, which is weak. Black also has no inner board yet, which is also weak. Here the issue is not so much that White is strong, but that Black’s pretty weak.

> White has no particular threats. True, 6-1 makes his 5-point, and a few numbers will run his back checker into the outfield. But that’s more the sort of background threat noise that’s present in every position.

Here, we can say that White has an edge in two out of the three criteria. Again, he has a solid double.

Now, what about the take/drop question? Here I’ve got my own rule. I ask myself three quick questions. If the answer to the first and third questions is ‘yes’, and the answer to the second question is ‘no’ I’m pretty sure I’ve got a take. If not, then I’ll look at the position more closely. My questions are:

> Do I have an anchor?

> Does my opponent have a 5-prime?

> Is there still contact on both sides of the board?

Take a look at Problem 1 and Problem 2. In both cases Black has an anchor, in both cases White hasn’t yet built a 5-prime, and in both cases we still have contact on the other side. With all these conditions in place, it’s hard (although not impossible) for Black to be a 3-to-1 underdog in the game. In both positions, Black’s best guess should be that he probably has a take. And in fact, rollouts show that’s the correct action.

 

A Post-Ace-Point Game Problem

Oct 15, 2022 |

Cash game. White owns the cube. White on move.

(a) White to play 5-1.

(b) White to play 5-1.

These two positions take us into the fun world of post-ace-point games.

“Post-ace-point” is a little bit of a misnomer. These positions can be reached from ace-point games, but also from deuce-point games, or back games, or even games where someone was on the bar and closed out. The main idea is that you held on and finally hit a shot, then contained the hit checker or two, then completed a closeout, and finally started to bear off. Mostly your problem is figuring out exactly when to redouble, but sometime the problem lies in how safely you should play your checkers.

These positions show two examples of the most common checker play quandary. In each case, White has a choice between bearing off one checker and playing completely safe (5/off 5/4), or bearing off two checkers while leaving a shot (5/off 1/off). What’s right, and how do we make the decision?

The first metric we want to calculate is the crossover count. A crossover is simply a move of a checker from one quadrant to another, or from the bar to the opponent’s inner board, or from the inner board to the bearoff. Let’s start with Position A. White has 15 checkers in his inner board to be borne off, so his crossover count is easy: it’s just 15. Black’s is a little more difficult. His six checkers in his inner board represent six crossovers obviously. His checker on the bar represents another five crossovers: one to enter, three more to get from White’s inner board to Black’s inner board, and one more to bear off. Black’s total crossover count is 11.

So in Position A, White trails in the crossover count by four, 15 to 11. In Position B, he also trails by the same four crossovers, 14 to 10.

Next we employ the following rule of thumb:

If you trail by two or less in the crossover count, play safe. You’re doing well enough in the race that there’s no need to take additional risks.

If you trail by five or more in the crossover count, take two checkers off and leave a blot. You’re a big underdog in the race, and you need the extra checker speed.

If you trail by three or four, you’re in a grey area.

Well, that’s nice. We’re in the grey area in both positions. What next?

In the grey area, decisions depend very much on the exact arrangement and count of checkers in the inner board. You next want to look at all of the following considerations and see if they point toward one play or another.

(1) If you trail by three crossovers, tend to play safe. If you trail by four, tend to bear off.

(2) If Black has a blot in his board, tend to bear off. If no blot, tend to play safe.

(3) If taking two checkers off brings you to an even number of checkers, tend to bear off, otherwise tend to play safe.

(4) If you have a speed board, tend to play safe, otherwise tend to bear off. A speed board is one where White’s home board spares are heavily concentrated on the one and two points, which implies that small doubles are more likely to bear off four checkers through the bearoff. With a slower board, where the checkers are spread evenly across points, small doubles often won’t save a roll.

Now let’s see how Positions A and B compare across these four criteria.

(1) Crossover count? White trails by four in each position.
Problem A – favors bearing off.
Problem B – favors bearing off.

(2) Black blot? Black doesn’t have a blot.
Problem A – favors playing safe.
Problem B – favors playing safe.

(3) Getting to even? Taking two off in A brings White to 13 checkers, an odd number. But in B, taking two off brings him to 12, potentially saving a roll.
Problem A – favors playing safe.
Problem B – favors bearing off.

(4) Speed board? White has a slow board in both positions.
Problem A – favors bearing off.
Problem B – favors bearing off.

For Position A, our four criteria split two and two. Rollouts show the position is actually a tossup, with a minute edge for playing safe.

In Position B, three of our four criteria favor bearing two off, and rollouts show that’s the correct play by a wide margin.

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