Bill Robertie's Blog

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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Asset or Liability?

Jan 1, 2023 | Backgammon Problems: Holding Game

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

White to play 6-2.

Extreme Gammon (XG) is the most useful tool ever invented for improving at backgammon. It’s both the strongest commercially available backgammon software, and, when used properly, the best teacher.

Getting the most out of XG’s teaching ability, however, requires a little thought and planning. In this post I’ll give an example of how using XG’s power, combined with a little critical thinking, can help you patch weak spots in your game.

A Back Game with Questionable Timing

Dec 15, 2022 | Backgammon Problems: Back Games

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

White to play 4-3.

This isn’t a particularly hard position when presented as a problem. The right play is 8/5 13/9, keeping both back points, slotting the 5-point, and playing 13/9 so as to create two cover numbers for the 5-point.

Over the board, with no one hinting that this is actually an interesting position, it’s fairly easy to make a small mistake. I’d expect to see a lot of players move either 13/9 13/10, a slight error because it doesn’t start the 5-point, or 8/4 8/5, another slight error because the builder on the 4-point is somewhat misplaced and White has fewer cover numbers for the 5-point than he should.

Leaving a blot on the midpoint after 13/9 8/5 is not especially costly because for the most part Black doesn’t want to hit it. Let’s take a quick look at how Black should play his aces after White plays 13/9 8/5.

Black needs to notice these features of the position:

> If he can play safe and not hit, he should do so. Not hitting leaves White’s timing in jeopardy, while hitting improves White’s timing somewhat and may give White a shot at Black’s blot on his ace-point. Right now White trails by 65 pips in the race, which is enough to give him some reasonable winning chances, but not enough to say that he has a well-timed back game. One extra checker back, especially if White could dance for a turn, would make a big difference.

> Playing safe is essential for Black, so if he can only play safe by hitting, he will do so. Black very much doesn’t want to get hit right now, because White’s board is already strong enough to cause real trouble.

> If Black can’t play safe, hitting wins more gammons, and may decrease the count of hit and cover numbers.

So with 6-1, 5-1, and 4-1, the best plays are 13/6, 13/7, and 13/8, all without hitting.

With 3-1, Black can only play safe by hitting, so the right play is 13/12* 4/1.

With 2-1, Black can’t be safe no matter how he plays, so he should hit. Hitting substantially increases his gammon chances compared to the non-hit play (13/11/10), while his losing chances are close after both plays.

As a last point, note that White shouldn’t consider playing 23/16 with his 4-3. While it’s true that his back game/holding game isn’t ideal, it’s the only game he has. Playing 23/16 breaks much of the contact and leaves him 58 pips behind in a game that will mostly become a 5-point holding game, an essentially hopeless situation. If White really wanted to break one of his anchors, the better choice is to keep the back anchor and play 20/13.

Priming Games: Escape or Build Structure?

Dec 1, 2022 | Backgammon Problems: Priming Games

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 | Backgammon Problems: Holding Game

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.

Two Middle Game Doubles

Nov 1, 2022 | Backgammon Problems: Middle Game

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 | Post-Ace-Point Games

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.

Prime versus Prime Tactics

Oct 1, 2022 | Backgammon Problems: Priming Games, Uncategorized

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

White to play 2-2.

This problem is an example of a somewhat rare breed, a true prime against prime game. Although we talk about priming games a lot, real priming battle don’t arise all that often. Much more common are positions where one side has a prime and the other just a loose connection of points, or games where one side has a prime but the other is conducting a strong attack.

Handling a Proto-Back Game

Sep 15, 2022 | Backgammon Problems: Back Games

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

White to play 2-2.

First, let’s try to orient ourselves. White looked like he might get stuck in some sort of miserable ace-point game, but has just thrown a fantastic shot, 2-2, which is so good it actually lets him pursue a few different options. In backgammon, it’s good technique to try to list all the reasonable plays before you start analyzing the merits of any one play. With that goal in mind, let’s see what we can find for candidate plays.

When Your Opponent is About to Crunch

Sep 1, 2022 | Backgammon Problems: Priming Games

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

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

In this position, White took an early cube based on his ownership of Black’s 2-point and the fact that Black still had a checker left to escape. After that, the game developed almost perfectly for him. His deuce-point game caused Black to bear in awkwardly, while White’s front position came together and prevented Black’s back checker from escaping. After Black’s last roll (an awkward 4-4), White finally has a clear advantage, although he still trails by 47 pips in the race. Is this the right time to double?

Playing Against a Busted Back Game

Aug 15, 2022 | Backgammon Problems: Back Games

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

White to play 4-3.

Something a little different this time. Identify the worst of these three plays:

(a) 11/7 5/2

(b) 11/4

Blitz or Consolidate?

Aug 1, 2022 | Backgammon Problems: Blitzes, Uncategorized

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

White to play 3-3.

White’s off to a good start in this position. He’s already made a three-point board, whereas Black hasn’t yet made a new point, and White has hit a blot, leaving him 17 pips ahead in the race. Black, meanwhile, is still scrambling to make an anchor. Last turn White offered an aggressive double, and Black quite reasonably took.

Now White throws one of his best shots, 3-3, and has three game plans:

(a) The consolidation play with 14/8 13/10(2), leaving him firmly in control with a nice edge, or

(b) Consolidation plus a little attack with 24/21 14/8 6/3*, or

What’s the right idea?

Here’s the general approach for handling these sorts of positions. If your opponent has no structure, and the cube has already been turned (activating gammons), then the blitz dominates any safe game plan. If the blitz fails, White can just drop back into some sort of holding game where he holds a slight edge. If White makes one of the solid plays, he’ll reach those holding games anyway since almost all of Black’s rolls will anchor somewhere. White will be slightly better off if he goes for the holding game right away, because of his racing lead, but the difference is small. But if the blitz succeeds White wins a gammon, and with the cube already turned that’s a quick four points and a huge swing.

As Black acquires more structure, the blitz drops in value. If we alter Black’s position and give him his 5-point (as though he had rolled a 3-1 at some time), then the blitz plays are only slightly superior to the consolidating plays. If we give Black two extra points, say the 5-point and the 3-point, then the blitz plays become pretty big errors and the consolidating plays becomes correct. (There’s very little difference between Play (a) and Play (b) no matter what structure Black has.)

So we’re blitzing. Next question: what’s the right way to blitz?

What makes this problem especially interesting is that White has two distinct ways to blitz: the obvious 13/4*/1* and the obviously riskier 13/4* 6/3*. Problems with two plausible blitzing moves are rare, but we can choose between them by noticing that the double-hit with 13/4*/1* exposes only one blot in the board, and a hit may only allow Black to get an ace-point game later. If White hits on the 3-point and 4-point with two checkers and Black then throws a three or four, he may get a good anchor quickly. The two blitzing plays are close (and far superior to the non-blitzing plays) but the play that exposes only one inside blot is slightly better.

Where to Leave Blots

Jul 14, 2022 | Backgammon Problems: Middle Game

Both positions: Cash game. Center cube. White on move.

(a) White to play 5-4.

(b) White to play 6-2.

In Problem 140A, White has no way to safety the blot on his 16-point. In fact, he can’t avoid creating a second blot as well. He has a few reasonable plays: 13/4, 16/11 13/9, 16/11 6/2, 13/8 13/9, and 6/1* 13/9. None of these plays look terribly strong. How should he decide among them?

Bearing In Against the Ace-Point

Jul 1, 2022 | Backgammon Problems: Ace and Deuce-Point Games

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

White to play 5-1.

When bearing in against an ace-point or other low anchor game, you generally have two goals in mind. The first is safety; you want to create formations that are less likely to leave blots as you bear off. The second is winning a gammon; you’d like to maximize your chances of winning a gammon if you can.

Split or Run?

Jun 15, 2022 | Backgammon Problems: Early Game

Cash game. Center cube. White on move.

White to play 5-2

The early part of a backgammon game is dominated by two key goals: hit blots and make points. The easy moves are the ones where you can only do one good thing. The hard moves are those where you can do two good things, and you have to make a tough choice, or no really good things, and you have to decide how best to arrange your checkers for future action.

This position is an example of the latter situation. White can’t make any points with a 5-2 roll, and his only hit, 6/1*, doesn’t accomplish anything good. So he has to shuffle his checkers around somehow and get ready for action next turn.

My cardinal rule in these positions comes from the medical profession: “First, do no harm.” In backgammon terms, that means don’t try plays that make your distribution worse rather than better. Here, I’ll reject 13/8 for just that reason. After 13/8, White has gone from a nice position with a spare on both the 13-point and 8-point to a position with a small stack on the 8-point and no spares on the midpoint. That’s not an improvement, so let’s reject all the plays involving 13/8.

Since we’ve already rejected the awful 6/1*, we’re now left with just two candidates: 23/18 13/11 and 23/16. Running all the way out and trying to escape with 23/16 is the safer play: fewer ways to get hit and fewer blots. Since Black has a better board right now, extra safety is not a bad idea.

The alternative, 23/18 13/11, tries for a bit more. White creates a new blot and exposes himself to more hits in return for a chance to make a great anchor on Black’s bar-point. The problem with the move is a bit subtle. The purpose of the new blot on the 11-point is to give White some extra chances to make his 5-point with rolls like 6-3 and 6-1. However, White won’t have a chance to execute those threats because he’ll most likely be on the bar next turn. Black is going to hit on his bar-point with all his ones and sixes, and he will probably hit on his ace-point with fives as well. In fact, Black’s only non-hitting numbers are 4-3 and 4-4, and 4-3 actually makes White’s 5-point, rendering the blot on the 11-point somewhat useless!

Here’s a quick rule of thumb: a move like 13/11 is excellent when you have an anchor somewhere, so the blot on the 11-point is a useful builder immediately. It’s not so useful when a hitting contest is about to ensue on the other side of the board. As long as the battle for Black’s bar-point is unresolved, a blot on the 11-point is really just an extra target. Play the simple 23/16 instead and try to escape a checker.

Improving Your Technique

Jun 1, 2022 | Backgammon Problems: Middle Game, Uncategorized

Cash game. Center cube. White on move.

White to play 2-2.

The advent of the bots in the late 1990s enabled players to solve a myriad of small technical plays that recurred frequently but couldn’t really be tackled with hand rollouts or pure reasoning. Hand rollouts were so slow that they really had to be reserved for positions where the solution was unknown but the difference between plays was likely to be large and important. Players ignored what appeared to be small technical stuff, on the theory that solving these problems, even if possible, was most likely a huge waste of energy.

Creating Mobility

May 15, 2022 | Backgammon Problems: Middle Game, Uncategorized

Cash game. Center cube. White on move.

White to play 6-4.

This is a comparatively easy problem if you can properly balance the key features of the position. Let’s step back for a second and look at just what is happening, before we try to evaluate the different choices.

The race: White will trail in the race by 16 pips after he plays his 6-4. Considering that he has five men back to Black’s two, he’s not as far behind as one might think at first glance. Since he’s trailing in the race, however, he wants to maintain a good anchor (to generate some shots) and a good blockade (to contain blots he may hit).

Blockades: White has four good points in front of Black’s anchor. That’s a solid plus for him, if he can maintain it. Black has a motley collection of scattered points, which indicates that he probably won’t be able to build a good block anytime soon, and that he’ll likely have to start leaving shots in the near future.

Weaknesses: For White, what might seem a strength is actually a long-term weakness. He has two great anchors, on the 20-point and the 18-point, but that’s one great anchor too many. The 20-point/18-point combination doesn’t work well together; they tie up 76 pips at a time when maneuvering freely is still key.

Black’s weakness is glaringly obvious; it’s the 2-point, too deep in his board to be useful at this stage. Black might have had good reason to make it in the past, but now he’d be better off if those checkers were back on the 4-point or the 9-point.

Now let’s put all this together and see just what we can do with the 6-4.

8/2 6/2. A bad choice. White burns two of his remaining builders to make a useless point far behind Black’s anchor. Now all his remaining points are stripped and his only convenient rolls next turn are those that can be made entirely with the blot on the 24-point. Take a look at how numbers like 4-1, 3-2, 6-1, 5-2, 4-3, 5-1, and 6-4 play next turn. In complex middle games with action on both sides of the board you need checkers that can move easily, and sometimes you have to take risks to preserve those checkers.

24/18 6/2 and 24/20 8/2. Not as committal as making the 2-point, but half-hearted versions of the same idea. You only have 15 checkers, and you want everyone in play at this stage of the game.

20/10. To those who worship the 5-point, this looks like a shocking idea. White breaks the defensive 5-point before he must. But it’s really a fine move, which solves all White’s problems at once. White doesn’t need both anchors, so he gives one up voluntarily.

Take a look at the position after 20/10 and notice how White has solved most of his problems. He now has five spare checkers, ensuring that he won’t have to concede any valuable points in the near future. He’s got more combinations to make his 5-point or 7-point, as well as more ways to attack if Black should split his back checkers for some reason. Finally, he’s resolved the issue of too many anchors in a neat and efficient fashion.

If you missed this problem, it’s probably because you’re too focused on static features of the position, and not enough on the flow of the game. Try to anticipate how the game is likely to develop over the next couple of rolls, and avoid positions where you have a real shortage of checkers that can move.