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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Running from a Holding Game

Dec 1, 2023 | Backgammon Problems: Holding Game

Cash game, White owns the cube.

White to play 6-3.

Checker play in holding games is generally a pretty simple matter. When you’re holding onto an anchor and you’re way behind in the race, you try to follow three rules:

1) Keep your anchor as long as you can.

2) Run off your anchor when the alternative is breaking your board.

3) Run off the anchor if staying raises your gammon chances a lot.

If you’re familiar with these rules, you’ll be able to handle most normal holding game positions well.

Things get trickier when you have a third checker back. The third checker can generate more potential shots; it can also get you gammoned if Black can point on the checker and you get stuck on the bar a long time. This position shows a typical situation: Should White stay to get more shots, or run to eliminate gammon chances?

Early Doubles

Oct 1, 2023 | Backgammon Problems: Early Game

Cash game, center cube.

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

In the last post we talked about the importance of cube benchmark positions — positions where one of the cube decisions (either doubling or taking) was perfectly marginal, while the other was completely clear. Learning typical benchmark positions gives us the ability to analyze a wide variety of related positions over the board with unusual accuracy.

This position shows us another type of useful benchmark. We’re currently just four moves into the game. The opening sequence was

White: 5-3, making the 3-point.
Black: 4-3, bringing down two builders.
White: 6-2, hitting.
Black: 6-3, dancing.

With Black on the bar and White clearly having the upper hand, White now contemplates a double. Considering Sylvester’s three criteria for offering an initial double, here’s how White stands:

Race: solid edge for White. His hit and Black’s fan leaves White up 25 pips, 151 to 176.

Threats: small edge for White. He’s threatening to hit Black’s other blot, but White’s weak board means this is really just a threat to gain a little more ground in the race.

Position: Small but solid edge for White. He has a 2-point board, while Black’s board is undeveloped. White’s extra point, however, is just the 3-point, and there’s no prime in the immediate future. White has almost escaped one of his back checkers, another plus.

To summarize, White has a sizeable edge only in the race, while his other edges are small. Rollouts show that this is a small but correct double, which of course means that the take is very clear. White’s problem is simply that a big lead in the race isn’t as significant as one might think if the inner board is weak. The most likely sequences in that case are ones in which Black easily makes a good anchor or exchanges of hits occur; either of these scenarios minimizes White’s racing lead.

If you were at all tempted to drop this position as Black, just remember that the combination of a weak board, few builders, and an anchor for Black almost always guarantees an easy take. That’s the case here.

Once you know the value of this position in a cash game, you can easily make some practical adjustments for tournament play. If White were trailing in a match, this would be an easy double. If White were the better player, it would also be an easy double, since this will be a long game and White should expect to outplay Black in the later maneuvering.

Benchmark Doubling Positions

Sep 15, 2023 | Backgammon Problems: Blitzes

Cash game, center cube.

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

A key idea in understanding the proper use of the doubling cube on a practical level is that of the “benchmark” position. A benchmark cube situation is a position where one of the decisions (doubling or taking) is a toss-up, while the other is completely clear. Properly understanding a benchmark position is very useful since it unlocks the key to many related positions. Just compare your actual position to the benchmark, spot what the relevant differences, and you should be able to make a good cube decision over the board. Better players are aware of hundreds of good benchmarks, so they can make their over-the-board decisions quickly and accurately.

Action Doubles

Sep 1, 2023 | Backgammon Problems: Middle Game

Cash game, center cube.

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

This position shows a pretty interesting middle game position. Both sides have an anchor, and some points scattered around. White, however, is on roll and shooting at a bunch of blots. He has a total of 27 hits: all sixes, all fives, 4-3, 4-1. 3-2, and 3-3. That’s a lot of hits, so he’s naturally thinking about doubling, and Black is probably worrying whether or not he’ll have a take if White ships the cube.

Doubling Blitzes

Aug 15, 2023 | Backgammon Problems: Blitzes

Cash game, center cube.

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

We’re in the early stages of the game and White is contemplating a double. Some time ago Joe Sylvester developed a rule for evaluating early doubles. Sylvester advocated looking at three aspects of the position:

(1) Positional advantage (board strength, primes)

(2) The race

(3) Threats

A solid lead in two out of three areas usually translates into a good initial double. A lead in all three guarantees a good double and brings the take into question. Let’s look at all three features of the position in light of Sylvester’s Law and see what we get.

(1) Positional advantage. No one really has a priming structure yet. White has one more home board point and one more outfield point, but Black has his 5-point. Slight edge to White.

(2) Race. Huge edge for White, who leads in the pip count, 118 to 152.

(3) Threats. Another big edge for White, who has five crushing doubles (1-1, 2-2, 3-3, 4-4, and 6-6) plus another six rolls that make the 4-point (6-4, 6-2, 4-2). In addition, White can at least hit loose with most of his other numbers.

A big edge in two out of three categories certainly implies White can double. At the same time, Black has a pretty easy take. White only has three really crushing numbers (2-2, 4-4, and 6-6). Everything else gives Black a chance to anchor on his next turn, with a long game in progress. And of course, Black does have his 5-point, which is a big asset in his favor.

Split to the 18-Point or Something Else?

Aug 1, 2023 | Backgammon Problems: Early Game

Cash game, center cube.

White to play 6-3.

This position shows one of the most commonly misplayed early game situations. White opened with a 43 and made the building play, 13/9 13/10. It’s the most aggressive choice for an opening 43, designed to make a prime quickly and create a complicated position. Black responded with a 44, making his 9-point and electing to make an advanced anchor rather than hit. (Hitting is also very reasonable.) Now White has a 6-3 to play.

Holding Game: Leave Anchor or Not?

Jul 15, 2023 | Backgammon Problems: Holding Game

Cash game, center cube.

White to play 5-2.

Here we have a position from the tail end of a mutual holding game. These positions typically arise as follows:

> Both sides make an advanced anchor in the opening.

> Both sides bring down some builders from the midpoint and make a few blockading points.

Neither side ever rolls a big double that would allow it to escape the back men safely.

>Both sides slowly dismantle their blocking points and build inner board points behind the opponent’s anchor.

> Crunch time! Both sides start to face tricky decisions about when to leave the anchor.

Make Point or Hit Twice?

Jul 1, 2023 | Backgammon Problems: Middle Game

Cash game, center cube.

White to play 4-1.

Is backgammon a simple game? No, not at all. There’s a lot you have to know, a lot of technique you have to master, a few formulas to memorize. But some elements of backgammon are easy. At bottom, backgammon’s about hitting blots, making points, and winning the race. read more…

Which Point to Break?

Jun 15, 2023 | Backgammon Problems: Middle Game

Cash game, Black owns the cube.

White to play 6-2.

Early Blitz Cube – Take or Drop?

Jun 1, 2023 | Backgammon Problems: Blitzes

Cash game, Center cube.

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

In this position we have an opening blitz with a few little twists we don’t always see in such situations. Let’s quickly review the features of the position and look at which are important and which are not.

Hit or Make a Point?

May 15, 2023 | Backgammon Problems: Middle Game

Cash game, White owns the cube.

White to play 3-1.

White has a simple choice in this position: hit with 13/9*, or wait and make a point with 15/12 13/12. Last time we looked at some choices between hitting a blot or making a point in the context of early game play. This position occurs much later in the game, but, as it turns out, the very same principles are still useful. Let’s again list the criteria we explained last time, and see how they apply to this position.

Hit or Make a Point?

May 1, 2023 | Backgammon Problems: Early Game

Cash game, center cube.

(a) White to play 3-1.

(b) Same position, White to play 3-2.

Here we see a typical sort of early game position where neither side has made much progress yet. Black has played a 5-3 and a 6-3, making the 3-point and running a checker into the outfield. White has rolled a 5-1, balancing his builders and splitting his back men.

Balanced and Unbalanced Positions

Apr 15, 2023 | Backgammon Problems: Middle Game

Center cube. Money game. White on move.

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

White seems to be doing pretty well in this position. He has a 4-point board, while Black as yet has no new home board points made. Black doesn’t have an anchor yet. White can hit on the 4-point with 18 numbers (all 4s, 3-1, 2-2, 1-1, 6-3, and 3-3.) He has a few more numbers to hit on the 1-point, although that’s certainly not his top choice. White leads by a whopping 38 pips in the race. Looks like White’s concrete assets and threats combine to give him a good double. Can Black even take this? Over the board, a lot of players would drop almost instantly.

Before we pass final judgment on this cube, let’s alter the position just a little bit:

Position A: White on roll.

We’ve moved White’s spare on the 3-point back to the 6-point, where it’s active, and we moved the third checker on the 8-point back to the midpoint. White has lost 8 pips in the race, but his checkers are now where they belong and his position is much stronger.

Position A is a strong double for White and a clear pass for Black. (By the way, it’s not remotely close to being too good to double.) Our original position, by contrast, is also a good double but a clear take. White has threats, but he also has a number of bad rolls, and even when he rolls well to start, his checkers aren’t sufficiently well-positioned to follow up.

Now let’s look at the two positions a little more closely. Position A is what I like to call a balanced position. Given the underlying structure, White’s spares are well-placed and effective. Our original position is unbalanced; here White’s spares are in the wrong places. The spare on the 3-point is mostly useless. The extra spare on the 8-point doesn’t do much, and the broken midpoint is costly in both the long and short term.

The difference between balanced and unbalanced positions is visually pretty clear, but the real difference shows up when we examine White’s bad rolls. (The good rolls will play well anyway.) Let’s list White’s worst rolls and see how they play in both the original position and Position A.

6-6: In the original position, this is a disaster; White is forced to play 13/1* 8/2(2), killing two checkers. In Position A, this is a very good roll; White makes the 1-point.

5-5: In the original, this is another awful roll; White switches with 6/1*(2) and plays 13/3, killing a checker. It’s not as bad in Position A, where White plays 6/1* 13/8 13/3.

6-5: In the original, White kills a checker with 13/2. In A, he plays 6/1* 13/7, much better.

6-2: White plays 3/1* 13/7 in the original. In A, he plays 23/15 because he owns the midpoint, rather than having a blot there. Big edge to A.

6-1: In the original, White makes the 7-point, but gives up control of the outfield. In A, he gets to play 23/16 as before. Another big edge for A.

5-3: In the original, he plays 13/8 with either 24/21 or 23/20. In A, he again takes advantage of owning the midpoint by playing 23/15. Huge edge to A.

5-2: Same story. In the original he plays either 13/6 or 13/8 23/21. In A, he gets to play 23/16. Another big edge to A.

5-1: In the original he plays 13/8 23/22. In A he plays the much stronger 6/1* 2/1.

3-2: In the original he gets to play 3/1* 23/20, activating the checker on the 3-point. In A he plays the massively stronger double-hit.

2-1: In the original he plays 3/1* 2/1 as above, activating a bad checker. In A he gets to play 6/4* 23/22, hitting on the more important point.

As this listing shows, the difference between the standard-looking position in A and the inferior position in the original isn’t slight; it’s actually huge. A lot of players look quickly at the original position and actually “see” something more like A. But the exact placement of all the spares matter, and it especially matters in the case of the bad rolls. In tough cube decisions, try to pay at least a glancing impression as to how concrete rolls actually play, rather than get caught up in forming a general sense of the position.

How Match Score Affects Early Game Play

Mar 13, 2023 | Backgammon Problems: Tournament Tips, Uncategorized

Center cube. Black on move.

Black to play 3-3

(a) in a cash game.

(b) at double match point.

(c) trailing 1-2 in a 5-point match.

(a) Cash game.

As a cash game play, this position has an interesting history. When I started playing serious backgammon in the late 1970s, the game was dominated by a group of aggressive young New Yorkers centered at the legendary Mayfair Club, who emphasized making big plays early on, to set up quick cube turns and gammons. They were bold, ingenious, highly aggressive, and very successful, and most aspiring players followed their lead.

At the time, the old-fashioned play with 3-3 after an opening split to the bar was the obvious 13/7*(2). Why not? It hits a blot, makes a good point, leaves no blots, and unstacks the midpoint. That’s a lot of good things at zero risk. The New Yorkers rejected this play and instead played 13/7* 8/5(2), in accordance with the new (at the time) emphasis on making the 5-point early on no matter what the cost.

When I saw the new play I enthusiastically switched, following my general rule of thumb for beginners: “Ape your betters”. (At least until you know enough to question their judgment.) After a few years, though, I started to have second thoughts. How bad could 13/7*(2) really be? It had a lot to recommend it: good point, no blots, takes a solid initiative. I did some analysis and just couldn’t convince myself there was anything wrong with the play, so I switched and started to play it. I got some hoots of derision, but pretty soon more and more players were switching over, and by the 1990s this simple play was the standard, and the ‘old-fashioned’ 13/7* 8/5(2) looked ‘too loose, too fancy’.

Extreme Gammon rollouts long ago confirmed that 13/7*(2) is in fact best, while 13/7* 8/5(2) is a fairly close runner-up. Also in the mix is 13/7* 6/3(2), also making an inner point, unstacking, and leaving fewer shots and blots. Prior to the bot era, no one would even have considered making the 3-point, although I think most modern players would immediately spot it as a strong alternative.

(b) Double match point.

Double match point is simply any match score where gammons don’t count for either side and the result of this game decides the match. The simplest example occurs when each side is one point from victory. Other match scores can convert into double match point (DMP) pretty easily. For instance, if both players are two away from victory, and someone doubles quickly and the other side takes, then we have a double match point situation by default.

With gammons not counting, strategy in this situation undergoes a few changes. Here’s a quick summary of the major alterations.

1. The best game plans at double match point are (a) escaping your back checkers and winning the race, and (b) building a prime and winning the race. Racing advantages create a lot of wins but not a lot of gammons, which is perfect.

2. Blitzes are a poor choice of game plan unless the dice allow no reasonable alternative; too many gammons, not enough wins.

3. Anchors are less valuable because one of their functions is to prevent being gammoned, which is no longer necessary. The strength of an anchor lies in its ability to transition to a favorable race.

4. Inner board points are still good, but not quite as good. We don’t care about their ability to create gammons but we do care about their ability to create primes.

5. Slotting to build an inner board quickly is mostly wrong.

6. Plays where you run off an anchor to avoid being primed later are commonplace.

7. Escaping the back checkers is even better than usual.

Taking all this into account, it’s not hard to see that 13/7*(2) is even better at DMP than in a cash game. It gains ground in a race while taking no risk of losing ground in the race. The point is useful as well.

(c) Trailing 1-2 in a 5-point match.

Trailing 1-2 to 5, or ‘4-away 3-away’ as it is sometimes called, is a score where gammons matter more than usual for the trailer. If the trailer wins a doubled gammon, he wins the match. If the leader wins a doubled gammon, he still wins the match but some wastage is involved (he doesn’t need the fourth point). As a result, the trailer needs to create positions where he has an elevated chance of winning a gammon, at a reasonable cost. He doesn’t want to go crazy, he just wants to take a little more risk for extra gammon chances.

Both 13/7* 6/3(2) and 13/7* 8/5(2) fit the bill here. They’re the second and third best plays in a cash game, but here the extra inner point creates more gammons at a small cost in raw winning chances. Which of the two is best? A rollout left the two plays in a dead heat. Playing 6/3(2) makes a weaker point, but as compensation it unstacks a big stack and leaves fewer shots.

Back Games: Redoubling and Taking

Feb 1, 2023 | Backgammon Problems: Back Games

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

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

In our last problem we looked at a back game where the back game player got a double shot, but still couldn’t double until he actually hit the shot.

While that’s a generally good rule for many normal back game positions, it’s not always the case. When playing a massive back game, stay alert for positions where your opponent’s game has deteriorated so much that you can double much earlier.

Back Games: When to Redouble

Jan 15, 2023 | Backgammon Problems: Back Games, Uncategorized

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

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

Positions like this are fairly commonplace when playing back games, and they’re tricky enough to lead many players astray.

White has played a 5-2 back game and has just gotten a double shot. Besides fives and twos, he can also hit with 4-1, so he has a total of 22 hits and 14 misses this turn. In the future of course, White may get even more shots.

Some players, encountering this position for the first time, might reason as follows:

> Wow, I have 22 hits! I’m already the favorite!

> And if I hit, I can easily lose my market!

> And I might get even more shots in the future!

> And I could win a gammon!!

> I double!!!

Anything wrong with this reasoning? Well, just a little bit. Let’s look more closely.

Let’s start by examining what happens when White doubles. True, he then hits 22 times out of 36, a bit more than 60%. But how many of those can he win, once Black owns the cube? Let’s give White a pretty average hitting roll, like 4-2, and see how we think he’s doing.

Position after White hits with 4-2 and plays 20/18*/14.

Although he just got hit, Black still leads by 50 pips in the race, which has to be worth something. In addition, he has some pretty good shots in this position: 6-2, 5-2, 6-1, and 1-1, all of which leave Black in a lot of trouble. Let’s be conservative and say that Black can pull the game out a little less than a quarter of the time from this position. In that case, out of White’s 22 hits, we’ll say he can win about 17 of them, losing the other five.

What about White’s 14 misses? Now he’s in real trouble, trailing by 60-70 pips in the race, with his opponent owning the cube. Black won’t redouble immediately, but he’ll be able to use the cube very effectively in the near future when his position improves a little more. At worst, he’ll at least be able to play the game out to the end. I’ll give White four of these games, but no more.

Overall, White’s chances after doubling look like this:

If he hits, he wins 17 and loses 5.

If he misses, he wins 4 and loses 10.

With the cube on 4, White wins about 21 and loses about 15, for a net of 6 games, worth 4 points each. Total, +24 points.

Now suppose White keeps the cube and rolls. Again he hits 22 and misses 14. But now his 22 hits are very strong. Black needs a great shot immediately or he’ll pass a double, and even if he gets his shot, White can hang around until the end. Let’s make White about a 20 to 2 favorite in these games.

If White misses, he still has plenty of chances in the game. Let’s give him 6 games of these 14, losing the other 8. Now, his chances after not doubling look like this:

If he hits, he wins 20 and loses 2.

If he misses, he wins 6 and loses 8.

With the cube on 2, White wins about 26 and loses about 10, for a net of 16 games, worth 2 points each. His total here is +32 points. So he does substantially better by not doubling.

This is a pretty typical result when you get a double shot in a back game. You’re a big favorite if you hold onto the cube, but just a small favorite if you double. Barring some unusual features, these positions are mostly all no double and take.