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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Three Interesting Problems

Aug 15, 2021 | Backgammon Problems: Middle Game

Here are three problems the early stages of a long match. Try your hand and see how you do.

(A) Match, score 0-0 to 17, center cube.

White to play 3-1.

(B) Match, White leads 1-0 to 17, center cube.

White to play 5-4.

(C) Match, White leads 1-0 to 17, center cube.

Should White double? Should Black take if doubled?

Position (A): This one should have been pretty easy. When you have a 5-prime with a checker trapped behind it and not at the edge, your game plan is to make a 6-prime, and the easiest way to do that is usually to slot the prime from the back, with the idea of covering next turn. White should therefore see this as a pretty good roll and just play 13/9. The play has the added bonus of duplicating Black’s aces, since he now needs ones to hit and ones to get to the edge of the prime.

Hitting with 6/2* is a major blunder. White needs the 3-point or the 9-point to complete a 6-prime, and he only has three checkers that can participate in that fight. Playing 6/2* effectively burns one of those checkers, since the 2-point has no importance yet and White has no need for a tempo hit.

Position (B): A 6-6 on the second roll of the game is usually a great shot, giving White a lead in the race plus a couple of good points. The follow-up, however, can be tricky. With a 5-4 on the next turn, the best play is usually breaking off the anchor with 18/13/18/14. When White doesn’t get hit, he’s got plenty of builders and spares and a good chance of capitalizing on his racing lead.

Attacking with 8/3* 7/3 looks appealing at first glance, but it’s not as strong as you might think. Black has 12 immediate hits (52, 56, 43, 46, 26 and 16) that catch up in the race, plus 5-4 as a great anchoring number. Even when Black doesn’t immediately hit, the game frequently evolves into a holding game where White wants to get off his anchor on the 18-point but can’t.

Position (C): This position is tricky over the board because the solution depends on just how you ‘see’ the situation. If you see this as just a blitz, then it’s clearly not a double. White doesn’t even have a checker in the air and Black just has a 2-point board.

But if you see this through the lens of Joe Sylvester’s Position-Race-Threat matrix, then it looks very different. White leads in the race by 25 pips, 134-159. His position is better, with an extra inner point on his side and a strong anchor on Black’s side. White has threats, with a bunch of numbers to make the 4-point and other numbers that put two checkers in the air. His position is better and it’s threatening to get better still, maybe by a lot. Looked at this way, it’s an easy double and Black has the tough decision. He can take because so far he’s only facing a 2-point board and the threats are not crushing.

Holding Game — Building the Board

Aug 1, 2021 | Backgammon Problems: Holding Game

Cash game, center cube.

White to play 1-1.

This position shows a slightly unusual mutual holding game structure. Both sides have anchors, White on his 21-point and Black on his 18-point. Right now White trails in the race by 16 pips (123 to 107), but trailing in the race isn’t much of a disadvantage in these positions because the side that’s ahead in the race usually has to break anchor and expose himself first.

White has two decisions to make:

(1) Should he move the checkers on the 21-point or the 13-point, or leave them alone?

(2) What’s the best way to improve his inner board?

The first question is the easiest. Since White trails in the race, he wants maximum contact. The way to get maximum contact is to stay back as much as possible. so White doesn’t want to move the checkers on the 21 and 13-points unless there’s no recourse. In this case it’s even more important than usual to keep both points, because Black’s sixes are horrible if White stays where he is. Notice that in the current position 6-1, 6-3, and 6-4 all leave shots, while 6-2 and 6-6 continue stacking checkers.

So let’s leave those checkers on the 21 and 13-points alone and concentrate on the inner board.

If White wants to play only in his inner board, the obvious first choice is 4/1 6/5, building a 4-point board. It’s a perfectly safe play, and if White gets a shot next turn and hits, he won’t have to worry about an exposed blot. However, although it’s perfectly safe, it’s also poor technique. When building a board to prepare for future shots, the right idea is to build it as quickly as possible by slotting, covering, slotting, and covering. Playing 4/1 6/5 creates a 4-point board, but making the important fifth point will take a while.

A better try is 6/4 3/2(2), which creates a 4-point board with the fifth point slotted. Still, that slot on the ace-point is a little hard to cover. Better still is 6/4 3/1! which moves the slot backwards, where it’s in direct range of the 8-point. Now White has a 4-point board with the fifth point slotted and easy to cover. That approach gives him the best chance of having a 5-point board when he finally hits a shot.

Cracking a 6-Prime

Jul 1, 2021 | Backgammon Problems: Priming Games

Cash game, White owns the cube.

White to play 6-1.

In this position, Black has managed to build a full 6-prime, and White has one checker trapped behind it. A single checker behind a full prime is normally a pretty bad position. If Black could escape all his back checkers and arrange them on top of his prime, while White just filled in his board, Black would be about a 90-10 favorite, with gammon chances in the 5% to 6% range.

Fortunately, Black hasn’t yet escaped all his checkers, which gives White some extra resources. In fact, if he makes the right play here, his winning chances bounce up into the 25% range! That’s a hefty increase, so let’s see if we can figure out the best way to proceed.

Game Planning in the Middle Game

Jun 15, 2021 | Backgammon Problems: Middle Game

(A) Cash game, center cube.

Should White double? Should Black take if doubled?

(B) Assume White doubles and Black takes. White to play
(b1) 55
(b2) 33
(b3) 53

Holding Games with Stragglers

Jun 1, 2021 | Backgammon Problems: Holding Game

One of the most common middle game structures in backgammon is the holding game, where at least one side has made an advanced anchor, and the other side has to get his checkers home while leaving as few shots as possible. Holding games are even more common now than previously, because of the tendency to split the back men with most opening rolls, which tends to result in anchors for both sides.

Here are a couple of examples of interesting holding game problems:

(A) Cash game, center cube.

(A) Cash game, center cube.

White to play 6-2.

(B) Cash game, White owns the cube.

(B) Cash game, White owns the cube.

White to play 3-3.

Slotting in the Middle Game

May 1, 2021 | Backgammon Problems: Middle Game

Slotting is an easy idea to understand in the opening. When we slot the 5-point with an opening 2-1, we threaten to make a very strong point while unstacking a big stack. Since our opponent has no board, getting hit is just a minor inconvenience. Although it’s not a hugely correct play (splitting our back men is almost as good), it’s not a hard play to make because the downside seems pretty small.

Slotting in the middle game or the endgame is very different. Now your opponent almost certainly has a reasonable home board, so the cost from being hit is much greater. It’s also unlikely that you still have a stacked position at this point, so unstacking probably isn’t a big goal.

With a hit being more expensive and unstacking not so important, we’ve knocked out two of the three pillars supporting an early slot, and we’re reduced to just one: the value of the point itself. When we slot in the middle game, the point needs to be really important, and the chance of making it cleanly without slotting not so good. There is, however, a new factor affecting a middle game slot: the cube. A slot followed by a miss from your opponent may give you a good double, which in some cases is enough to tip the play in favor of slotting.

Root Numbers

Apr 15, 2021 | Backgammon Problems: Priming Games

Cash game, White owns the cube.

White to play 5-1.

Root Numbers

In backgammon, a root number is just a dice throw that damages or destroys your position. We mostly encounter these by accident, when we throw an awkward shot that can’t be played except by wrecking our inner board or leaving a bunch of blots somewhere.

Root numbers don’t always happen by accident, however. Sometimes the only way of saving a hopeless position is to notice that by making a certain play, you can create a few root numbers for your opponent which wouldn’t exist otherwise.

The Squat Zone

Apr 1, 2021 | Backgammon Problems: Middle Game

In the 1970s, the New Yorkers invented a term for the new style of backgammon they were playing, a style based upon aggressive hitting and slotting. They called it pure play. The essence of pure play was the willingness to take risks in the race to build a crushing prime quickly. If the plays worked, you had a winning prime. If your opponent got lucky and hit you a few times, you just had to outplay him in the resulting back game/holding game. (Since the top players played these complex positions very well, this was usually no problem.)

Cash game, center cube.

Black to play 3-2.

While they were naming their own style, the New Yorkers also coined a name for the opposite style – the beginner style of playing safe and stacking up your checkers. They called it playing squat.

Bearing Off Against Contact

Mar 15, 2021 | Backgammon Problems: Ace and Deuce-Point Games

Cash game, Black owns a 2-cube.

White to play 4-1.

Back at World Cup VI, in 1998, Kent Goulding and I introduced a ‘Quizgammon’ contest, consisting of a set of 30 problems taken from all phases of the game. Everyone who was interested paid an entry fee of $20 and sat down for an hour with their problems and answer sheet. After everyone handed in their solutions, Kent and I went over the answers and announced the winners.

Priming Games – Escape or Attack

Mar 1, 2021 | Backgammon Problems: Priming Games

Money game, White owns the cube.

White to play 4-1.

This position is not difficult but it illustrates a key idea in priming games, whether prime against prime or prime against blitz: Do the hardest thing first, and force your opponent to do a hard thing in reply.

By “hard thing” I mean anything that you are a 70-30 underdog (or worse) to do. Usually this implies anything that must be done and which requires a single number on the dice. When we begin thinking in terms of “doing hard things” and “making our opponent do hard things”, complicated positions can start to look pretty simple.

Here, for instance, it’s clear that Black’s prime will not break. Black has to come in from the bar, which might take a while, after which he has the checkers on the 18-point to move, as well as the checker which just entered and the checker on the midpoint. So to win, White will have to escape his rear checker, and that will require an ace (a “hard thing”) plus a six (another “hard thing”). Since he just threw an ace, he wants to play 24/23 if at all possible. Since he can use the four to make both a 5-point board and a 5-prime, that’s his play. He should move 24/23 and 6/2.

What would it take for White to pass up 24/23 with the ace? In most variations of this position, 24/23 will remain correct, but here’s an example where it’s a mistake:

Position A: White to play 4-1.

Without a 5-point board to give Black something “hard” to do, White doesn’t have the security of moving to the 23-point. Here he has to play 2/1, to keep Black on the bar for some time. After that, either 8/4 or 13/9 are about equal.

Priming Games: Action versus Timing

Feb 15, 2021 | Backgammon Problems: Priming Games, Uncategorized

The next position is an interesting problem with a few non-standard elements. On the one hand, it’s a prime versus prime problem; both sides have 5-point primes, and both sides have some escaping to do. On the other hand, it’s an action play problem. White is on the bar shooting at a couple of blots, and a lot hinges on whether he hits or not next turn.

Money game, center cube, White on roll.

Should White double? What should Black do if White doubles?

Creating Bad Numbers

Feb 1, 2021 | Backgammon Problems: Priming Games

This next problem shows a somewhat unusual middle game position. White, with one checker in the air, has an outside prime with the 5-point slotted. Black has a bizarre position with four checkers back on his 24-point. His front game is normal enough, with the start of a little block. Last turn, White doubled from the bar and Black bravely took. (A small mistake, actually. The position is a pass, although not by much.)

Money game, Black owns the cube, White on roll.
White to play 5-2.

White’s 5-2 from the bar gives him a few choices. Here’s a quick list of the main options:

(1) Bar/23 13/8. The safest play, this keeps the back checker from being attacked on the 20-point, while adding another cover number for the 5-point.

(2) Bar/20 5/3. Another safe option, this time duplicating twos. This also prevents Black from simultaneously hitting and getting to the edge of White’s prime. The downside of the play is that it becomes hard for White to build on his early advantage. Covering the 3-point won’t make his game appreciably stronger.

(3) Bar/20 13/11. This play is a different way of bringing down another cover number to make a 5-prime.

(4) Bar/20 7/5. This play shifts points, covering the 5-point and leaving the bar-point slotted.

Those are all the reasonable plays; anything else we can eliminate quickly. The next step is pruning our tree a little bit more. Are there any of these play that don’t stand up to a closer inspection?

To make progress, let’s focus on our opponent for a second. What is his big weakness, and what are his awkward numbers?

Black’s main problem, clearly, is that mass of checkers on his 24-point (our ace-point). Black needs to get those checkers moving quickly, before his front game stalls and collapses. He can move them with aces through fours, but his fives and sixes are blocked. That insight lets us toss two of our candidates right away. Move (1), Bar/23 13/8, makes fives and sixes somewhat useful by letting him hit on our 23-point. Move (4), Bar/20 7/5, makes sixes not only active but highly useful, letting him step out to our bar-point while hitting at the same time. Let’s eliminate both those moves and focus on the last two, Bar/20 5/3 and Bar/20 13/11.

The choice between these two plays hinges on the cube position. We’ve given the cube away, so we want to finish Black off as quickly as possible. Making a prime is the best way to do that, and the risk (a single shot) is not that great. Playing 5/3, after all, still gives Black a shot, and on a point we don’t really care about making. So let’s leave our blot where it belongs and play Bar/20 13/11. Making the prime wraps up the game – if Black misses, he’s in a hopeless position with nowhere near the timing to play a back game.

(Incidentally, if we had forgotten to double last turn so the cube was still in the middle, then 5/3 would be right. The idea in that case would be to minimize the chance of a big downswing so we could keep our advantage and turn the cube on the following turn.)

Playing a Blitz Part 2

Jan 15, 2021 | Backgammon Problems: Blitzes

Here we’re returning to the theme of the previous post: a late game blitz with a choice of hitting outside or making a point inside. (In this case, making the inside point also has the nice advantage of putting a checker in the air at the same time.) These problems are inherently very difficult, and require looking at all the features of the position before making a decision.

Money game, Black owns the cube, White on roll.
Black to play 2-2.

Playing a Blitz

Jan 1, 2021 | Backgammon Problems: Blitzes

This position shows an interesting blitz situation. Black’s been caught with a checker on the bar, another exposed blot in White’s home board, and a third blot in his own outfield. White has a three point board with a fourth point slotted, plus a few builders on hand.

Money game, Black owns the cube, White on roll.
White to play 6-1.

If Black were helpless, White would have a strong attack. Unlike the case with an opening blitz, however, Black actually has a position here, with a strong board and a four-point block. If White’s blitz fails, Black will get the upper hand very quickly.

Studying Your Opponent’s Position

Dec 15, 2020 | Backgammon Problems: Holding Game

This position shows a pretty normal-looking mutual holding game. White was two pips down in the race (114-112) prior to rolling. But he fired a great shot, double-fives, which moved him to an 18-pip lead. What should he do?

Money game, center cube, White on roll.

White to play 5-5.

Coming Home in a Holding Game

Dec 1, 2020 | Backgammon Problems: Holding Game

These next two positions show a couple of closely related holding game situations. Black has the 20-point, but now he’s got a man stuck on the bar. White has a nice 5-point board, and a couple of blots not in direct range of Black’s anchor. He also has the 9-point, which was an asset for a while, but is now a liability to be cleared. How much risk should he be willing to take while Black is on the bar?

Money game, Black owns the cube, White on roll.