• Early game … which point to make?
  • Run or Anchor?
  • Making the 5-Point
  • Using Benchmark Positions
  • Split or Slot?
  • Volunteering a Shot
  • Duplication
  • More on Duplication
  • High Anchor Holding Games
  • Holding Game Doubles
  • Position or Race?

  • Early game … which point to make?

    Take a look at Position 1. Black has a 4-2 to play. What should he do?

    Black to Play 4-2

    There are two clear candidates here; make your own 4-point, or your opponent’s 5-point (your 20-point). Anything else is a waste of a great shot. But which point should we pick?

    Early game problems where you have a choice of good points to make can usually be solved by asking yourself three key questions

    First, which point is intrinsically more important?

    Second, how do the particular circumstances of the position affect the absolute value of the point?

    Third, what’s the degree of difficulty for making each point?

    Part 1. We’ll start with the intrinsic value of the points. This is pretty easy to determine. The most valuable points in the early going are the two 5-points, closely followed by the 4-points and the bar-points, which are about equal. Other points are much weaker than these key blocking points. Only considering intrinsic value, the White 5-point (your 20-point) is the top choice

    Part 2. Now we have to look and see how the actual position we’re in affects the value of the points. This part requires more judgment

    On Black’s side of the board, not much has changed from the starting position. Black has moved a builder from the 13-point to the 8-point, giving him a little better diversification than he had before. White is still anchored on Black’s 1-point. All in all, Black’s 4-point is just about as valuable as on the opening roll

    But on White’s side of the board, the position has changed a lot. First, White has actually made an inner board point. That means an anchor, any anchor, is more important than it used to be, because any attack that White launches is now more likely to be successful

    In addition, however, the point White has made is his 4-point. With the 4-point made, White’s 5-point becomes even more valuable (for both sides) because of the strength of the 4-5-6 structure. Back in the 1970s, Paul Magriel, in his classic book Backgammon, labeled the 5-point the “Golden Point”, signifying its importance in the opening. While the 5-point is the best point to have in the early going, its power can be mostly neutralized if the opponent then makes the 4-point anchor. But the combination of the 4-point, 5-point, and 6-point, which I like to call the Golden Structure, is a real game-changer. Whoever makes that structure in the early game is on the verge of a powerful double. Even anchoring on the 3-point in front of the structure merely allows the defender to hang on in a clearly inferior position. The only road to equality is hopping the structure entirely and anchoring on the bar-point, and that will be hard to do

    Conclusion: White’s 5-point has risen in important, while Black’s 4-point hasn’t changed much. Making the anchor with 24/20 22/20 now gets the edge

    Part 3. Finally, we have to consider degree of difficulty. How hard is it to make a good anchor, compared to the difficulty of making blocking points? This question almost always favors making the anchor

    Right now Black has one non-double (4-2) that makes the 20-point, and another one (6-4) that makes the almost equally valuable bar-point. On Black’s side of the board, he currently has six rolls (3-1, 4-2, and 6-1) that make a good blocking point. But that number will grow dramatically as soon as he adds even a single builder in his outfield. Pull a checker from the midpoint to the 9-point, for example, and Black will suddenly have nine non-doubles working on those points (6-1, 6-2, 2-1, 3-1, 4-1, 4-3, 4-2, 5-2, and 5-4). Add in his doubles, and Black becomes a favorite to make a key blocking point, each turn!

    Meanwhile, his chances of making a good anchor won’t get bigger, because unless he gets hit, he can’t add any new checkers to his anchor-making list. Upshot: good anchors are much harder to make than good blocking points, so your desire to make them is greater

    All three considerations point clearly to 24/20 22/20 as the best play with a 4-2. When in doubt
    between an anchor and a blocking point, make the anchor!


    Run or Anchor?

    In Position 2, Black has a 6-2 to play. What’s the right idea here?

    White – Pips 161 Black – Pips 160 Black to Play 6-2

    Black has a few reasonable choices in Position 2. If he wants an anchor at all cost, he can button up with 24/22, after which he has to choose between 13/7 and 8/2 for his six. If he wants to stay flexible and run a checker out, he can try either 22/14 or 22/16 13/11. All the plays have some merit, and there’s no obvious standout. What’s the right idea?

    Here’s a key principle that will guide you through a lot of early positions: Points are good, and points that are anchors are especially good. Period

    Now it’s true that the 22-point is not the best anchor to have. Given a choice, you’d rather be on the 20-point or the 18-point. But right now it’s the only anchor available. As we discussed already in the previous part, the 20-point and bar-point anchors are hard to get, so when you’re under pressure you should be happy to take what’s available

    After playing 24/22, the best six is obviously 13/7. The bar-point is much stronger than the 2-point, so you slot the bar even though you give White a few more shots. Now that you have an anchor, being hit isn’t a potential disaster

    Of the running plays, the best is 22/16 13/11, simply because it moves a checker into the outfield and tries to stay out of trouble, a very good idea when your opponent has a better home board and you don’t have an anchor. Black has a few too many blots after this play, but White has to throw a four to really hurt him

    Several plays here are outright blunders: 13/5, 24/18 22/20, and 24/18 13/11

    The first play (13/5) violates a good general rule: DON’T SLOT WHILE YOUR BACK CHECKERS ARE SPLIT. When you slot a point, you’re hoping for your opponent to miss so you can cover next turn. If your back checkers are split, your opponent will attack you there if he doesn’t hit your slot, and you’ll have to get in from the bar before you can try to cover

    The other two plays (24/18 22/20 and 24/18 13/11) violate a different rule: DON’T LEAVE YOUR BACK CHECKERS SITTING ON POINTS YOUR OPPONENT REALLY WANTS TO MAKE. Violate this rule and your opponent will just start hitting everything in sight, while you scramble to survive. The exception (sort of) to this rule is the split on the opening roll with a play like 24/20 or 24/18. If your opponent is in the starting position, he doesn’t have quite enough ammunition in place to really hurt you. But once he starts making points, you’re in danger. Either keep your blots safely tucked away back on the 24, 23, or 22-points, or run for safety in the outfield, but don’t dawdle on the target range


    Making the 5-Point

    Here are two early game positions where Black has not much and White has an inner point and some pressure

    Position (a):
    Black to Play 3-1

    Position (b):
    Black to Play 4-2

    When Paul Magriel wrote his seminal book Backgammon in 1976, one chapter that was particularly noteworthy was entitled “The Golden Point”. There he described the importance of the 5-point, both for offensive and defensive purposes, and showed how making the 5-point was a key goal of early game play

    Over the years, theory regarding the 5-point has never really changed much. We’ve found a few exceptions, and certainly expanded our knowledge of when to break the 5-point later in the game, but the 5-point remains a key opening goal in most positions

    The two examples given above are very typical cases. In each position, Black has a chance to make either the offensive 5-point (Position (a)) or the defensive 5-point (Position (b)). In each position, there are alternatives that seem to have strong merit. In Position (a), Black’s rear checkers are under some pressure and seem to require a defensive anchor, which he can grab with 24/21 22/21. In Position (b), Black can actually hit while making a somewhat inferior anchor with 13/9* 24/22

    But in each case, simply making one of the 5-points is better. In Position (a), making his own 5-points smooths Black’s distribution while starting to put White under some pressure. In Position (b), grabbing the defensive 5-point with 24/20 22/20 prevents White from ever building a priming position, after which Black can start to build points on his side of the board

    It’s incredibly hard to go wrong by making one of the 5-points at an early stage. The exceptions are rare and tend to be exceptions by only small amounts. When in doubt, go for the 5-point


    Using Benchmark Positions

    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

    Black on roll. Cube action?

    This early cube decision shows an excellent benchmark position. White started the game with a 5-1, splitting his back men, and Black responded with a 4-4, making two inner-board points. (Not best, by the way; making the 20-point and the 9-point is better, with a more enduring positional edge.) White then danced, and Black is now contemplating a double

    An analysis by the Extreme Gammon program (highly recommended, by the way) showed that the double/no double decision was completely marginal, with only a tiny difference between the two plays. If doubling is theoretically marginal, then taking is, of course, hugely correct. Dropping is a mistake costing almost one-third of a point. (As a practical matter, this means that doubling is mandatory, since it theoretically costs nothing and might prompt a huge blunder on your opponent’s part.)

    Better players are aware of hundreds of good benchmarks, so they can make their over-the-board decisions quickly and accurately


    Split or Slot?

    Slotting to make a key point and splitting your back checkers are two tactical ideas that dominate early-game play when more obvious choices like hitting blots and making points aren’t available. The 1970s and 1980s were the heyday of slotting. The preferred method of winning a game was to build an imposing prime (often by slotting points, then covering) and follow it with a crushing double. The older method, taking the points you were given and looking for a chance to escape your back checkers, was seen as antiquated and wimpy, a game plan only suited for geezers playing in the park

    This all changed in the 1990s with the arrival of the bots, first Jellyfish, then Snowie, and then in 2010 Extreme Gammon, the current top bot. The early bots didn’t slot their 5-point with an opening roll of 2-1, 4-1, or 5-1, as had been customary; instead, they split their back men with an ace. (The latest version of Extreme Gammon now prefers slotting with the 2-1 roll, and rollouts back up that decision.) These results swept the backgammon world, and soon almost everyone was splitting rather than slotting with opening aces

    While there was nothing wrong with copying the bot’s plays with the opening rolls, players soon began making serious mistakes in other parts of the game. Since these opening rolls were the most obvious examples of slotting, they “learned” that slotting was simply an error except in a few bizarre circumstances. As a result, they started missing strong slotting plays in all sorts of opening and middle-game situations. They’d discarded a key tactical idea on the basis of a tiny set of opening positions

    So when is slotting to be preferred to splitting? In general you’re looking for a combination of factors, some of which argue against splitting, others of which argue in favor of slotting. The next position illustrates these ideas pretty clearly

    Cash game, Black on roll, Black owns the cube

    White – Pips 129 Black – Pips 152 Black to Play 2-1

    Here Black finds himself in a weak position with stacks and stripped points, while facing a strong White board. With the 2-1 roll, Black can try various things. He can play very safe with 13/10, split his back men with 24/21, split and build with 13/11 24/23, or purely build with 13/11 6/5. At first glance, no play leaps out as clearly right. Let’s see if we can whittle down the possibilities

    The problem with the splits is that White’s game has become just a little too powerful to abandon the anchor. White doesn’t actually have a lot of rolls to fill in the gaps in his prime, but he’ll be happy to launch a blitz if he can, and splitting gives him that opportunity. In fact, either split boosts Black’s chances of losing a gammon enormously – from about 20% after the non-split plays to around 28% after the split plays. Such high gammon chances would require the split plays to win at least 4% more games than the non-splits to be contenders. There’s nothing in the position to suggest that could happen, so let’s toss out the splits

    Absent the splits, we’re now down to a choice between the aggressive 13/11 6/5 and the quieter 13/10. The key here is to remember that Black doesn’t want to split anymore. But if splitting is too dangerous, then Black will need to build a front position quickly to stay in the game. There’s no guarantee that 13/10 will give him a position anytime soon. That play, after all, leaves five shots but still doesn’t give Black a lot of good point-making numbers. 13/11 6/5, on the other hand, leaves 13 shots but gives Black a ton of point-makers if it works. Slotting with 6/5 is right by a wide margin, and it’s right whether the cube is centered or Black already owns it

    One footnote to this position: you might reasonably think that duplication plays a role in this decision. When Black slots his 5-point, White needs fours to hit, but 4-2 and 6-4 already make good points in his board. But in fact the play is structurally correct and the duplication is irrelevant. If we move White’s inner-board points to the 4-point and the 2-point, so that fours don’t build any new points, then the slot is still correct, and by almost as wide a margin


    Volunteering a Shot

    Backgammon is basically a race, and losing ground in a race is usually a bad idea, to be avoided if at all possible. Safe, constructive plays are generally good. Constructive plays which leave a few indirect shots aren’t bad, and are often necessary to make progress

    But sometimes there aren’t any safe plays, or even moderately risky plays, that make progress. What if the safe plays all hurt your position in some way? Then you may start looking at plays that leave a direct shot. These plays may be costly if your opponent hits, but they may improve your position if your opponent misses (which he’s generally favored to do.)

    Let’s look at a few criteria for volunteering a direct shot. Since we’ve been talking about high anchor positions in the last few articles, we’ll start with a high anchor problem. Consider Position 1

    White – Pips 133 Black – Pips 111 Black to Play 6-2

    Black leads in the pip count by 22 pips, 111 to 133. He’s already doubled, and now he’s trying to bear his checkers home against White’s high anchor on his 5-point. He’s a favorite to win, but not an enormous favorite; on roll, he’s just about 2-to-1 to win the game

    His 6-2 roll, however, is one of his worst. There’s only one safe play: 8/2 8/6, clearing the 8-point. The strength of the play is solely that it leaves no blots. The downside is pretty obvious. By clearing the 8-point, Black removes a crucial landing spot that he’ll need later when he tries to clear the 11-point and the 13-point

    There’s another play to consider, however. It’s 13/7 4/2. Black leaves a blot on his bar-point which White can hit with a deuce. If White misses, however, Black’s game is better in every respect. He’s kept the 8-point as a landing spot, and next turn he’ll have several rolls, like 6-5 and 4-3, which make the 7-point while clearing one of his troublesome outer points

    13/7 4/2 is what we call a “pure” play. Pure play simply means putting your checkers where they belong, assuming they don’t get hit. Slotting the 7-point certainly qualifies as a pure play, since if White doesn’t roll a deuce, Black will be much better off in all future variations

    Are pure plays right? That depends. Basically, when considering a pure play which volunteers a direct shot, you need to balance the upside (ease of future play) versus the downside (the cost of getting hit). That’s often not an easy choice. Here are some of the issues you should consider:

    Arguments against volunteering a shot:

    Arguments for volunteering a shot:

    Let’s apply these arguments to Position 1 and see what they tell us

    How strong is my opponent’s home board? It’s actually very strong. This is a powerful argument against leaving a shot. White is very close to completing a prime, so a hit will probably win the game for him. At the very least, he’ll be a solid favorite

    How easily do my future rolls play? This is ambiguous. If you clear the 8-point, you still have a spare on the midpoint, which probably represents one free roll. You may be able to shift some of the checkers in your home board, which might represent another roll or two. All in all, you might have two or three rolls to play before you have to break a key point

    Will my opponent have to concede a key point (his 20-point or midpoint) before me? No

    How crucial is the 7-point to winning the game? It’s certainly helpful. Actually, by slotting the 7-point you get to keep the 8-point as a bonus, and the two points together are very useful

    Is my opponent vulnerable after hitting? He’s somewhat vulnerable. He’ll have a couple of blots floating around, which might allow you to reenter and attack, but you’ll still be a big underdog after getting hit

    The biggest consideration here is the strength of White’s home board. Hitting is probably a winner for him. If all the other arguments came out in favor of slotting, then slotting might be correct, but here they’re collectively ambiguous. So play safe with 8/6 8/2 and wait. Leaving a shot is a blunder

    To see when leaving a shot is right, take a look at Position 2

    White – Pips 137 Black – Pips 111 Black to Play 6-2

    Now White’s home board is not impressive at all, and Black doesn’t need to be afraid of being hit, so 13/7 4/2 is the best play. White will hit if he can, but in the resulting positions, White will be a long way from winning


    Duplication

    Duplication is a cute tactical idea which can lead you to make the right play in a wide variety of situations. The basic idea is pretty simple. You find yourself in a vulnerable position. You roll an awkward number. No matter what move you make, your opponent will have some bad things he can do to you next turn. You want to minimize the number of his rolls that can hurt you. What do you do? The answer? Duplication! Try to play your number in such a way that your opponent needs the same number to accomplish his goals everywhere on the board, rather than different numbers in different places. In this way, you reduce his effective numbers to a minimum, giving yourself the best possible chance to survive

    Let’s start with a very simple example

    White – Pips 113 Black – Pips 76 Black to Play 6-1

    Black owns the cube, and leads by 37 pips in the race. That’s the good news. The bad news is that his 6-1 roll forces him to break the 16-point, leaving two blots

    Where should he leave his two outside blots? Duplication gives the answer. If he foolishly plays 16/10 16/15, White can hit with any 5, any 3, and a few more combination numbers (2-1, 1-1, 4-1, and 6-4), a grand total of 27 shots. That means a full 75% of White’s possible throws will hit a blot and almost certainly win the game (or even a gammon)

    But suppose Black alertly plays 16/10/9. Now he’s duplicated White’s fours! White needs a four to hit on the 16-point, and another four to hit on the 9-point. Needing a four in both places means that White’s total shot numbers are greatly reduced. He can hit with any four, plus the combination numbers of 1-1, 2-2, 3-1, and 6-5, for a total of only 17 shots. Less that half of White’s numbers now hit, and that’s a big improvement over the first play. (Of course, Black may leave another shot next turn, but that’s a separate problem. He might also have left a shot next turn after the other play.)

    This was actually a pretty easy example of duplication. Black had to leave a shot in two different places, so he arranged his checkers so that the same number hit in both cases. Other examples of duplication are more subtle. See if you can find the duplication in the next problem

    In this murky position, Black has already doubled but is now trying to rescue his two loose checkers and get them to the safety of his prime. White’s game is choppy, but if he can keep hitting Black’s blots, he may develop solid winning chances

    With the 2-1 roll, Black will obviously enter with the ace and then look around for the best deuce. He has only two choices: 16/14, which leaves White twos to hit, and 7/5, which creates better development but leaves White fours to hit. So two questions arise:

    - What’s the right play?, and
    - What does duplication have to do with this problem?

    White – Pips 139 Black – Pips 117 Black to Play 2-1

    The right play is actually 16/14. This seems strange since at first glance it doesn’t seem to matter whether Black leaves White twos or fours to hit, whereas it’s obvious that 7/5 improves Black’s distribution.

    To see why 16/14 is the best play, we have to look deeper and see what White will actually do with his various rolls

    Suppose Black plays 16/14 and gives White deuces to hit. Now imagine the position without the loose Black checker on the 14-point, and take a look at how White’s deuces would otherwise play

    - 62 would be played 1/9, escaping a checker
    - 52 would be played 19/24 22/24, making the ace-point, putting Black’s rear checker on the bar, and activating the partly-dead checker on the 3-point
    - 42 would be played 17/21 19/21, making the 4-point
    - 32 would be played 1/4 22/24, moving a spare to the edge of the prime and hitting loose
    - 21, the worst roll, can still be played 1/4, reaching the edge of the prime

    What’s important to notice here is that each of White’s rolls containing a deuce is already constructive. If Black leaves the blot on the 14-point, White will elect to hit with a deuce, but his relative gain is not very great since he could have played the deuce effectively in any event

    Now let’s imagine the loose Black checker off the board and see how White would play his fours

    - 64 is awkward; White has a choice between 4/14 and 12/22, both of which are bad
    - 54 would be played 12/17 12/16. White surrenders control of the outfield
    - 43 would be played 1/4 12/16. A reasonable roll
    - 42 makes the 4-point as before. A constructive roll
    - 41 is played 12/17

    As we look at the individual rolls, it’s clear that White’s fours, as a group, are much less effective than his deuces. Leaving White a four to hit turns his fours into good numbers rather than mediocre numbers

    Now we can see why this is a duplication problem. Playing 16/14 duplicates White’s twos, but in a non-obvious way. White’s deuces were all playing effectively, but they were doing different things on different parts of the board; it takes some real effort to see that deuces were the number to be duplicated


    More on Duplication

    In my last post, I introduced the concept of duplication. It’s a powerful idea, one of the crucial tactical ideas in backgammon. Look for your opponent’s numbers that already play well, and remember that plays which expose blots to those very same numbers elsewhere on the board become stronger than they at first appear. Here’s another good example

    White – Pips 128 Black – Pips 155 Black to Play 6-1

    Black’s not crushed yet, but his game is starting to deteriorate. His back men haven’t moved yet, and White has a ton of attackers in play in case Black decides to split. Up front, Black’s made his bar-point but doesn’t have a lot of numbers to extend his little prime. Meanwhile, White’s checkers are poised to escape, and he’s got nice diversification, with small numbers building his 5-point, and large numbers hopping into Black’s outfield

    At first, 61 doesn’t look like a particularly good shot for Black. Splitting in back with 24/23 13/7 isn’t inviting. White’s few remaining awkward numbers, like 66, 55, and 44, now become crushers, while everything else continues to play well. Playing two men down with 13/7 13/12 looks constructive, but contains a subtle flaw. It’s not the immediate danger – only 63 and 64 hit for White. But if White hops into the outfield next turn without hitting – 61, 62, 51, and 53, for instance – Black has to deal with this blot rather than build his board. The longer Black goes without building his board, the more danger he faces. The simple 13/7 8/7 eliminates the outfield danger, at the cost of leaving even fewer point-making numbers

    The solution is hard to find: it’s 13/7 6/5! Slotting into a double shot is a rare play. The circumstances have to be just right, and here they are. First, there’s some duplication involved. The small number combinations now give White the choice of hitting or making the 5-point. He will choose to hit, but it’s only clear with the 32 roll. With 21 and 31, hitting gets the nod only because of the extra gammon chances generated by a third man back. (At double match point, White should build his 5-prime with these two rolls.) As for the other hitting numbers, Black is worse off for having slotted, but not by much. White still only has a two-point board, and Black’s checkers are suddenly well-developed and in play. And of course if White misses altogether, Black is delighted. After some rolls like 55 and 44, Black is already the favorite, while mediocre rolls like 54 and 41 leave the game even money!

    One reason that backgammon is a tough game is because a long series of completely routine and easy moves can be punctuated by the need to make a sudden, crucial and decisive play. Get it right, and the game can move quickly in your direction. Get it wrong, and the game will slip away from you


    High Anchor Holding Games

    Next to races, the most common type of position in backgammon is what we call the holding game. Holding games occur when one side escapes his back checkers to the safety of the midpoint or beyond, but the other side (the “defender”) does not. Instead, the defender manages to anchor his two back checkers somewhere in his opponent’s home board

    Take a look at this pretty typical position

    White – Pips 136 Black – Pips 116 Black on roll. Cube action?

    An anchor on the 4-point, 5-point, or bar-point (7-point) is considered a high anchor. An anchor on the 2-point or the 1-point is a low anchor. The 3-point constitutes a separate case, with characteristics of both high and low anchor games

    The side who has escaped his back checkers (Black in Position 1) is almost always the favorite in a high anchor holding game. Here Black has a 20-pip lead in the pip count (116 to 136), and that’s enough to make him almost a 3-to-1 favorite in the game. If he doubles (which he should), White has a clear take. Then Black will try to bring his checkers home without being hit. Sometimes he’ll succeed, occasionally he won’t. Most of White’s wins come when Black leaves a shot somewhere (often when trying to clear the midpoint or the 8-point) and White hits. Very occasionally, White will roll a couple of big sets of doubles and actually win the race. But mostly, White’s hoping to get a shot and hit it

    Clear a Point, or Wait and Build?

    Since clearing points is very important when bearing home against an anchor, many players tend to make point-clearing plays automatically. But in backgammon, no play is ever really automatic. Let’s look at some of the issues involved. Consider Position 2, for example

    White – Pips 114 Black – Pips 93 Black to Play 5-3

    Black is on roll and leads in the race by 21 pips, 93 to 114. He’s already doubled. He has one outside point, the 11-point, left to clear. One way for Black to lose this game is to eventually leave a shot on the 11-point, and then get hit by a subsequent 5-2 or 6-1 from White. With his roll of 5-3, he can eliminate that danger by simply clearing the 11-point now, with 11/6 and 11/8. It’s clearly the right play, leaving Black an enormous favorite. Now he’s only concerned with clearing his remaining outside points successfully

    White – Pips 80 Black – Pips 93 Black to Play 5-3

    Although Black’s pip count is the same (97 pips) as in the previous position, White’s has changed dramatically. Instead of trailing by 21 pips, White now leads by 13 pips! As a result, Black’s strategy has to change completely

    The danger of Black’s getting hit on the 11-point at some later time is now relatively inconsequential. White’s real threat is much more direct: he simply wants to win the race. At some point (perhaps next roll) White will run off the anchor with a 6 or a 5. Black will then need to attack the checker that remains and attempt to fill in his 3-point and 4-point, completing a prime. The best plan is to fill in the 3-point now, then attack the 4-point as soon as White leaves. This plan has more risk than Black would like, since a single 4 from the bar may win for White, but it’s all Black has. He should just play 8/3 6/3 and await developments

    The moral here is pretty simple. When playing against a high anchor, knowing the pip count is crucial. With a big lead (which is usually the case) look to bring your checkers home with minimum risk. If the race is close or you are trailing (as in Problem 3), White may have to leave his anchor before you can come home. In that case, being well-placed to attack is crucial


    Holding Game Doubles

    Last article, we talked about some of the tricky play problems that arise in high anchor positions. This time, we’ll start to look at doubling strategy in these common situations. (Remember, a high anchor game is one where one player has escaped all his back checkers, while his opponent has managed to secure an anchor on the 4-point or 5-point.)

    Take a look at Position 1

    White – Pips 131 Black – Pips 119 Black on roll. Cube action?

    In Position 1, Black has escaped his back checkers and White is holding the 5-point anchor. Black’s trying to bring his checkers on the midpoint home without leaving a shot. White hopes to hit any blot that Black is forced to leave, or, alternatively, win the race by outrolling Black later on. Black has the advantage, but White is not without resources. Should Black double?

    Before we answer that question, let’s look at the most important feature of the position: the pip count

    Black’s pip count is 119. (To calculate a pip count, just multiply the number of checkers on a point by the value of the point, and calculate the sum for all your points. Four checkers on the midpoint, for example, contribute 4 * 13 = 52 to your pip count.) White’s pip count is 131, so Black has a 12-pip lead, which represents about 10% of his pip count of 119

    If this were a straight race, where both sides had disengaged and there was no possibility of hitting a shot, a 10% lead in the race would be enough to double. Straight races have been extensively analyzed by computer since the 1970s, and an 8% lead is usually enough to offer a good initial double. (The trailer need to be down no more than 12% to have a take.)

    Here, however, White has more ways to win than just throwing bigger numbers in the race. There’s a very real chance that he could hit a shot, and that possibility adds a few percent to his winning chances. In addition, he usually has a better bearoff position than Black when the race actually starts, since he has the luxury of filling his board smoothly, while Black may be left with a gap on his 5-point

    The net result of all these factors is that Black’s winning chances are actually under 70%, and he doesn’t quite have a double yet

    Clearly, Black needs more than just a minimal racing lead to double in these high anchor holding positions. Just how big a lead does he need? Take a look at Position 2

    White – Pips 139 Black – Pips 119 Black on roll. Cube action?

    The pip count is now 119 for Black and 139 for White. Black’s lead is now 20 pips, about 16% of his pip count. In a straight race, that lead would mean a double for Black and a clear pass for White. Here, Black just has enough to double. White, however, still has an clear take. His combination of racing chances and hitting chances enable him to win slightly more than 25% of the time. As an added bonus, he’ll almost never be gammoned from this position, so as long as his winning chances stay above 25%, he can take

    How big a lead does Black need to have before White will have to pass? Let’s move on to Position 3

    White – Pips 139 Black – Pips 99 Black on roll. Cube action?

    Position 3 is similar to Position 2, but I’ve moved two of Black’s checkers from the 13-point to the 3-point, a distance of 10 pips each. The pip count is now 99 for Black and 139 for White, a lead of 40 pips. This must be a pass for White, right?

    Wrong! It’s still a take. In fact, Black’s winning chances are only about 1% better in Position 3 than Position 2. How can this be??

    What’s happening is that Black is gaining one asset (racing chances) but losing another asset (timing) simultaneously. If we compare Position 3 to Position 2, Black is now much less likely to lose a race, but much more likely to get hit as he tries to clear the 13-point. The two assets (racing chances and timing) are moving in opposite directions at about the same rate. Black’s double is solid in both positions, but White has a clear take in both cases, although for different reasons

    In almost all normal 5-point holding games like the ones shown here, White has a pretty easy take. Black needs about a 15% lead in the pip count to have a good double. Remember those rules, and you won’t make many cube errors in these common positions


    Position or Race?

    In this position, with Black on roll, who is a favorite?

    White – Pips 161 Black – Pips 140 Black on roll. Who’s a favorite?

    This is a good problem for two reasons

    (1) Many players look at this position and think the answer is almost too obvious to even require a discussion. At the same time, they often can’t quite agree on what the obvious answer is

    (2) It’s a position which illustrates in stark terms the relationship between a racing lead and a positional edge, and as such it has some real historical significance

    Back in the period 1977-1982, the elite backgammon world was ruled by what was then known as the ‘pure style’. The Bible of the pure style was Barclay Cooke’s Paradoxes and Probabilities, a collection of 168 checker and cube problems, which was published in 1978 and which became wildly popular among the tournament set. The essence of the pure style was that backgammon was a game of key points and primes. The race had some relevance, but not nearly as much as had been thought by the simpler players of an earlier generation. Playing for the race too early caused players to sacrifice positional assets, to their later detriment

    The theory of the pure style led naturally to a basic game plan: Grab both 5-points, slotting if you needed to, control all four quadrants, build a prime, and finally hit and trap a checker, with an easy win. If your blots got hit, just fall into a well-timed back game and turn things around later. It was a seductive plan, leading to beautiful-looking positions with powerful primes, high anchors, all checkers working, and a complete absence of stacks

    The pure style was very attractive to the new wave of former chess players who were moving into the backgammon world in large numbers. It offered a view of backgammon that made the game similar to chess: strong points, control of the center, good development of the pieces, all leading to victory in the end

    Most successful tournament players tried to play some version of this style, and the style seemed to work. The players who were winning big tournaments were (with a couple of exceptions) playing just this way. I tried to model my own game on this approach, and by 1981 I was having some success. I’d won a couple of big tournaments, as well as many smaller ones, and I was doing well in chouettes around Boston. Life was good

    Then I met Alex

    Alex was probably in his mid-70s when I met him. His location and date of birth were a little hazy, but according to his stories he’d bounced around the world a lot, spending most of his time in the Middle East and Eastern Europe. He’d played backgammon for a long time in a lot of different places. He never played for high stakes ($5 a point was his limit) and he didn’t like tournaments because they took too long. He liked to hang around the Cavendish Club in Boston and watch the $20 chouette (the big game in those days) and occasionally play heads-up for $2, $3, or $5 a point

    On Sundays the big game was a bit of a hit-or-miss affair, so sometimes I’d find myself at the club with nothing to do. Alex and I would get to chatting about his travels, and we started playing heads-up to pass the time until a chouette would start. I figured Alex played an old-fashioned game and would be pretty easy pickings for a veteran like myself, schooled in all the latest tricks

    I was right about Alex’s style. It was old-fashioned. He split his back men with most opening plays, and never ever slotted. His goal was to get into a race or a holding game as quickly as possible. He handled blitzes reasonably well, and never seemed to get into a back game. His cube action seemed a little weak – he was slow to double in positions where he had strong threats, and I thought he was too quick to drop some interesting positions

    I had faced opponents in tournaments who just tried to play a racing game, but they were beginners or intermediates who made lots and lots of obvious mistakes and were easy to beat. Alex was different; he wasn’t easy to beat. As the days passed and the count of games climbed to 200 and then 300 and then 400, I realized to my shock that I was just breaking even. As far as I could tell, I was supposed to be winning big. My cube action was clearly better, I saw Alex making technical errors in positions that I had rolled out and understood well, and to top it all he was playing this passive style that should have been cannon fodder for my state-of-the-art hyper-aggression. Had I just hit a really unlucky streak?

    I doggedly pressed on over the next few weeks, and the game count mounted to 500 and 600 and 700. My luck finally changed. It got worse. Alex was now up 30 points or so in our long session. At last he quit, as he was going on a long trip to see friends and relatives. I paid up and now had plenty of time to ponder just what had happened

    I was tempted to shrug and conclude that our sessions had just been an aberration, in which I had an extended run of bad luck against a much weaker player. But that just didn’t feel right. I really didn’t believe that I had been all that terribly unlucky. As I thought about the session, I realized that the mix of our two styles had led to a lot of holding games, where I had some nice holding position like the 5-point plus an extra man back, while Alex had escaped his back checkers and led in the race, but with little or no structure. According to the theory of the time, I was supposed to be better in those positions. But now I started to wonder about that

    As an experiment, I created the position at the start of this post, which is an extreme case of the sort of situation I was remembering. Black has a racing lead but absolutely no structure, and White is beautifully placed with both 5-points and control of all quadrants. I thought White had to be a solid favorite here. If I had taken this position to a tournament and shown it to a bunch of good players, I was certain they would concur unanimously. But I got a lot of these positions against Alex, and didn’t seem to win as often as I thought I should

    I decided to roll the position out 300 times, with no cube, and see what happened. I also decided to play Black’s position just as Alex had played it, never leaving a shot unless I had to. (Conventional wisdom of the day was that Black should slot points quickly, before White’s board got too strong.) The rollout took a few days (this was 1981, remember – no bots) and when it was finished Black had won 58% cubeless

    I was startled, but also excited. I understood why I had been losing to Alex. Whatever edge I had in complex positions and cube handling had been overcome by the number of times I had taken too many chances in the opening and been swept into playable but inferior holding games. Clearly, my early game play needed some serious adjustment, and I had some hard work ahead. On the bright side, I’d stumbled on an idea that would certainly improve my game a lot, and I couldn’t wait to refine it into a real weapon. Now suppose you were Black in this position. How would you play these rolls?

    (a) 5-2
    (b) 4-1
    (c) 2-1
    (d) 6-5

    Solutions:

    First note that Black is a favorite. White might get a shot and then hit it, but Black has a lot of safe rolls, and a lot of rolls that leave only a single shot. Note also that just being hit isn’t the end of the game. A cubeless Extreme Gammon rollout puts Black at 56, close to the 58 from my manual rollout many years ago

    (a and b) The right idea for Black is not to leave a shot unless he has to. With 5-2, he should just play squat with 13/6, while 4-1 should be played 13/8 rather than hitting on the 1-point. Alex understood that Black had time to wait, while most players of that era would have tried to clarify the position quickly with 13/8 6/4 or 6/1*

    (c) If you have to leave a shot, the outfield is usually the right place, since White will have to make a concession to hit by breaking his anchor. With 2-1, play 13/10

    (d) Occasionally a roll arises which is potentially so strong that it’s right to play big. With 6-5, the right play (but only by a little bit) is 13/7 6/1. White hits with 20 shots, but Black becomes a very solid favorite when White misses because of the slotted bar-point. Contrast that with the 4-1 play, where Black still has a ton of work to do if he plays 6/1 and White misses