Survey says ... 24/23, 13/11    60.1% 13/11, 6/5    35.6% 13/10    2.2% 24/21    1.5%

This is one of the most interesting opening rolls. Players have argued for centuries over the best way to play it. The two popular plays are:

• 24/23, 13/11 (splitting your back checkers and bringing a builder down).
• 13/11, 6/5 (slotting your five-point and bringing a builder down).

24/23, 13/11

The splitting play aims at making improvements on both sides of the board. Splitting your back checkers increases your chances of securing an advanced anchor and improves your coverage of opponent's outer board. Now it's more dangerous for him to bring builders down from his mid-point or slot his five-point.

The beginning of the game is the safest time to split your runners. Opponent is unlikely to hit you so deep in his home board before he has built other home-board points. Waiting too long to split can mean getting stuck back on the opponent's one-point with no easy way to get out.

Obolensky and James (1969):  You are immediately putting into effect the object of the game, that is, running and blocking.

Paul Magriel (1976):  Splitting the back checkers facilitates their escape at small risk since your opponent gains little by hitting on a point deep in his inner board.

Robin Clay (1977):  The checker on opponent's two-point makes it more difficult for the opponent to drop a blot onto his outer board.

13/11, 6/5

The slotting play concentrates all your efforts on offence. By slotting your five-point you increase your chances of making this important point next turn. Many beginners are reluctant to leave a blot within direct range of being hit. And so they should be! If your blot is hit, it will be sent back 20 spaces and you will be far behind in the race. Can the advantages of the slot really be worth this risk?

It turns out the answer is yes. The game is early and if you get hit now, there is still plenty of time to regroup and find another way to win. But when you're not hit, you can cover the blot on your five-point by rolling any 6, 3, or 1, plus double 4's—a total of 28 ways out of 36. Making the five-point is a major improvement in your position. (See the discussion of the 3-1 opener for an explanation of why.)

And there is another reason to slot here. Look at the stack of checkers on your six-point. Those checkers want to do something. 1 is the perfect number for taking a checker off your overcrowded six-point and setting it to work. As the popular backgammon aphorism says: Put your checkers where they belong. The extra checkers on your six-point belong on your five-point.

Paul Magriel (1976):  This variant leads to dangerous, exciting, but also more difficult games. The player just learning the game is advised to gain some experience before using this play.

Robin Clay (1977):  Leaving a blot on your five-point may look very exposed, but in actual fact, of the 36 permutations of the dice, only 15 of them will enable opponent to hit your five-point.

Bill Robertie (2000):  The five-point is the most important point in the early stage, and this play lets you slot it while distributing your checkers off the big stacks. Aggressive and strong.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
13/11, 6/5	+ .5058, .1415, .0059   − .4942, .1418, .0084	+.0088				(.0074)
24/23, 13/11	+ .4996, .1369, .0056   − .5004, .1319, .0053	+.0045	(.0043)	(.0124)	(.0216)
24/21	+ .4918, .1254, .0056   − .5082, .1315, .0057	−.0226	(.0314)	(.0280)	(.0602)	(.0148)
13/10	+ .4897, .1378, .0059   − .5103, .1419, .0068	−.0256	(.0344)	(.0322)	(.0396)	(.0398)
24/23, 24/22	+ .4868, .1213, .0051   − .5132, .1329, .0053	−.0382	(.0470)	(.0380)	(.0784)	(.0276)

Slotting comes out on top in the rollout. This play is now favored by most experts. In match play at gammon-save, the safer splitting play is best.

Survey says ... 8/5, 6/5    99.9%

8/5, 6/5

Beginning players are often surprised to learn that 3 and 1 are the best opening numbers you can roll. After all, with a grand total of four pips, this is a pretty puny roll. Sure, you get to make a point, but there are other rolls that make good points too, like 4-2 (the four-point) and 6-1 (the bar-point). What makes 3-1 so great?

The answer is that the five-point is a tremendously useful point to own. Here's why:

1. The five-point is a home-board point. Each additional home-board point you own gives your opponent fewer ways to enter when he gets hit. That means he must play conservatively while you get to play aggressively.

2. Of all the empty points in your home board, the five-point is the best one to close first because you can use it as a landing spot for more checkers. A spare checker on your five-point can be used to attack enemy blots or build more home-board points.

3. The five-point is a good blocking point. The easiest real estate on which to build a prime is: from your ten-point down to your five-point, from your nine-point to your four-point, or from your eight-point to your three-point. All of these include your five-point.

4. Owning the five-point prevents your opponent from anchoring there. If he acquires your five-point, it is almost impossible for you to prime him.

5. The five-point is enduring. Once you've made this point, you will continue to hold it and it will continue to have value for the rest of the game.

Paul Magriel (1976):  Your five-point is the most important point on your side of the board.

Bill Robertie (2002):  With this roll you accomplish two things: you make a blocking point, further hemming in opponent's two checkers on your one-point, and you make an inner-board point.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
8/5, 6/5	+ .5546, .1708, .0071   − .4454, .1150, .0051	+.1670

With one roll, your equity has gone from 0 to +.1670. That's a huge gain. For comparison, making the four-point with an opening 4-2 is only +.1234, and making the bar-point with an opening 6-1 is only +.1035. The 3-1 opener is by far your best roll.

Survey says ... 24/21, 13/11    51.8% 13/11, 13/10    40.6% 24/22, 13/10    5.6%

There are three reasonable ways to play this roll:

• 24/21, 13/11 (splitting using the 3 and bringing down a builder using the 2).
• 24/22, 13/10 (splitting using the 2 and bringing down a builder using the 3).
• 13/11, 13/10 (bringing down two builders).

Slotting the five-point, 8/5, is not a good idea with this roll because you are using the wrong checker. It's your overloaded six-point that you want to use for slotting, not your eight-point.

Phillip Martyn (1976):  You might be tempted to use the 3 to drop a man on your five-point. But it is less satisfactory to drop a man on your five-point from the eight-point than from the six-point. The reason is that you are leaving only two men on your eight-point, so if you want to use a man from your eight-point later, either to make your bar-point or your five-point, you have to leave a blot on the eight-point.

24/21, 13/11

This is the more popular of the two split-and-build plays. You use your 2 to bring a builder down from the mid-point where it can be used next turn to help make a blocking point. This is a nice way to play the 2. The blot on eleven is pretty safe from being hit and its presence helps cover your outer board in case the opponent tries to run with one his back checkers.

Advancing to the 21-point with your 3 has advantages and disadvantages. If you are not hit you have a chance to make an advanced anchor, a real advantage early in the game. The downside is that opponent's four-point is also a point he wants to make and he will be willing to fight to get it.

Paul Magriel (1976):  It is wise to split early—before your position becomes more dangerous. By moving a back man up, you not only try to acquire a valuable point, you also prevent opponent from bringing builders down to his outer board and developing naturally. This play is especially recommended if you are playing someone who is afraid to hit immediately in his inner board.

24/22, 13/10

The other split-and-build play is much less popular. In fact, it wasn't too long ago that you would never see players make this play. Everything about it looks bad. First, the resulting position is somewhat inflexible. Notice that your runners are two pips apart; the stacks on your eight and six-point are also two pips apart. That means many of the same rolls that make points with your back checkers also make points using your two front stacks. In other words, your good rolls are duplicated. All else being equal, it is better to not duplicate your good rolls.

The other reason players don't like splitting to the 22-point is the propect of the opponent rolling double 5's. This roll is devastating because you end up with two blots on the bar and your opponent has an immediate three-point board.

Today we know that this play isn't as bad as we once thought. Double 5's is only a 1/36 chance and, your opponent is less willing to hit you on his three-point than on his four-point. Still, if split-and-build is the way you want to go, the first play, 24/21, 13/11, seems to be safer and more constructive.

13/11, 13/10

This play concentrates on offence. Your plan is to build a blockade before opponent can free his back checkers. With two builders in your outer table, you're almost certain to make a good blocking point next turn.

But there is some risk. Opponent will hit you if he rolls 6-4, 6-3, 5-4, and 3-3—seven ways out of 36. Not a huge risk, but it's a factor to be weighed against the advantages of this play.

Obolensky and James (1969):  You are getting two men out as builders to block your opponent from getting out of his home board.

Jacoby and Crawford (1970):  Your blots are exposed to only a nine or ten, and you are in a fine position to make points if you are not hit.

Bruce Becker (1974):  Should neither blot be hit, you then can make one good point or another with any throw except a 5-4.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
13/11, 13/10	+ .4977, .1493, .0065   − .5023, .1387, .0072	+.0053		(.0080)		(.0172)
24/21, 13/11	+ .5017, .1355, .0064   − .4983, .1341, .0060	+.0052	(.0001)		(.0196)
24/22, 13/10	+ .4985, .1366, .0059   − .5015, .1345, .0056	−.0006	(.0059)	(.0064)	(.0238)	(.0072)
13/10, 6/4	+ .4918, .1369, .0061   − .5082, .1455, .0090	−.0279	(.0332)	(.0198)	(.0366)	(.0426)
24/22, 24/21	+ .4924, .1223, .0054   − .5076, .1350, .0055	−.0280	(.0333)	(.0186)	(.0646)	(.0204)
13/8	+ .4887, .1344, .0067   − .5113, .1469, .0064	−.0348	(.0401)	(.0260)	(.0478)	(.0516)

The result couldn't be closer in this cubeless rollout; a cubeful rollout here shows the splitting play, 24/21, 13/11, to be a very slight favorite. The other split-and-build play, while in third place, is not far behind—a surprising result. At gammon-go, it is worthwhile going all out for the blockade right from play one.

Survey says ... 24/23, 13/9    74.5% 13/9, 6/5    20.3% 13/8    2.2% 24/23, 24/20    2.0%

There are two reasonable ways to play this roll:

• 24/23, 13/9 (splitting the back checkers and bringing a builder down from the mid-point).
• 13/9, 6/5 (bringing a builder down and slotting the five-point).

24/23, 13/9

This is the most popular way of playing an opening 4-1. The builder on your nine-point provides many point-making opportunities up front. This is nicely balanced by having your runners split at the back. Splitting your runners increases your chances of making an advanced anchor next turn or hitting your opponent if he puts a blot anywhere on his side of the board.

Reese and Brinig (1975):  The move 24/23 does not look dynamic, but it contains some hidden power. First, it becomes more dangerous for your opponent to leave a blot anywhere in his front board. Second, if you throw 4-3 or 3-2, you will be able to make the opponent's five-point or four-point on your next turn.

Walter Trice (2004):  You have diversified the distances between your builders. The builders are one, two, and three pips apart: thus, rolls where the numbers on the dice differ by one, two, or three can make points.

Marty Storer (2005):  The builder on the nine-point provides many point-making chances at much smaller risk than 13/9, 6/5, while splitting makes progress on the opponent's side of the board too.

13/9, 6/5

This play was more popular in the past. The idea of slotting is to take risks early in the game before your opponent has had a chance to close any of the points in his home board. The question is, are the risks worth the rewards?

There are three opening rolls for which slotting the five-point is a reasonable possibility: 2-1, 4-1, and 5-1. Compared with an opening 2-1, slotting with 4-1 is more dangerous because there are more ways for opponent to hit your blot on the nine-point than a blot on eleven. And once you move 13/9 with your 4, the checker on your nine-point already gives you many ways to make a point in your home board. It is not quite so important to take more risk by slotting the five.

These two reasons make slotting with an opening 4-1 less attractive than slotting with a 2-1, and less attractive than the other way of playing your 1, namely, splitting your runners.

Jacoby and Crawford (1970):  This is wonderful when it works. The trouble is that your blot on the five-point is exposed to any 4, plus 3-1, double 2, and double 1, while your other blot is exposed to 6-2, 5-3, double 4, and double 2.

Phillip Martyn (1976):  If you drop a man from the six-point to your five-point, there is an increased risk that you will have a man hit there, and also a danger of having both hit. As you know, it is a disaster to have two men on a bar, particularly against a stronger player.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
24/23, 13/9	+ .4984, .1405, .0058   − .5016, .1348, .0059	+.0024		(.0032)	(.0050)
13/9, 6/5	+ .5000, .1414, .0062   − .5000, .1448, .0091	−.0063	(.0087)			(.0168)
24/23, 24/20	+ .4886, .1223, .0052   − .5114, .1320, .0045	−.0318	(.0342)	(.0228)	(.0610)	(.0140)
13/8	+ .4887, .1344, .0067   − .5113, .1469, .0064	−.0348	(.0372)	(.0226)	(.0366)	(.0436)
24/20, 6/5	+ .4879, .1270, .0059   − .5121, .1429, .0064	−.0406	(.0430)	(.0242)	(.0530)	(.0372)

It all comes down to gammons. The slotting play loses one percent more gammons than the splitting play, and that's the difference between the plays. But as bots get stronger, the difference between the plays has been shrinking. There may come a day where slotting wins out in the best computer rollouts.

In match scores where losing a gammon doesn't matter, the aggressive slot wins the most games. But when playing for money, or in a match at gammon-save, the safer splitting play is your best bet.

Survey says ... 8/4, 6/4    99.8%

8/4, 6/4

This is the second best opening roll. The advantages of this roll are similar to the advantages of an opening 3-1.

• The four-point is a home-board point. Each additional home-board point you own gives your opponent fewer ways to enter when he gets hit. That means he must play conservatively while you get to play aggressively.

• While not as strong as the five-point, the four-point is still a good point to own. It is place where your checkers can land safely and a useful launching pad for attacking enemy blots or building points lower in your home board.

• The four-point is good to own if you want to make a prime. Potential primes that include the four-point are: (1) from your nine-point down to your four-point and (2) from your eight-point down to your three-point.

There are two big advantages to 4-2 over 6-1. The first is that the four-point is a home-board point. You have an extra advantage when you own more home-board points than your opponent. It's like carrying a big stick around with you. Your opponent has to be more careful about leaving blots that you can hit, while you are more free to take risks to improve your position.

The other advantage of 4-2 is that it moves a checker off your overstacked six-point. It is very difficult to get these extra checkers into play early in the game, and 4-2 (like 3-1) is an excellent roll to do it.

Obolensky and James (1969):  This is a good roll. The player has made a point on his home board and has created an additional block against his opponent.

Bill Robertie (2002):  Opening 4-2 is not quite as good as 3-1 for this reason: after you make the four-point, opponent still has a chance to sneak behind you and bring his back men up to the five-point. If he can do that, the value of the four-point will be somewhat negated.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
8/4, 6/4	+ .5380, .1697, .0074   − .4620, .1242, .0055	+.1234

The rollout shows that a 4-2 opener is a powerful roll. It puts you well ahead in wins, and also well ahead in gammons.

Survey says ... 24/20, 13/10    38.8% 13/10, 13/9    32.3% 24/21, 13/9    25.0% 24/21, 24/20    3.1%

There are several ways to play this roll and it's hard to sort through them all. Before looking at rolls, let's look at the numbers individually.

With the 4, there are two reasonable choices:

• You can split your back checkers, 24/20. The fastest way to make a point is slot it, and the opponent's five-point is the best point to own in his home-board. Having a checker on opponent's five also provides nice coverage of his outer table, making it more difficult for him to bring builders down from his mid-point. The downside of this move is that the blot on opponent's five-point is vulerable to being attacked. He will not hesitate to knock you off this point if he can.

• You can bring a builder down from your mid-point, 13/9. The nine-point is a great location for a builder because it works so well with your checkers on the eight-point and six-point to make new points. And the nine-point is a good blocking point, so if you roll another 4 next turn you can simply cover this blot. The downside of 13/9 is that your blot on the nine-point might be hit (6 ways out of 36), sending that checker back 16 spaces.

• You can split your back checkers, 24/21. The upside of splitting with the 3 instead of the 4 is that a blot on the 21-point is not quite a vulnerable to being hit. If opponent hits you and ends up making his four-point, you still have a chance of anchoring on his five-point. The downside of playing your 3 to the 21-point is that it is not as good an anchor as the 20-point and it provides less coverage of opponent's outer table.

• You can bring a builder down from your mid-point, 13/10. The ten-point is not as easy for opponent to hit as the nine-point (only 4 ways out of 36—he wouldn't hit with 3-3), so this blot is a little safer. But it doesn't work as well in combination with the eight-point and six-point to create new points in your home board.

Putting these numbers together in all their combinations gives four possible plays:

• 24/21, 24/20 (moving both of your back checkers forward together).
• 13/10, 13/9 (bringing two checkers down from the mid-point).
• 24/20, 13/10 (splitting using the 4 and bringing down a builder using the 3).
• 24/21, 13/9 (splitting using the 3 and bringing down a builder using the 4).

When you move both of your back checkers off the opponent's one-point at the same time it is sometimes called a double split. The play in itself is not bad; it is just that using both numbers for essentially the same purpose is rather wasteful. In general, it is better to try to do two good things in different parts of the board with each of your numbers. This is the only play of the four combinations generally recognized as not being the best way to play an opening 4-3.

13/10, 13/9

This play goes all out to try to build a quick blockade before the opponent can escape his runners. You might think the play suffers from the same problem as the double-split above, that it is wasteful using both numbers for the same purpose. The reason that 13/10, 13/9 works well is that both blots have two uses. (1) They work as builders to make new points further forward. (2) They slot good points that you can turn into blocks on your next turn.

Elizabeth Clark Boyden (1930):  The position now is favorable to make a point on the next throw, and there is no throw which will permit the opponent to take up both of these men.

Jacoby and Crawford (1970):  If neither blot is hit they are in excellent position to help you build your bar-point, five-point, or four-point; or you may be able to cover one, giving you possession of your nine or ten-point.

24/20, 13/10

This is one of two balanced approaches to playing this roll. You split your back checkers, hoping to make an advanced anchor next turn, while at the same time bringing a builder down from your mid-point as the first step in improving your blockade. This play gives preference to slotting the best anchor at the expense of not having quite as good a builder.

Phillip Martyn (1976):  You are setting your opponent the problem of what to do about your man on his five-point and the man on the 10-point is a good builder.

Robin Clay (1977):  An opening move of this sort makes it difficult for your opponent to play his normal tactics. Firstly, by placing a man on oppenent's five-point you are threatening to cover it on your next turn, and to gain control of a point vital to him. Secondly, the man on opponent's five-point makes it difficult for him to drop a blot onto his outer board. Thirdly, your blot on the 10-point equally makes it dangerous for opponent to move a blot up to your four-point, five-point, seven-point, or nine-point.

Bill Robertie (1984):  If you're going to risk splitting at all, it makes sense to split to the most valuable point possible.

24/21, 13/9

This is the other balanced approach, splitting and building. Here you're giving preference to the best point for the builder at the expense of an anchoring point that's not quite as good. Surprising, this play was never popular before the mid 1990's. The thinking of experts at the time is explained by Bill Robertie above. Why not split to the point you most want to make?

But splitting to the opponent's four-point has its advantages too. It is not as easy for your opponent to attack you on his four-point. If he hits your blot, you now have two good rolls to enter with—you can roll a 4 and hit back, or you can roll a 5 and start opponent's five-point. If you enter with a 5, your opponent has a slight problem. He wants to attack your blot on his five-point but he also needs to cover the blot on his four-point.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
13/10, 13/9	+ .4984, .1529, .0075   − .5016, .1374, .0073	+.0125		(.0024)		(.0118)
24/21, 13/9	+ .4996, .1404, .0066   − .5004, .1342, .0060	+.0060	(.0065)		(.0226)	(.0030)
24/20, 13/10	+ .4989, .1355, .0061   − .5011, .1330, .0056	+.0008	(.0117)	(.0014)	(.0338)	(.0020)
24/21, 24/20	+ .4980, .1223, .0056   − .5020, .1311, .0048	−.0120	(.0245)	(.0032)	(.0620)

The rollout is far from definitive. All four plays are close and any one of them could conceivably be correct in match play depending on the score. It seems that bringing down two builders is the best play for money because of the extra gammons you win.

Survey says ... 24/23, 13/8    72.8% 13/8, 6/5    23.8% 24/18    2.8%

The first choice with this roll is deciding how to play the 1. You can slot your five-point, in which case there is only one decent way of playing the 5. Or you can split your back checkers 24/23, in which case you have two reasonable 5's: You can continue running with your back checker, or you can bring a checker down from your mid-point to your eight-point. Here's your choice:

• 13/8, 6/5 (slotting the five-point and bringing a checker down off your mid-point).
• 24/18 (running with your back checker).
• 24/23, 13/8 (splitting your back checkers and bringing a checker down off your mid-point

13/8, 6/5

Slotting your five-point has a couple desirable features: (1) You hope your slot is not hit and that you can cover it next roll thereby making a very valuable point. (2) You unstack your six-point.

Of course, slotting the five-point is risky. If you are hit, your blot will be sent back 20 spaces and you will now be well behind in the race. The only saving grace is that your opponent has not yet built up his home board yet, so if you're hit you should be able to enter easily and still have time to build and advanced anchor. Getting hit, while not pleasant, would not be devastating.

Walter Gibson (1974):  It has long been considered good strategy to put [your checker] where it will do the most good if the gamble succeeds.

Cooke and Bradshaw (1974):  It is best to gamble in order to secure the important five-point. You should not split the two men on your 24-point; the risks are serious and the rewards slight.

Paul Magriel (1976):  This variant leads to dangerous, exciting, but also more difficult games. It is neither necessarily better nor worse than the splitting play.

Bill Robertie (1998):  Since the five doesn't create a new builder, I have a strong incentive to slot the five-point with the 1, to get my offense going.

Kit Woolsey (2002):  Slotting with 5-1 is less attractive than slotting with 2-1. With 2-1, the checker on the 11-point is six away from the five-point, so it is in position to cover if the shot is missed or to hit back and continue the fight for the five-point if the shot is hit. And 2-1 is only three pips, so the cost of having a checker sent back is slightly less than it would be on a 5-1 because you aren't doing well in the race anyway.

24/18

This play has the advantage of slotting a potential advanced anchor and providing good coverage of the opponent's outfield. But this advantage comes at a fairly significant price. Your opponent will hit with any 1 or 6. Any time you are hit early in the game, you lose some ground—not so much in the race, but rather in developing your position. After a hit, you need to use half your roll to enter your checker. That portion of your roll cannot be used elsewhere to make a point or move another checker. Whereas, your opponent, when it hits you, is slotting a point he wants to make. If you don't hit back, he will be well on his way to making his bar-point or using that checker as a builder to make a point in his home board.

Bill Robertie (1982):  24/18 is a perfectly acceptable alternative to the two more usual plays. You make an immediate attempt to secure the opposing bar-point, and also hope to profit from an exchange of hits.

Marty Storer (2005):  24/18 forgoes the distributional improvement of 13/8, and takes a bigger risk of being attacked. Return hits are nice, but they don't come frequently enough for me.

24/23, 13/8

If you decide to use your 1 to advance one of your back checkers, it is safer to leave it on your 23-point rather than move up to 18. Having your runners split still gives good coverage of opponent's outer board but doesn't leave yourself open to attack.

It might seem that a fourth checker on the eight-point is unnecessary—you already have a spare checker there. But a second spare can be useful. You can use it to hit the opponent if he tries for an advanced anchor. Or if you roll 1-3, 2-4, 3-5, or 1-6, you can use the eight-point spare build a new point. There are enough uses for spares on the eight-point that having more than one there is ok.

Jacoby and Crawford (1970):  The split to the 23-point is quite good. If your opponent fails to hit either of your men on his one and two-points, you will be in position to make one of the advanced points in his board or his bar-point with one of several rolls. In addition, you will have doubled your coverage of the opposing outer board, so that if he chooses to move a blot into that terrain, you are twice as likely to be able to hit it.

Phillip Martyn (1976):  Splitting with the 1 achieves something because the throws with which you can make opponent's four and five-points, 3-2 and 4-3, are not useful for other purposes.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
24/23, 13/8	+ .5006, .1350, .0054   − .4994, .1311, .0049	+.0056
13/8, 6/5	+ .4976, .1374, .0058   − .5024, .1348, .0067	−.0031	(.0087)	(.0060)	(.0012)	(.0134)
24/18	+ .4930, .1179, .0048   − .5070, .1355, .0053	−.0321	(.0377)	(.0152)	(.0494)	(.0240)

The rollout confirms the choice of the players in the survey, that 24/23, 13/8 is the best way to play this roll. But the slotting play is not far behind and you may wish to experiment with the slot to see how it works for you in your games.

Survey says ... 13/11, 13/8    55.4% 24/22, 13/8    42.7% 13/8, 6/4    1.4%

There is only one decent way to play the 5—13/8 is essentially forced. So the question is how to play the 2. Here are the possibilities:

• 24/22, 13/8 (splitting your runners).
• 13/11, 13/8 (bringing down a builder off your mid-point).
• 13/8, 6/4 (slotting your four-point).

Before the 1990's, experts were unanimous that this was the only reasonable way to play an opening 5-2. In a survey of sixteen expert players conducted by Bill Robertie in 1984 (reported in the first edition of Advanced Backgammon), all sixteen played 13/11, 13/8. By moving 13/11 you create a nice builder with little risk.

Jacoby and Crawford (1970):  13/11, 13/8 is by far the best play because you begin to set up a strong blocking action in relative safety.

Reese and Brinig (1975):  The man on your 11-point is exposed only to 6-4 and is well placed to unite with another piece to make the bar-point or the five-point.

Phillip Martyn (1976):  The man on your eleven point is useful as an extra builder to make either your bar-point or your five-point. It is not as good a builder as one which is further along, but at least it is less likely to be hit. This is the best you can do with this bad throw.

Bill Robertie (1987):  The blot on the 11-point covers the outfield and provides a builder for the five-point, bar-point, and nine-point.

24/22, 13/8

This play was unheard of before the 1990's. The fear was that your opponent would roll double 5's. You'd then end up with two blots on the bar and your opponent would have an instant three-point board. Even though it is only a 1/36 chance, the result is devastating.

The other argument against splitting to opponent's three-point is that it puts your runners exactly two pips apart. This is the same distance apart as your checkers on the eight-point and six-point. Many of your subsequent rolls that make anchors on your opponent's side of the board also make good points on your side of the board. Your good rolls are said to be duplicated.

ROLL	PLAY
3-1	Makes 21-point or 5-point
4-2	Makes 20-point or 4-point
6-4	Makes 18-point or 2-point

Jacoby and Crawford (1970):  A really bad play with 5-2 is to use the 2 to split your back men by moving one of them to the 22-point. If your opponent rolls double 5, he makes both his one and three-points and puts both your men on the bar.

Reese and Brinig (1975):  To play the 2 move at the back is undesirable for two reasons. First, it would leave you with a lifeless position in front. Secondly, the split to opponent's three-point has the disadvantage that an opponent who threw 5-5 or 5-3 would be able to point on the blot, transforming a moderate roll into a good one; and 3-3, always a good roll, would be stronger than ever.

Phillip Martyn (1976):  Never use the 2 to split your back men. It is too dangerous. If your opponent gets double 5, your game is dead in one roll. Splitting your back men achieves little anyway, because the throws you need to make opponent's four or five points are throws for which you have a better use.

Are there any redeaming qualities that make playing 24/22 reasonable? One is that the play is fairly safe. If your opponent doesn't roll 5-5, 3-3, or 5-3, you have a chance to hit back if he hits your blot. The other advantage is that you have now slotted a semiadvanced anchor. If you roll a 2 next turn, you can cover the 22-point blot. It's not as good as owning the 20-point or 21-point, but the 22-point is still a nice asset to have early in the game.

And maybe 13/11 with the 2 isn't as strong as we've always thought. It leaves only three checkers on your mid-point. Over the years, players have realized that you don't want to strip your mid-point of spare checkers too early in the game. Those spares are valuable for protecting your outer table.

This doesn't make 13/11 a terrible roll. The builder on your 11-point is great and your mid-point is not yet stripped. It's just that unstacking is not so important when it leaves you with just three checkers on your mid-point.

13/8, 6/4

Slotting your four-point is worth looking at because you now have four checkers on your eight-point. Those checkers, and the checkers on your six-point, are looking for a place to go. That means you want to try even harder to create some home-board points. If your slot is not hit, you can use a 4 to cover it next turn and still be left with a spare on the eight.

But slotting is too much risk for too little gain. The four-point is worth a lot less than the five-point because, even if you successfully cover the slot next turn, you are left with a swiss-cheese formation. With two checkers used up on the four-point, it becomes harder to fill the holes on five and seven. Notice how much higher your equity is after an opening 3-1 (+.1670, making the five-point) versus an opening 4-2 (+.1234, making the four-point). It is better to make your points in order, five-point then four-point, if you can.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
24/22, 13/8	+ .5007, .1334, .0058   − .4993, .1327, .0047	+.0032			(.0142)
13/11, 13/8	+ .4970, .1442, .0074   − .5030, .1414, .0065	−.0023	(.0055)	(.0074)		(.0248)
13/8, 6/4	+ .4899, .1335, .0057   − .5101, .1403, .0063	−.0276	(.0308)	(.0216)	(.0356)	(.0368)

The surprising result of this rollout is that the strange splitting play comes out on top! It means the prevailing expert opinion for decades was dead wrong. Not that 13/11, 13/8 isn't a decent play, but prior to strong computer rollouts nobody ever suspected that splitting to the 22-point could be just as good. Only at gammon-go is 13/11 clearly best.

Survey says ... 8/3, 6/3    97.8% 13/10, 13/8    1.2%

There are two ways you might see this roll played:

• 13/8, 13/10 (bringing two builders down from your mid-point).
• 8/3, 6/3 (making your three-point).

This play, rarely seen today, was popular in the 1970's. The feeling at the time was that making the three-point was too committal. Players believed the three-point was too advanced to be a good blocking point, and making it early in the game used up checkers that could be better deployed elsewhere.
 

Cooke and Bradshaw (1974):  At this point in the game, the three-point is almost irrelevant; it does not become really valuable until the five and four-points have been secured.

Bruce Becker (1974):  Making your three-point now will have the disadvantage of effectively removing two men from action; your mobility will be markedly decreased, and you will soon find yourself in trouble.

Paul Magriel (1976):  Despite the importance of making points in your home board, deep points—namely the three, two, and especially the one—are not effective in blocking opposing checkers unless the intervening four and five-points have already been made.

8/3, 6/3

It wasn't until the 1980's that thinking began to change and many players who had been playing "two off the mid-point" came to see that making the three-point was really the way to go. What makes 8/3, 6/3 such a great play? The advantages are simple and few:

• It makes a home-board point.
• It is completely safe.

The three-point can also be a good blocking point. Eventually you may be able to make a prime from your eight-point down to your three-point. Of course, it would be easier to make your points in the opposite order (five-point, four-point, and then three-point), but you have to play the rolls the dice give you. And these dice are telling you to make your three-point.

Phillip Martyn deserves credit for bucking the fashion trend of the 1970's and seeing early on that anything other than making the three-point is a huge error.

Phillip Martyn (1976):  Make your three-point. Some people say the three-point is not worth having early on. They are wrong. As you gain experience you will realize how useful any point in your board is. When you have made the six and three-points, your opponent, if he has a man on the bar, will more often than not get at least one 3 or one 6 which he can't come in with. So he is forced to use his other throw to come in, assuming it is a 1, 2, 4, or 5, instead of using it for something more constructive. And more than 10 per cent of the time he will be moaning about his "unbelievable" bad luck as he throws double 6, double 3 or 6-3, and can't come in at all.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
8/3, 6/3	+ .5173, .1617, .0076   − .4827, .1339, .0062	+.0638
24/21, 13/8	+ .5061, .1386, .0071   − .4939, .1338, .0045	+.0196	(.0442)	(.0224)	(.0686)	(.0222)
13/10, 13/8	+ .4970, .1498, .0073   − .5030, .1406, .0062	+.0042	(.0596)	(.0407)	(.0645)	(.0540)

Nothing else comes close. Making the three-point is clearly the best for money and at all scores in match play.

Survey says ... 24/20, 13/8    63.1% 13/9, 13/8    30.5% 24/15    6.3%

There are three reasonable ways to play this roll:

• 24/15 (running with one of your back checkers).
• 13/9, 13/8 (bringing two builders down from your mid-point).
• 24/20, 13/8 (splitting your back checkers and bringing down a builder).

If this play succeeds and you escape a runner, you'll have a real advantage in the game. But the problem is your runner gets hit 13 times out of 36. Now you've got a checker on the bar, you're down nine pips in the race, and your opponent has a builder in place ready to make a new blocking point. The down side of getting hit is just too great. Better look at some other ways to play this roll.

13/9, 13/8

The idea behind this play is to put more checkers where they can be used to build home-board points or attack your opponent if he tries to step up to your five-point, four-point, or bar-point.

The only problem is that this leaves your position a little front-heavy, with many checkers rather far forward and only one spare on your mid-point. Spare checkers on your mid-point are valuable to have early in the game. They defend your outer board in case your opponent tries to escape. They can be used to make points in your outer table. And they provide flexibility, giving ways to use numbers that can't be played safely elsewhere. You want to avoid taking too many checkers off your mid-point too early in the game.

Elizabeth Clark Boyden (1930):  13/9, 13/8 leaves an exellent chance of covering the five-point or bar-point on the next throw.

Kit Woolsey (2002):  The building play puts pressure on the inner board. The opponent cannot split safely, so he will probably bring his own builders down if he doesn't roll a good number. This will lead toward both sides building up their boards quickly

24/20, 13/8

This is a balanced play, working on both sides of the board at the same time. You hope to roll a 4 next turn and cover the slot on the opponent's five-point. This is a great point to own. It causes headaches for your opponent as he brings his checkers home. And it means you can play more aggressively knowing that you always have a place to reenter your hit checkers.

The down side of this play is that opponent will hit your blot if he can, especially if he rolls a 1, and if you are unable to hit back it may be he who first makes his five-point. Of course your opponent takes a risk by hitting you. If you hit back, you'll send his checker back 20 pips.

Phillip Martyn (1976):  If your opponent does not hit, you may well make his vital five-point. If he does hit without covering it he is in great danger of being hit back. You only need a 5 or a 4 (other than 6-4) to hit him; and if you should throw a 5-4 again you will be in great shape, hitting him and making his five-point.

Paul Magriel (1976):  It is wise to split early—before your position becomes more dangerous. By moving a back man up, you not only try to acquire a valuable point, you also prevent your opponent from bringing builders down to his outer board and developing naturally. I have no strong preference between this play and 13/9, 13/8. The major difference is that this play is more provocative since your opponent is likely to be forced to hit you immediately.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
24/20, 13/8	+ .5051, .1362, .0072   − .4949, .1331, .0050	+.0155			(.0170)	(.0002)
13/9, 13/8	+ .4999, .1499, .0077   − .5001, .1365, .0064	+.0145	(.0010)	(.0104)		(.0174)
24/15	+ .5034, .1168, .0052   − .4966, .1313, .0046	−.0071	(.0226)	(.0034)	(.0592)
13/4	+ .4852, .1382, .0066   − .5148, .1426, .0070	−.0344	(.0499)	(.0398)	(.0528)	(.0590)

For money, there is very little to choose between the top two plays. At gammon-go, the extra gammons provided by 13/9, 13/8 make it the better play.

Survey says ... 13/7, 8/7    99.8%

13/7, 8/7

There is only one reasonable way to play this roll—make your bar-point. The bar-point is a great point to own early in the game. It's good blocking point because it is exactly six pips away from the opponent's runners and it nicely fills in the gap between your eight-point and six-point. Sequences of points with no gaps are strong blocking formations because it is hard for your opponent to get by them and easy for you to extend them. You can now bring extra checkers down from your mid-point and use them to make additional points in your home board.

Some players are surprised to learn that 6-1 is only the third best opening roll, behind 3-1 and 4-2. Why isn't it as good as the others?

The answer is that the bar-point is not a home-board point. Home-board points are surprisingly valuable early in the game. When you own more home-board points than your opponent, he has to be particularly careful about leaving you shots, whereas you can afford to take extra chances to improve your position.

Both the five-point and four-point are more valuable to own than the bar-point. However, your three-point and two-point are not as valuable as your bar-point, so opening rolls of 5-3 and 6-4 are not as good as 6-1. The problem with the three-point and two-point is that they are too far away from the already made six and eight-points to work effectively with them. Once you place two checkers so far forward, it's hard to fill up the intervening space.

Walter Gibson (1974):  The ideal opener. You move 13/7, 8/7, making your bar-point. This gives you a "half-prime" of three blocks in a row and prevents opponent from moving his runners if he makes such big rolls as 6-6, 6-5, or 5-5.

Bill Robertie (2002):  You have succeeded in creating a block three points long. The only drawback to this roll is that the seven-point is not an inner-board point, so it doesn't help keep your opponent from entering if you send him to the bar.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
13/7, 8/7	+ .5353, .1516, .0063   − .4647, .1201, .0049	+.1035

Survey says ... 24/18, 13/11    81.4% 24/16    10.4% 13/5    6.4% 13/11, 13/7    1.0%

There are three popular ways to play this roll:

• 24/16 (running a back checker).
• 13/5 (slotting your five-point).
• 24/18, 13/11 (splitting to opponent's bar-point and bringing down a builder from your mid-point).

Your plan with the running play is to continue with the same checker next turn, moving it to safety if it is not hit. This play is great if it works, but the problem is that you get hit 14 times out of 36. Getting hit puts you down nine pips in the race, with a checker on the bar, and leaves your opponent with a builder in an ideal location for making a new blocking point. The gains from running just aren't enough to justify the risk.

Jacoby and Crawford (1970):  We don't like the running play at all since it exposes your blot to a straight 4 or 3-1 or double 2, a total of fourteen possible shots.

Kit Woolsey (2000):  24/16 isn't nearly as bad as many players believe. Try it sometime. You will find that it isn't so easy to play against. Some of the hitting rolls play very well otherwise, and the misses aren't too easy to play.

13/5

The fastest way to make a point is to slot it. This aggressive play to secure the valuable five-point right from the start. If your slot is not hit, you can cover it with any 1, 3, or 8. But if you are hit your checker will be sent back 20 spaces.

Is slotting worth the risk? The five-point is certainly valuable. But the problem with this play is that it slots with the wrong checker. The checkers on your mid-point already have many uses. It's the spare checkers on your six-point that need to find work. That's why slotting is reasonable with rolls such as 2-1, 4-1, or 5-1; they get a checker from the six-point involved in the game. Slotting from the mid-point needlessly exposes a checker that can be usefully deployed elsewhere.

Paul Magriel (1976):  This variant leads to dangerous, exciting, but also more difficult games. It is neither necessarily better nor worse than the splitting play. The split is often made by experts. The player just learning the game is advised to gain some experience before using this play.

Bill Robertie (1984):  Once upon a time, this play was the mark of a modern player. Nowadays the move has fallen into relative disrepute.

Bill Robertie (1998):  What players gradually realized was that if you made the five-point but still had a stack of five checkers on the six-point, your game just wasn't all that powerful.

24/18, 13/11

This play tries for improvements on both sides of the board. By bringing one of your runners up to the opponent's bar-point, you hope to either make his bar-point next turn or continue with the same checker and run it to safety. Meanwhile, the checker provides good coverage of opponent's outfield.

The builder on your 11-point protects your outer table and is in good position to help create a block next turn. It is quite safe because only a roll of 6-4 will hit it. The checker on opponent's bar-point is not so safe since opponent can hit it with any 1 or 6. But if he hits you, you have good chances of hitting back with a 6 from the 24-point or a 7 from the bar. And your hits are more costly than his in terms of the number of pips each checker is sent back.

Paul Magriel (1976):  This play is more constructive than running since you bring a builder into your own outer board. It is also more provacative since the man on opponent's bar-point and the builder you bring down creates added pressure on both your outer and inner boards. It restricts opponent's choices and makes it hard for him to develop naturally.

Bill Robertie (1998):  Modern players are looking for the right combination of aggression, building, defense, and risk/reward, and 24/18, 13/11 feels better on these criteria.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
24/18, 13/11	+ .5068, .1270, .0058   − .4932, .1346, .0052	+.0066			(.0028)
13/5	+ .4931, .1421, .0067   − .5069, .1390, .0069	−.0109	(.0175)	(.0274)		(.0362)
24/16	+ .5028, .1187, .0053   − .4972, .1363, .0050	−.0117	(.0183)	(.0080)	(.0274)	(.0114)

The splitting play, 24/18, 13/11, comes out best in the rollout. In match play, the only exception is gammon-go, where slotting is slightly better.

Survey says ... 24/18, 13/10    76.4% 24/15    20.9% 13/10, 13/7    1.3%

There are two feasible ways of playing an opening 6-3:

• 24/15 (running one of your back checkers).
• 24/18, 13/10 (splitting your back checkers and bringing down a builder from your mid-point).

Your plan with the running play is to continue with the same checker next turn, moving it to safety if it is not hit. This play is great if it works, but the problem is that you get hit 13 times out of 36. Getting hit puts you down nine pips in the race, with a checker on the bar, and leaves your opponent with a builder in an ideal location for making a new blocking point. The gains from running aren't enough to justify the risk.

It is interesting to compare this to running with a 6-2. Running with 6-3 is slightly better. Your opponent has only 13 chances out of 36 to hit you. And when you're not hit you are one pip further ahead in the race.

Jacoby and Crawford (1970):  The old-fashined play was to run. Your blot is exposed to a direct 3 and a 2-1 from one of opponent's men on his mid-point; such vulnerability makes this play slightly less desirable than the split.

Bill Robertie (1984):  The running play doesn't enhance your chances of making an additional point very much. Except for a subsequent 6-4, the same rolls which make an outer board point also make an inner board point.

24/18, 13/10

Bringing a checker up to the opponent's bar-point gives you a chance to either make this point next turn or continue with the same checker and run it to safety. The builder on your ten-point can either be turned into a block, if you roll 3 again, or used with another spare to create a block on nine or five.

The checker on opponent's bar-point is not particularly safe since he can hit you with any 1 or 6. But if you're not hit, you have a chance to make opponent's bar-point, which is a good asset to have early in the game. And if you are hit, you have good chances of hitting back with a 6 or a 7. In a blot-hitting-contest your hits are better than his in terms of the number of pips gained each time you hit.

Jacoby and Crawford (1970):  The odds are two-to-one that your man on the opponent's bar-point will be hit. But unless he is hit by a point-making roll, you will have a lot of possible return shots against your opponent's vulnerable blot, and you have lost little anyway. If your man is not hit, your position is highly advantageous.

Paul Magriel (1976):  This play is more constructive than running since you bring a builder into your own outer board. It is also more provacative since the man on opponents's bar-point and the builder you bring down creates added pressure on both your outer and inner boards. It restricts opponent's choices and makes it hard for him to develop naturally.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
24/18, 13/10	+ .5053, .1299, .0062   − .4947, .1339, .0056	+.0072				(.0014)
24/15	+ .5034, .1168, .0052   − .4966, .1313, .0046	−.0071	(.0143)	(.0038)	(.0300)
24/21, 13/7	+ .4863, .1346, .0062   − .5137, .1403, .0063	−.0332	(.0404)	(.0380)	(.0286)	(.0522)
13/4	+ .4852, .1382, .0066   − .5148, .1426, .0070	−.0344	(.0416)	(.0402)	(.0236)	(.0590)
13/10, 13/7	+ .4816, .1405, .0077   − .5184, .1489, .0087	−.0462	(.0534)	(.0474)	(.0262)	(.0788)

The splitting play, 24/18, 13/10, is the clear winner, but running is not far behind. The main problem with the running play is that it wins fewer gammons. Running is perfectly fine at double match point, and probably best at gammon-save.

Survey says ... 24/18, 13/9    37.0% 24/14    35.0% 8/2, 6/2    27.3%

A very interesting roll, perhaps the most interesting of all fifteen opening rolls. There are three completely different approaches to playing it:

• 24/14 (running one of your back checkers).
• 24/18, 13/9 (splitting your back checkers and bringing down a builder from your mid-point).
• 8/2, 6/2 (making your two-point).

If your checker is not hit, your plan is to continue with the same checker next turn. If you're lucky, you'll roll numbers that allow you to make an outfield point. Rolls of 3-2, 4-3, and 5-4 work in this regard. If you succeed in safely escaping your runner, you'll have established a significant advantage in the game; it is much harder for your opponent to contain a single checker than two checkers.

The only problem with this play is that you might get hit. Getting hit puts a checker on the bar and leaves you down five pips in the race (one pip for the checker on the bar plus four pips because your opponent is now on roll). Furthermore, your opponent will have a builder ideally placed for making a new blocking point. Getting hit would be a real setback.

But you get hit only 11 times out 36. Twenty-five times out of 36 you don't get hit. You're well ahead in the race, so running is a very reasonable way to play this roll. ("When ahead in the race, race.") Note that running with 6-4 is a better option than running with 6-3 or 6-2. With 6-4 you have less chance of being hit and when you're not hit you're further ahead in the race.

Walter Gibson (1974):  This move is like taking a lover's leap but landing one step short, as it puts a blot on the 14-point. However, it is a well-calculated risk, for if your opponent fails to hit the blot, you will have a good running start.

Walter Trice (2004):  The bad news is that this play leaves a blot, and you'll be sorry if you get hit. The good news is that if you don't get hit you'll probably have escaped a man. You may even be able to use the runner to make a good point in your own outfield, linking up with a checker off the mid-point.

24/18, 13/9

This play gives you a diversified position and good coverage of the board. By bringing a checker up to opponent's bar-point, you hope to either make this point next turn or run the checker to safety. The builder on your nine-point creates many chances to make a new point next turn.

The only problem with the play is it offers many ways for your opponent to hit you. Any 1 or 6 hits the blot on opponent's bar-point, and any combination totalling 8 hits the builder on your nine-point. Opponent has 27 ways out of 36 of hitting you. Ouch!

Still, getting hit isn't fatal; you can often hit back. Anything can happen and it is difficult to assess the overall plusses and minuses of this play.

Georges Mabardi (1930):  The odds are 3-to-1 that one of the blots will be hit. But it is very difficult for the opponent to hit and also cover. Moreover, on reentry into an open board you have an excellent opportunity to take up one or more of the opponent's men. In case the blots are not hit, you have a chance to cover an important point.

Phillip Martyn (1976):  This play gives you a builder to make points in your home board and, if the man on opponent's bar-point is not hit, you have a good chance of covering it next time, making opponent's bar-point. But the fact is that 27 out of 36 hits is simply too dangerous.

Cooke and Orlean (1980):  Although this opening is favored by quite a few experts, to us it is too much like leading with one's chin. Why invite assault when there is no need for it? The strategic gains are dubious. Even if you do hit back, you cannot at the same time establish any attacking point on your side of the board. This split opening move immediately puts you on the defensive.

Marty Storer (2005):  The split-and-build play is a risky and aggressive try for quick improvement. If your opponent hits loose on the seven-point, you can gain quite a bit by hitting back. If he misses, as with 4-3 or 3-2, you also come out ahead. But if opponent hits on your nine-point, or if he hits on his bar-point and you miss the return, then your opponent is doing well.

8/2, 6/2

Conventional wisdom is that making the two-point does little to block the opponent and takes two valuable checkers out of play where they can't work with the rest of your army. Further, it is considered poor form to build points six pips apart (the two-point is six pips from the eight-point). The reason is that both points cannot form part of the same prime. Once you have placed two checkers on your two-point, it makes it almost impossible to create a prime that includes your eight-point. Prior to the 1990's experts decried this play.

Georges Mabardi (1930):  8/2, 6/2 takes two men out of play. This is called the novice-point.

Obolensky and James (1969):  This play creates a large gap between your points and is not recommended.

Jacoby and Crawford (1970):  Don't be tempted to make your two-point. A point made in your board is always valuable, but the ones to aim for first are the five and four-points. Men on the two-point are almost entirely out of play since their only possible move is to the one-point.

Phillip Martyn (1976):  Although 6-4 could make the two-point, this is definitely inadvisable since the two-point is too far advanced to have much blocking potential.

Bill Robertie (1987):  The two-point is too deep in the board to be useful at this stage of the game. By making it, you remove two valuable builders from the struggle for the key four and five-points.

Only with the advent of modern computer rollouts did experts consider more seriously making the two-point. What computers have taught us is just how valuable it is to own home-board points. Every additional point you own adds to the value of your position. When you own more home-board points than your opponent, you have a real advantage. Your opponent has to play more cautiously, while you get to play more aggressively.

This is not to say that the two-point is a wonderful point to own. It's not nearly as good as your five-point, four-point, or even your three-point. But it is a home-board point and it is an asset, even though it requires you to use up two checkers that might be more useful elsewhere.

The other thing about this play is that it is completely safe—at least for now. There are no blots for the opponent to hit. On the other hand, your position is not very flexible, so your present safety may be short-lived.

Paul Lamford (2001):  8/2, 6/2 used to be regarded as a beginner's error but with stronger and stronger backgammon programs it has started to be taken seriously. The move makes a new home-board point and leaves no loose checkers. It also makes some replies containing a 1 awkward to play.

Kit Woolsey (2001):  This play used to be laughed at as a beginner's play, but the new wave of bots has demonstrated that it is a serious contender. It is a good play to make when behind in a match, since it leads to sharper positions with more gammon potential. It can be quite effective against players who are not used to playing against this structure.

Marty Storer (2005):  Today, most players still prefer either 24/14 or 24/18, 13/9, but a significant minority make the two-point. No doubt some prefer the two-point because they feel better able than their opponents to handle the followup. Many, however, believe making the two-point is not only practically but technically best.

So, what's best?

Comparing the different ways of playing an opening 6-4 is difficult. Each play leads to quite different types of games. It is fair to say that nobody knows for sure which of these plays is best.

Notice that the three plays have about equal support in our survey. You might use this as evidence that 6-4 is the hardest opening roll of all, because players are so undecided about what to do. (Or maybe you'd say that 6-4 is the easiest opening because the rollouts below show it hardly matters which play you make!)

It may happen one day that a future bot will discern that one of these plays is truly better than the others. But will this information have practical value? Can human players play at the level needed to achieve that edge? I doubt it. Try all three plays to see what types of games develop and which play best suits your style. Then go with the play that feels best. At least you have the security of knowing, whatever play you choose, it can't be wrong by much.

Kit Woolsey (2003):  My choice is generally dicatated my the match score. When I am behind in the match I am looking for sharp gammonish positions, so I usually make my two point. When the match is about even, I tend toward the flexible 24/18, 13/9. When I am ahead in the match I try to steer toward simple running and holding type games, so I usually choose 24/14.

Marty Storer (2005):  How should you play an opening 6-4? In a normal situation, for money or early in a match, the best move is anybody's guess. The enterprising 24/18, 13/9 is probably most likely to lead to complicated play, so you may want to try it if you think you're clearly stronger than your opponent. Otherwise, just make the move you're most familiar and comfortable with. 8/2, 6/2 is unfamiliar to many opponents, so if you invest some time studying the types of positions that are likely to occur thereafter—including early cube decisions—you may have a potent weapon.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
8/2, 6/2	+ .4981, .1540, .0077   − .5019, .1417, .0060	+.0102		(.0168)		(.0376)
24/18, 13/9	+ .5034, .1348, .0061   − .4966, .1350, .0058	+.0069	(.0033)	(.0062)	(.0278)	(.0136)
24/14	+ .5065, .1179, .0053   − .4935, .1313, .0046	+.0003	(.0099)		(.0554)

The rollout results are fascinating. If they are to be believed, then making the two-point is actually the best play, directly opposite of what for years was conventional wisdom. But the results are far from clear. For example, this cubeful rollout shows very little difference between the top three plays.

It is interesting that the split-and-build play, which was (barely) first choice in the survey, is the only play that is never correct in match play. At gammon-go, making the two-point is best because it wins more gammons. At double-match-point and gammon-save, running is best because it wins the most games.

Survey says ... 24/13    99.3%

24/13

Today's experts are agreed that there is only one way to play this roll, a play so famous it has its own name: Lover's Leap. 6-5 is the largest roll possible for an opener, so it is natural to make a running play to capitalize on your racing lead. Further, 24/13 is completely safe. What more could you ask?

Normally you want to avoid putting six checkers on one point. But six checkers on your mid-point is not a big concern. Next turn you'll bring one or two checkers down to your outfield where they can work as builders. Meanwhile you'll still have some spares back on the mid-point that can work with your builders to make new points. Or they can be used to attack your opponent if he tries to escape. In general, having spares on your mid-point gives you a more flexible position.

The first player to safely escape one of his back checkers has established a significant lead. It is much harder for your opponent to contain just one checker than two. The combination of racing lead and safety is enough make 6-5 one of the Big Five opening rolls.

Jacoby and Crawford (1970):  You have gotten one of your back men halfway home safely, and are off to a strong running game.

Walter Gibson (1974):  Since you advance your runner the maximum distance with no danger, this can prove an excellent opening if subsequent moves keep up a fast pace. Leaving a blot on your 24-point means nothing because, if it is hit, you can reenter with any roll except a 6 this early in the game.

Bill Robertie (1984):  Running to the mid-point is quite strong; not because of the lead in the race, which is insignificant, but because of the great strategical advantage of having only one man back.

During the wild days of the 1970s some players experimented with alternatives to lover's leap. They felt the running play looked too much like a beginner's move and wanted a more constructive way to play the roll.

Bruce Becker (1974):  Other authors recommend moving one man 24/13. This is called "lover's leap," though no one seems to know why. I pondered this for a long time, and then it suddenly dawned on me: a lover's leap is a death jump, and that's exactly what this is. Not only is this a game that will be very hard to win, but it also is going to be very dull and plodding, and too often you will find yourself at the bottom of the cliff.

Rollout

PLAY	W        G       BG	EQUITY	CL	DMP	GG	GS
24/13	+ .5282, .1164, .0053   − .4718, .1200, .0036	+.0545
24/18, 13/8	+ .5099, .1287, .0068   − .4901, .1350, .0045	+.0158	(.0387)	(.0366)	(.0120)	(.0666)

It's clear from the rollout that lover's leap is the only way to go with an opening 6-5.

Georges Mabardi (1930):  Vanity Fair's Backgammon to Win
Elizabeth Clark Boyden (1930):  The New Backgammon
Obolensky and James (1969):  Backgammon, the Action Game
Jacoby and Crawford (1970):  Backgammon
Walter Gibson (1974):  Fell's Guide to Winning Backgammon
Cooke and Bradshaw (1974):  Backgammon: The Cruelest Game
Bruce Becker (1974):  Backgammon for Blood
Reese and Brinig (1975):  Backgammon the Modern Game
Paul Magriel (1976):  Backgammon
Phillip Martyn (1976):  Phillip Martyn on Backgammon
Robin Clay (1977):  Teach Yourself Backgammon
Cooke and Orlean (1980):  Championship Backgammon
Bill Robertie (1982):  Lee Genud versus Joe Dwek
Bill Robertie (1984):  Advanced Backgammon, first edition
Bill Robertie (1987):  Reno 1986
Bill Robertie (1998):  Inside Backgammon, Volume 8
Kit Woolsey (1999-2004):   GammOnLine, Online Match
Bill Robertie (2000):  501 Essential Backgammon Problems
Paul Lamford (2001):  Starting Out in Backgammon
Bill Robertie (2002):  Backgammon for Winners, third edition
Walter Trice (2004):  Backgammon Boot Camp
Marty Storer (2005):  Backgammon Praxis