Backgammon is not played in a vacuum. You have an opponent, and your plan of campaign must be to improve your position at the expense of his. It is interesting to note, and always worth bearing in mind, that backgammon is one of the few games involving both luck and skill that allows each player to see what his opponent is doing.
Safety vs. Flexibility
You must take chances. No one can win backgammon games by playing safe all the time. As a simple example, let us refer back to the opening roll of 5-2. As you saw, it isn’t much of a roll but there is a correct way to play it. You move two men from your opponent’s twelve point. One goes to safety at your eight point; the other becomes a blot on your eleven point. How does your position stand now?
||After 13/11, 13/8.|
First, only a 6-4 can hit that blot, a slim probability. And you lose very little even if the blot is hit. Your man is sent home to the bar, but you will have no trouble bringing him back into play since your opponent holds only one point in his inner board. You will have dropped behind in a running game (which will be discussed later in this chapter), but you will have three men back in his inner board, so it will be a long time before your opponent can get into a straight running game .
Now let’s see what you gain by this play if you are not hit. Your man on the eleven point is bearing directly on your five, bar, nine, and ten points. All sorts of rolls that would have done nothing for you now become valuable. Some even become outstanding, such as 6-3 or 4-1. With 6-3 you make your five point (moving a man each from your eleven and eight points); and 4-1 enables you to make your bar point. Several other rolls are almost as advantageous.
Suppose that you play absolutely safe with your 5-2 by moving one man all the way from the enemy twelve point to your six point. Nothing can hurt you, but you haven’t improved your position at all.
Of course you shouldn’t take chances for the sheer joy of taking chances. Don’t expose a blot to a single-number shot (a direct hit) if you have some other convenient play, unless you have something really worthwhile to gain by this exposure.
When it comes to exposing a blot you must always consider what can happen if your blot is hit. The more points your opponent has made in his inner board, the more dangerous it is to be hit (as you know from the discussion of the previous chapter). If he has made only one point in his inner board, you have thirty-five out of thirty-six chances (thirty-five-to-one odds) of coming in. If he has made two points, you have thirty-two out of thirty-six chances (eight-to-one odds); with three points made you have twenty-seven out of thirty-six chances; with four points made you have twenty out of thirty-six, and with five points made you have only eleven out of thirty-six chances of entering. If he hits you when he has a closed board (a prime of all six points in his inner board), you can’t play at all until he vacates or leaves a blot on at least one point.
When you have two men on the bar and he has as many as three points made in his inner board, you have twenty-seven ways of bringing one man in on your next move, but only nine ways to bring in both. When he has four points made, leaving only two open, you have only four ways to get both men in on your next move.
Even with five points open there are eleven ways that won’t bring in both men. So you always try to avoid getting two men hit at the same time. And the more points your opponent has made on his inner board, the more you try to avoid having two men off the board at all.
Conversely, you should always consider hitting two of you opponent’s men if you get a chances to do so.
Your first aim in early play is to make your five point. This point helps to block any men your opponent has in your inner board. It puts pressure on him to avoid letting you send any of his men back home; it serves as a base of operations to bring more men into your inner board safely, and also to work on making the other points there. It will remain a tower of strength until such time as you get into a running game.
The bar point and four point are almost as valuable. The bar point gives you three good blocking points in a row (the six, bar, and eight points), but it does not give you an extra point in your inner board; while the four point still allows your opponent to play to your five point and thus get a man past two of your men.
The three point is both an asset and a liability. It does start to block your opponent’s back men (and his men on the bar), but it is comparatively easy to pass and if you then put extra men on that three point, they are practically out of play. Still, we recommend making your three point with an opening roll of 5-3. Having made the three point will become of real value if you can make the four or five point later on; and you should put even more emphasis on making those two point after you have made the three point.
As an example of this, look at the following diagram. You opened with 5-3 and made your three point. Black rolled 4-3 and decided to move one back man to your five point and one man from your twelve point around the corner to his nine point. Now you happen to roll another 5-3.
White to play 5-3.
The 5 is easy to play: move from the black twelve point to your eight point. But there are three ways to handle the 3. You can move a back man to the black four point, but this is a very poor move since any combination of 6-4, 6-2, 4-2, 4-4, or 2-2 would allow him to “point ” on you there. You can move from your six point to your three point; this leaves you completely safe but in poor position since you have advanced a third man to the three point long before there is any good reason to do so.
The best play with the 3 is to hit the blot on your five point.
This play would never have been considered in the early days of modern backgammon. You are exposing a man in your home board to eighteen rolls (the man on the bar can hit you coming in with any roll containing 5, plus 4-1 and 3-2; and he can bring his man in off the bar and then hit you with his man on your one point if he rolls 4-2 or double 4). It is thus even money — eighteen out of thirty-six chances — that you will be hit; and if you are hit, a man goes all the way back from your own five point to the bar.
The modern expert doesn’t care at all. He doesn’t see great loss if he is hit. All it does is to give him three back men instead of two. He will plan to deploy these back men in the black inner board. If possible, he will keep one on the one point and pair the other two on the four or five point. (In any case he will maintain some point in the black inner board and will not split his men onto three separate points. That sort of play leads to destruction: black will try to point on one of those three blots, or if black fails to point directly on you, there are any number of combination shots that will enable him to hit two of your men — even though he may leave a blot himself — and leave you with two men on the bar.)
Now look at the good side of the coin. It is also even money that he won’t hit your blot on the five point. If he rolls double 6, double 3, or 6-3, he won’t be able to play at all and will have missed an excellent roll. If he gets any of these or a playable roll that doesn’t hit your blot, it will leave you ready — and probably able — to make your five point on your next roll. You would then have three good points made in your inner board, as against his solitary six point in his home board. Remember that the three point becomes a good point once you are able to make either your five or four point.
Splitting Your Back Men
In the early days of modern backgammon it was standard tactics to split your back men, and in general to run one forward to the enemy four or five point. This advanced man would attack your opponent’s outer board and even one or two points on your outer board. It would be bad luck if he were pointed on, but otherwise he would stay there until you either ran him out or brought the other back man up to pair him safely.
Today you just can’t make this sort of play with the same impunity. Modern players have learned to hit this man even if they have to leave a blot in doing so.
Of course we still make this split when there is no better play or some good extra reason to do so. But, as we have said, in general the only split of the back men we do like is to move one man from the one to the two point. You don’t mind being hit or even pointed on at either the one or two point, and you get a lot of advantage from this split. To begin with, you have twice as many possibilities of hitting a man in your opponent’s outer board. Also, you discourage him from dropping a blot on his five point, and you are in a position where 3-2 allows you to make his four point, 4-3 to make his five point, and 6-5 to make his bar point.
As we mentioned before, moving one back man to the thee point is the least desirable split. For example, double 5 is usually a poor roll. But when you have blots on the black one and three points you transform your opponent’s double 5 into a crusher: he points on both your blots at one time (moving two men each from his eight and six points). You then have two men on the bar, while he has three points made in his inner board. But say your opponent doesn’t hit you on his roll, and you then roll 3-1 or 4-2. You can make the four or five point in his board — but you pass up the chance of making the four or five point in your own inner board, as you would much prefer. In other words, the split to the black two point makes the normally poor rolls of 3-2 and 4-3 very good ones; the split to the black three point merely gives you an alternate good play with 3-1 or 4-2.
Hitting Two Blots
We have mentioned casually that it is always good policy to hit two blots. The following example of a double hit demonstrates how important it is to learn the laws of probability as quickly as possible; we urge you once again to familiarize yourself with the previous chapter, and to refer to it frequently as you read this book.
In the following diagram you roll 4-2.
White to play 4-2.
The obvious play is to make your four point (moving a man each from your eight and six points). This will give you four points made in your board and a good sound position.
But if black then rolls any 2, he will bring that man in off the bar and make your two point. He can then develop his own board at his leisure while you are bringing your men around and in. He is very likely to get a shot or two at you, at a time when it will cost you the game if you are hit.
Of course, if he rolls 2-5, 2-6, 1-5, or 1-6, he will be able to come in off the bar and hit one of your blots on the bar or eight point. (He should do this with 1-5 or 1-6; it is probably better just to hold your two point if he rolls 2-5 or 2-6 and to wait for the shot or shots that may come later on. )
The play we recommend with 4-2 is to move a man from the black twelve to your eleven point, and to hit the blot on your two point with a man from your six point.
||After 13/11, 6/2*.|
Your opponent’s best roll is then double 2, which will allow him to bring both his men in, hitting your blot on the two point, and then bringing them forward to your four point. This will actually give him a very slight over-all advantage in the game. Double 1 will allow him to bring both his men in and to your two point, hitting your blot and leaving the game almost evenly matched (you’d still have a slight advantage). With double 4 he won’t hit your blot, but he will make that good advanced point in your inner board. Either 4-2 or 2-1 will allow him to bring both his men in while hitting your blot; 6-2, 5-2, and 3-2 will also enable him to hit your blot, but he’ll still have one man left on the bar.
Thus, only these thirteen rolls will give him a playable game. If he rolls any one of the nine possible combinations of 6, 5, and 3, he will be left with both men on the bar and such a bad game that you will play on to try for a “gammon”; while, in a gambling game, if he rolls any of the fourteen remaining possibilities you would double him and be very pleased if he accepted the double, since a gammon is still quite possible.
Certain games develop into blot-hitting contests . The early rolls are such that one man exposes a blot somewhere and it is promptly hit. He hits back in return, and the succeeding rolls are such that both players keep hitting and exposing men. Blot-hitting contests are apt to lead to long games, and it is good to bear in mind that there is no law compelling you to hit a blot merely because it is there. If your men are advanced a lot further than your opponent’s you don’t have to worry about your chances in a running game; you do have to worry about his chances of developing a satisfactory back game against you by making and holding a couple of points in your board.
The term “contact ” is applied to all positions in which all of each player’s men have not yet gotten past all of his opponent’s men, and it is therefore still possible for one or both players to leave a blot or blots. When there is no more contact, you are in what is known as a “running game.” In a running game the advantage lies with the player whose men are further advanced. It is important while you are still “in contact” to be able to estimate how you stand, in order to determine whether or not you should try to get past all of your opponent’s men and break off contact.
There is a simple way to estimate how you stand, or “count your position,” which is to count one for each of your men in your inner board; two for each man in your outer board; three for each man in your opponent’s outer board, and four for each man in his inner board. If you total is smaller than his, your positions is advantageous. We will amplify this discussion of how to count your position in the next chapter.
The Running Game
At the start of the game every one of your men is in a position where you have to expose him as a blot at some time during the game. As the game develops your men will go past your opponent’s men, his will pass yours, and eventually there will be no further contact and all you will have to do will be to bring your men into your inner board and bear them off. This is known as a running game, since your object is to roll big numbers and run as fast as possible.
The advantage in a running game clearly lies with the player whose men are further advanced; even a one-point lead is worth something. If you are ahead, you want to disengage any men that otherwise may become blots later on in order to make sure that the faster runner will win. If you are not ahead, it is better to keep contact in the hope that you will force your opponent to leave a blot for you to hit. These two situations are illustrated in Diagrams 31 and 32.
White to play 5-5.
In each instance you roll double 5. In the first position you are obviously ahead in the running game, so you should move the two men from black’s bar point (the seven point) to your own eight point. This will make a running game of it, and you will be a long way ahead.
White to play 5-5.
In the second position you cannot afford to move your three back men on black’s bar point since you will be miles behind in the running game. Instead, you should move one back man twice, to bring him from the black bar point to your eight point; use your other two 5s to move the man from your nine point to your four point and the man on your eleven point to your six point. Black will still be far ahead, but it will not be a running game as yet since he will have to find some way to get his two men on your twelve point past the two men you’ve kept on his bar point. Unless he rolls a double he is going to have to leave a blot for you to aim at.
When you are in a straight running game you should try to move your men into your inner board as quickly as possible. Do not waste even an ace to move men already in the inner board. To be sure, try to distribute your men well as you move them into your inner board, rather than pile them up on one point, but do bring them in.
Preparing for the Running Game
To all intents and purposes, a slight interlock with your opponent still leaves a running-game position. Thus if each player’s first two rolls are 6-5 and both run with their back men, all men are disengaged except that each player will have seven men left on the enemy twelve point. Theoretically, someone may have to give his opponent a shot at some point, but the chance that this will actually take place is negligible.
In slightly more complicated positions the chance is very great that a running game will develop. Even some extremely complicated positions may quickly develop into a running game, so the astute backgammon player must always consider the possibility that one will develop. If he sees that he will be ahead in a running game, he tries to simplify the position in an effort to get the running game started; if he sees that he will be behind, he tries to keep the position as complicated as possible.
In this connection, you shouldn’t mind getting further behind as long as you aren’t risking a gammon. In the following position you are way behind. Without bothering to count, you have three men in your opponent’s inner board and only three in your own, while he has one man in your inner board and five in his own.
White to play 6-3.
You roll 6-3; your best play is to hit the blot on your five point with your man on his eleven point. You don’t mind if he hits you back; you hold his five point and are in no danger of being gammoned, and with four men back you can expect to get a shot at him later on after you have built up some sort of board against him. If he doesn’t hit your blot on your five point, you have a good start toward making that key point and have also slowed him down a trifle.
In the following position you also roll 6-3.
White to play 6-3.
You can see that your running-game position is superior, and your best play is to move your two men from black’s nine point to his twelve point and your ten point. In effect, this makes the game a running one.
As we said at the end of Chapter 1, in the very early game the four back men — yours and his — are your chief concern. You want to extricate your two back men, and you want to block his two back men.
The position below was reached the following way: You started with 6-3 and ran with a back man to the black ten point. Black rolled 2-1 and hit you with one of his men on your twelve point. You rolled 4-3, came in off the bar, and made the four point in his board. He made his five point with 5-1, and you made your five point with 3-1. Then he rolled double 6 and made both bar points. You now roll 5-3.
White to play 5-3.
Your first thought is to bring one of your back men on black’s four point to safety on his twelve point. Discard that though quickly. Not only are you behind in the potential running game, but your blot on his four point becomes extremely weak. He can hit you with several shots, and he can point on your blot with several more.
The best way to play the roll is to move from his twelve to your eight point, and from your six to your three point. You are thus getting ready to make your three point, and you plan to exert pressure on his men on your bar point. Meanwhile, you two men on his four point serve as an anchor: you are behind in a potential running game — but you aren’t in a running game yet, and you aren’t going to get into one if you can avoid doing so. Furthermore, you aren’t in any danger of being gammoned, and your position is now only slightly worse than his.
After you play 5-3 the way we have suggested, black rolls 5-4. He is immediately embarrassed. He can play safe by moving two men from his six point, or one man from his six and another from his eight; but if black is smart, he will run his two back men on white’s bar point to the white twelve and eleven points.
This produces the following position:
Black has a man exposed to any 2; and if you roll 2-3 or 2-5 you will be able to hit his blot, cover your own blot on your three point, and thus develop a good game. With any other 2 you will also hit his blot, but you won’t be able to cover your blot and thus will be exposed to a lot of return shots. You can also hit with one of your back men on the black four point if you roll 6-4 or double 5. Indeed, the double 5 would probably win the game for you, since you can hit with one back man, bring the other out to the black nine point, and use your last 5 to cover the blot on your three point.
Thus you have a total of fourteen rolls out of thirty-six that hit (eleven 2s, plus 6-4 and double 5). Of these, 2-3, 2-5, and double 5 are very good, the others only fair. In addition, if you roll double 6, you could run with both back men and have a running game in which your position would now be equal to your opponent’s.
Once all men are disengaged your whole problem is to bring your men into your home board as quickly as possible and then to bear off. There isn’t too much skill involved here, but in many instances there is definitely a right play and a wrong play.
As we discussed in Chapter 1, as soon as a player has brought all of his men into his inner, or home, table he can begin to take men off the board. On any given roll he may move men forward within his inner board, bear off, or both.
This brings up a very important consideration that we touched on briefly in Chapter 1: You don’t have to make the maximum move if you still play both numbers on the dice. Now look at the following position.
White to play 5-1.
You left a blot after your last play, but your opponent failed to hit it. Now you proceed to roll either 6-1 or 5-1. You play the 1 first and use it to move your blot from the give point to the four point. Now you use the 5 to bear that same man off. This way you don’t leave a blot. Had you played the high number first you would have been forced to use the 1 to expose a blot on your four or three point.
How should you play 6-3 in this position?
White to play 6-3.
You can either move forward from the five point to the two point with the 3 and then bear a man from the four point with the 6, or you can bear off the blot on the five point with the 6 and bear a man from the three point with the 3. Either play leaves a blot exposed to a direct shot.
At first glance the plays appear equal, but there is a decided advantage in making the second play: it gets two of your men off instead of only one. If black proceeds to hit your blot (wherever it is exposed), the game is likely to come down to a photo finish, and that extra man off man mean a win instead of a loss for you.
How to Bear Off
When you are bearing off and your opponent has no men on the bar or behind you in your inner table, bear off a man in preference to moving a man within the board. The reason for this is that the more quickly you bear off your men, the fewer rolls you will need to finish the game.
When you are reduced to the last couple of men, familiarize yourself with the chances of getting them both off in one roll from various positions. You can work these out, but as a start it would be helpful to study Table 4 on page 91 once more.
Even good players sometimes make wrong moves. Look at the following position; we recently saw a good player in white’s position play 6-2 badly.
White to play 6-2.
He used the 6 to take his man off the six point; but he used his 2 to move from the five to the three point, instead of moving his man on the three point down to the one point.
Black rolled 5-1 and made his best play, which was to bear off the man from the five point and move a man from the four to the three point. The wisdom of this play, and the folly of white’s became apparent a moment later. White rolled 6-2 again and of course could get only one man off; black rolled double 3, bore all three of his men off, and won the game.
White was unfortunate enough to lose the game because of the way he played the 6-2, but it was a bad play, properly punished. Leaving himself with two men on his three point meant that he had only seventeen rolls that would get both these men off. Those seventeen rolls were any combination of 3, 4, 5, and 6, plus double 2.
If he had used his 2 to move from the three point to the one, he would have left himself with one man each on the five and one points, and he would then have had twenty-three possible winning rolls. These rolls would have been any roll with a 6 or 5, plus double 4, double 3, and double 2.
As another example, suppose that you have borne off all but two men and they are left on your four and six points. You roll 3-2.
White to play 3-2.
Apart from the fact that you aren’t happy with that roll, you have two ways to play it. You can play it so you’ll be left with men on the four and one points, or on the three and two points.
If you leave them on the four and one points, you will be able to win the game at your next throw unless you roll 3-2, 3-1, 2-1, or double 1. In other words, you have seven bad rolls and twenty-nine good ones.
On the other hand, if you leave them on the three and two points, you won’t get off with any roll that includes a 1. There are eleven of these bad rolls as against twenty-five good ones — so you clearly want to move your men to the four and one points.
Eventually you should learn how to compute your chance of getting off in one roll. For practice, why not take pencil and paper right now and figure out a few other positions? If you want to check your computations, you can do so by referring to Table 4.