How Shall I Win This Game?

How Shall I Win This Game?
by Walter Trice – 4 July 2006

Backgammon is a complex game. In the course of analyzing a position and deciding on a play it is easy to get lost in the details – the counting of pips and shots, the comparisons with reference positions and other factors.

Those factors influence the stereotyped decisions about whether to hit, split, slot, point, break, jump, run, or anchor. One may lose track of the big picture, or even forget that it exists. That is when the big blunders come and the crucial plays get overlooked.

So I have decided to present some problems and analyses, now and in the coming weeks, that will illustrate the game planning process. Some expert readers will find some of the problems to be easy, especially when they are presented as problems. But I can assure you that any of them is capable of tripping up anyone who has forgotten to ask himself the question posed in our title. For others, future experts, who do not have under their belts the zillions of games that have contributed to the expert’s “big picture”, the problems will hopefully clear up some mysteries about plays that are obvious (on a good day) to some of us and utterly baffling to others.

How many ways are there to win a game of backgammon? Ask an experienced player this question and he may well say that the number is limitless. He will have played many thousands of individual games, all different from one another, except for a few standard opening blitz sequences quickly ended with a double and a drop. He will have learned to detect hundreds of subtle positional features that dictate different strategies in superficially similar positions, and if he has played long enough he will have learned that the one thing you can always expect in any given game is – the unexpected.

But I believe that fundamentally there are only three ways to win. Whenever you see a position in which one player has a substantial advantage, he has either a big lead in the race, a strong attack in progress, or a prime that pretty securely locks up one or more of his opponent’s checkers. The three ways to win are racing, attacking, and priming. I have learned that in backgammon it pays to keep an open mind, and I am still looking for a fourth way to win, but I haven’t found it yet.

Thus in a broad sense the game-planning problem is multiple choice. But since the dice are random, the choices are not mutually exclusive, and many positions contain the potential to evolve into any of the three types of advantages for either player, often more than once in any given game.

Let’s start with an easy one:

Problem 1: Red to play 4-3.

It’s always tempting, when you don’t roll what you need, to just do something safe and hope for a better roll next time. In this case the safe play would be 8/1. Actually that’s a blunder, and Red’s natural game plan suggests a much better move.

What is Red’s plan, given that it must be to win by racing, priming, or attacking? Well we can discount racing, down 34 pips. As for attacking, that might come about in the course of things, since Red has one man back and cannot anchor. Red could commit to an attacking plan right off the bat with 7/3* 7/4, hoping that White won’t roll the 3. Possibly Red could even pick up the other blot and close out both! But the offensive asset that stands out is the prime, so Red should think about using it to win.

Now the trouble with the prime is that it’s not good enough to do the job, with White sitting there at the edge just a six away from escaping – he is a favorite to escape in two rolls if left unhindered. Red would like to hit White’s blot off the edge or extend to a six-prime.

The stand-out play is 13/9, 13/10. Red gets hit if White rolls the 6, but a 6 was very strong anyway, so the hit doesn’t cost much. The 69% of the time White doesn’t get hit 6 Red is in great shape, with all aces and 6-5 to make the full prime, and literally every other roll hitting White’s blot.

Note that 13/6 would be very illogical, giving White good 6’s and good 1’s instead of just good 6’s, but it would still be better than 8/1. The last thing you want to do when you are trying to win by priming is to bury a checker out of play where it can’t help.

Problem 2: Red to play 3-2.

We need not count to see that Red is far ahead in the race. Does this mean that he should ignore other assets that produce priming and attacking chances, and just make the only safe play, which happens to be 9/7, 9/6? Not necessarily.

White is playing the game too. White’s primary game plan is to attack Red’s blot. It is hard to build an effective prime against a single blot, because it constantly threatens to escape, so one must generally take the hits and home board points as the dice present them. In the course of attacking White might still produce a prime that contains Red’s straggler effectively.

White’s chances of attacking or priming improve greatly if his back checkers can get into the action. For example, if Red plays 9/7, 9/6 he’ll be quite sorry if White rolls 6-6. The men on the 22, previously blocked, leap into action 6 pips away from the Red blot, making a broken prime that puts the blot in great jeopardy.

Red’s prime is potentially useful in many other scenarios too. White could attack successfully but then fail to escape, especially if Red extends his four-in-a-row to five or six. If Red’s blot escapes, the prime could keep White from getting into the race with big doubles and make it easier for Red to bear in, and off, safely.

Another possibility, which one sees frequently with a 22-point game, is that White could crash when Red still has a strong board, then get squeezed off the anchor and succumb to an attack.

So we see that Red’s solid four-prime is an asset well worth preserving, and that an alternative to 9/7, 9/6 should be sought, but which? Playing 7/4, 6/4 or 8/5, 7/5 make good home board points but leave a double shot that might let White simultaneously hit and escape a checker, and this is even more dangerous because Red already has one blot. Playing 8/5, 6/4 is pure and pretty, perhaps best if you know that White is going to roll 6-6, 5-5 or 6-5… but 32 shots with 3 blots is really overdoing it. Moving 13/10, 13/11 leaves a bunch of fly shots while making it easier for White to diversify in the outfield.

The right play is something easily overlooked until you have examined the alternatives. Playing 6/1* preserves Red’s assets. The fact that it is a hit softens the danger of leaving a second blot exposed to a direct shot. It works as a tempo play, slowing down White’s incipient attack. At worst, if Red gets hit, he is still playing 4-prime vs. 4-prime with the advantage of only two back to three. Playing 6/1* isn’t the sort of thing you’d really like to be doing. It either gets hit or buries a checker. But it is the least damaging out of a rather weak set of possibilities.

To properly appreciate the value of Red’s 4-prime, especially the point six away from White’s anchor, it helps to play the game out a few times and take note of the role played by the prime in what follows. Let’s just glance at a few of the innumerable possibilities after 6/1*.

Position 3: Red on roll. Cube action?

A lot has happened here. White advanced his anchor, Red got hit but managed to escape one checker, and added the 5 point to his prime. Now Red has a doubling advantage, with one back to three, and a five prime vs. a four. If he had not kept the 9 point he would have a good deal less, and certainly would not be doubling.

Position 4: White on roll. Cube action?

This time White did quite well, making a 5-prime and knocking Red’s blot back. The blot that Red hit with from Problem 2 never got re-circulated, and Red had to dump another one on the deuce point. White has enough to double, but Red can take. Without the 9 point he would have to drop.

Position 5: Red on roll – cube action?

Red had to make a big play, hitting two blots and leaving a direct return shot from the roof. But White missed, and a roll with a 6 left one of his checkers on the bar. Now Red’s position may look a bit shaky at first glance, but in fact it is crushing. In a match, or if he happened to own the cube, Red would be thinking about whether he is too good to double. The 4-prime is about to turn into a 5-prime, and quite likely to grow a 6th point before too long. White will have five checkers stuck behind it, and the value of a prime is proportional to the numbers of enemy checkers behind it. Once again Red can thank his 9 point, and the 6/1* play in Problem 2 (possibly now forgotten after all the excitement) for the strength of his position.

 

Here are the rollouts for the positions above:

 

Problem 1: Red to play 4-3.

Problem 2: Red to play 3-2.

Position 3: Red on roll. Cube action?

Position 4: White on roll. Cube action?

Position 5: Red on roll – cube action?