Endgame Planning

Endgame Planning
by Walter Trice – 22 August 2006

Long-range planning doesn’t stop in the endgame. A player holding an anchor in a defensive position, with limited choices from roll to roll, still needs to be acutely aware of the different game plans that may become available to him.

Often you’ll see opponents (not yourself, hopefully!) play almost at random with their spare checkers outside the zone of contact, or else make semi-automatic, thoughtless plays that could have been rejected out of hand if just a little thought had been given to the needs of the position. But just as often these positions pose problems that call for thoughtful analysis.

Problem 1: Red to play 4-2.

Problem 1 could easily be dismissed as insignificant, and indeed the difference between the top two plays is less than 1% in winning chances for Red. But then, 1% is quite a lot in backgammon. Increasing your chance to win every single game by 1% would be enough to take you from the middle of the pack to being a frequent tournament winner.

The reason I noticed this position (which actually comes from a match) is that the player of the Red side made the wrong play and wound up losing the game as a direct result.

Red played 5/1, 4/2 – undoubtedly best if White immediately rolls 6-1 or 5-1 and Red hits. But these account for only 44 out of the 1296 2-roll sequences, or about 3%. Red is a good deal less likely to get a second chance to hit and still have a five point board. If Red fails to hit immediately then he’ll have to run, with or without leaving a blot behind, or else break his board anyway.

What Red needs to see is that his chance of winning a plain race is not bad at all. He is 11 pips behind and, of course, a distinct underdog, but if he rolls a decently large set of doubles he will be at least back to even. Saving the home board point at the cost of burying two checkers while leaving men on the six and a gap on the five hurts him quite a bit in the racing variations that make up his best chance of winning the game. Red can play 6/2, 6/4, which may result in his later being able to bear off two checkers with 5’s instead of having to bury them on the ace point. In so doing he can still benefit from a hit in the outfield by gaining ground in the race. He will still have a four point board; most of the time (64%, actually) if White would have danced on the five point board he will still be dancing on the four-pointer.

I have given away the ending, so I won’t bore you to death with the whole plot. Experienced mystery fans will already have guessed that Red rolled 5-5 later on in this game. In fact he rolled the “snowflakes” three times. Twice the fact that he had buried checkers and left the gap did not matter, but along the way he had to play 6/1 twice, which cost him the game by exactly one roll!

Problem 2: Red to play 5-3.

We have seen problems somewhat similar to #2 in a previous article. Red is probably focused on attacking as he contemplates playing his 5-3 roll, but he should keep in mind the possibility that he might want to build a prime and win that way if he does not get the rolls he needs to close White out. For instance, if White brings both checkers in, Red would rather not have anything better than a loose hit with several blots around the board. He is still out-boarded four to three. His biggest edge over White, after the immediate initiative, lies in his priming chances, since all his checkers are alive for priming while White has six dead men behind Red’s anchor.

Hence 10/7 with the three is an absolute must! A blot on the seven does double duty as a builder for home board points and as a slot for the fifth of six consecutive points.

For the rest of the play Red must choose between adding a builder (11/6) and escaping a back checker (21/15). This part is not so easy. I have no simple explanation of why 21/16 ought to be the best way to play the five, though it is what I would have played. But it should be fairly evident that just building his prime is the most comfortable and risk-free way for Red to go about winning the game. When you have crashed with 4-4 from this type of position as many time as I have over the years you learn to take these chances to break out a spare checker when they come, even when they come before the escape begins to feel urgent.

Against a weaker White home board it might be better to place more emphasis on the attacking possibilities.

Problem 3: Red to play 4-1.

In Problem 3 Red is down so far in the race (even apart from his having four men back) that he is probably going to get gammoned when he loses. In addition White has two very badly placed checkers on his deuce point, so Red’s chances of hitting a shot and winning the ace-point game are a lot better than usual. Refusing to play past the six point in an effort to avoid wasting pips in the race to save the gammon would be seriously misguided here, when Red has a chance of an immediate shot (on White’s 6-5, 6-4, or 5-5) and a home board blot to cover. 8/4 is quite clear with the four.

Finding the right ace takes just a little common sense and foresight, even though the two logical candidates seem to be pretty close. Assuming that Red hits on his next turn, he won’t be all that eager to go hitting loose in his home board, since White will still have four or five points. And what if White hops from the bar into Red’s outfield with something like a 6-3? Then Red will want to be split to give himself the best chance of hitting again. So his best ace now is 13/12.

Later on in the game, assuming that Red does not hit immediately, he will almost surely roll the ace that lets him diversify his home board builders or the three that lets him slot the next open point. But for now, outfield control is the most important factor.

Problem 4: Red to play 4-2.

The race is even, but Red’s anchor puts him at a disadvantage. At some point he is likely to get squeezed off the anchor and come under attack. Should he, then, save as many outfield sixes as he can and try to defer the squeeze as long as possible, by playing 5/1, 3/1?

This sort of play is a common error. All Red buys himself, usually, with his “six-saving” efforts is a one roll window of opportunity to roll 6-6 or 5-5. If this window is missed then the squeeze happens anyway (or else the joker falls outside the window so that the six-saving was unnecessary.) Meanwhile there is a very real cost if Red has damaged his home board in the process, as 5/1, 3/1 would do here by leaving a gap on the three point. Red could save himself the trouble of having to roll a racing joker by hitting a shot. With a strong board a hit should win, but with a trashy board it might not. White has a blot in the outfield and Red could hit it before it finds safety. Red might also hit on White’s midpoint when White breaks it.

If Red later has to break anchor before he rolls the big doubles, a strong board may still save him. White won’t always point on the blot that is left behind. If he has to hit loose then Red may be able to hit back in return. That return hit is more likely to win the game if Red does not have a gap among his home board points.

 

Here are the rollouts for the positions above:

Problem 1: Red to play 4-2.

Problem 2: Red to play 5-3.

Problem 3: Red to play 4-1.

Problem 4: Red to play 4-2.