Bill Robertie

Holding Game — Building the Board

Aug 1, 2021 | Backgammon Problems: Holding Game

Cash game, center cube.

White to play 1-1.

This position shows a slightly unusual mutual holding game structure. Both sides have anchors, White on his 21-point and Black on his 18-point. Right now White trails in the race by 16 pips (123 to 107), but trailing in the race isn’t much of a disadvantage in these positions because the side that’s ahead in the race usually has to break anchor and expose himself first.

White has two decisions to make:

(1) Should he move the checkers on the 21-point or the 13-point, or leave them alone?

(2) What’s the best way to improve his inner board?

The first question is the easiest. Since White trails in the race, he wants maximum contact. The way to get maximum contact is to stay back as much as possible. so White doesn’t want to move the checkers on the 21 and 13-points unless there’s no recourse. In this case it’s even more important than usual to keep both points, because Black’s sixes are horrible if White stays where he is. Notice that in the current position 6-1, 6-3, and 6-4 all leave shots, while 6-2 and 6-6 continue stacking checkers.

So let’s leave those checkers on the 21 and 13-points alone and concentrate on the inner board.

If White wants to play only in his inner board, the obvious first choice is 4/1 6/5, building a 4-point board. It’s a perfectly safe play, and if White gets a shot next turn and hits, he won’t have to worry about an exposed blot. However, although it’s perfectly safe, it’s also poor technique. When building a board to prepare for future shots, the right idea is to build it as quickly as possible by slotting, covering, slotting, and covering. Playing 4/1 6/5 creates a 4-point board, but making the important fifth point will take a while.

A better try is 6/4 3/2(2), which creates a 4-point board with the fifth point slotted. Still, that slot on the ace-point is a little hard to cover. Better still is 6/4 3/1! which moves the slot backwards, where it’s in direct range of the 8-point. Now White has a 4-point board with the fifth point slotted and easy to cover. That approach gives him the best chance of having a 5-point board when he finally hits a shot.

Cracking a 6-Prime

Jul 1, 2021 | Backgammon Problems: Priming Games

Cash game, White owns the cube.

White to play 6-1.

In this position, Black has managed to build a full 6-prime, and White has one checker trapped behind it. A single checker behind a full prime is normally a pretty bad position. If Black could escape all his back checkers and arrange them on top of his prime, while White just filled in his board, Black would be about a 90-10 favorite, with gammon chances in the 5% to 6% range.

Fortunately, Black hasn’t yet escaped all his checkers, which gives White some extra resources. In fact, if he makes the right play here, his winning chances bounce up into the 25% range! That’s a hefty increase, so let’s see if we can figure out the best way to proceed.

Game Planning in the Middle Game

Jun 15, 2021 | Backgammon Problems: Middle Game

(A) Cash game, center cube.

Should White double? Should Black take if doubled?

(B) Assume White doubles and Black takes. White to play
(b1) 55
(b2) 33
(b3) 53

Holding Games with Stragglers

Jun 1, 2021 | Backgammon Problems: Holding Game

One of the most common middle game structures in backgammon is the holding game, where at least one side has made an advanced anchor, and the other side has to get his checkers home while leaving as few shots as possible. Holding games are even more common now than previously, because of the tendency to split the back men with most opening rolls, which tends to result in anchors for both sides.

Here are a couple of examples of interesting holding game problems:

(A) Cash game, center cube.

(A) Cash game, center cube.

White to play 6-2.

(B) Cash game, White owns the cube.

(B) Cash game, White owns the cube.

White to play 3-3.

Slotting in the Middle Game

May 1, 2021 | Backgammon Problems: Middle Game

Slotting is an easy idea to understand in the opening. When we slot the 5-point with an opening 2-1, we threaten to make a very strong point while unstacking a big stack. Since our opponent has no board, getting hit is just a minor inconvenience. Although it’s not a hugely correct play (splitting our back men is almost as good), it’s not a hard play to make because the downside seems pretty small.

Slotting in the middle game or the endgame is very different. Now your opponent almost certainly has a reasonable home board, so the cost from being hit is much greater. It’s also unlikely that you still have a stacked position at this point, so unstacking probably isn’t a big goal.

With a hit being more expensive and unstacking not so important, we’ve knocked out two of the three pillars supporting an early slot, and we’re reduced to just one: the value of the point itself. When we slot in the middle game, the point needs to be really important, and the chance of making it cleanly without slotting not so good. There is, however, a new factor affecting a middle game slot: the cube. A slot followed by a miss from your opponent may give you a good double, which in some cases is enough to tip the play in favor of slotting.

Root Numbers

Apr 15, 2021 | Backgammon Problems: Priming Games

Cash game, White owns the cube.

White to play 5-1.

Root Numbers

In backgammon, a root number is just a dice throw that damages or destroys your position. We mostly encounter these by accident, when we throw an awkward shot that can’t be played except by wrecking our inner board or leaving a bunch of blots somewhere.

Root numbers don’t always happen by accident, however. Sometimes the only way of saving a hopeless position is to notice that by making a certain play, you can create a few root numbers for your opponent which wouldn’t exist otherwise.