Bill Robertie

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.

The Squat Zone

Apr 1, 2021 | Backgammon Problems: Middle Game

In the 1970s, the New Yorkers invented a term for the new style of backgammon they were playing, a style based upon aggressive hitting and slotting. They called it pure play. The essence of pure play was the willingness to take risks in the race to build a crushing prime quickly. If the plays worked, you had a winning prime. If your opponent got lucky and hit you a few times, you just had to outplay him in the resulting back game/holding game. (Since the top players played these complex positions very well, this was usually no problem.)

Cash game, center cube.

Black to play 3-2.

While they were naming their own style, the New Yorkers also coined a name for the opposite style – the beginner style of playing safe and stacking up your checkers. They called it playing squat.