**Cash game. Center cube. White on move.**

**Part (a): Should White double? Should Black take if doubled?**

**Part (b): Should White double? Should Black take if doubled?**

**Part (c): Should White double? Should Black take if doubled?**

One note before we begin. When I said ‘Cash game’, I meant ‘Cash game with the Jacoby Rule in effect.’ The Jacoby Rule simply states that you can’t win a gammon unless the cube has been turned. Every cash game I’ve ever played has had this rule in effect, (except for a few weird chouettes I played long ago in Istanbul), so I didn’t mention it explicitly, but I should have. For future problems, always assume ‘cash game’ also means ‘Jacoby Rule in effect’.

**Backgame Review**

A backgame is a position where one side (the side playing a backgame) has established two or more points in his opponent’s inner board, while his opponent (who is said to be defending against the backgame) has a prime in front of the points. In our diagrams, Black is playing a backgame, and White is defending.

Both conditions need to be met for a position to be a backgame. If one side has a bunch of men in his opponent’s inner board, but his opponent hasn’t built at least a four-point prime, the position isn’t a backgame, since the player with the checkers back can (and almost certainly should) try to slither some checkers into the outer board. We call these and many other related positions proto-backgames. They might turn into backgames, but then again they might not.

Backgames are labeled by the points that the backgame player holds. The three positions given above are examples of a 1-3 backgame, because Black holds the 1 and 3-points in Black’s board. The 1-2, 1-3, and 2-3 are sometimes called the deep backgames, because the backgame player has points deep in his opponent’s board. Backgames like the 3-5 or 2-4 are sometimes called high backgames, for the obvious reasons.

Backgames depend upon timing. A backgame player is said to have timing when he’s able to move his remaining checkers and wait for a shot without destroying his home board. A backgame position that’s likely to be good when a shot comes is said to be well-timed; otherwise it’s poorly timed. Unlike normal positions, in backgames you want to be well behind in the race, and the further behind you are, the better.

**Ranking Backgames**

Not all backgames are created equal. To win a backgame you need to be able to do three things:

(1) Get a shot.

(2) Hit the shot.

(3) Win after hitting the shot.

Condition (2) is obviously a matter of luck. Your backgame might yield a triple shot, but if you miss it, that’s just bad luck. Conditions (1) and (3), however, are inversely correlated. The more likely a backgame is to get a shot, the harder it is to time, and therefore the less likely it is to win after hitting. The best backgame for getting shots is the 1-2 backgame, which can often generate a whole series of shots as the opponent tries to clear his points. However, the 1-2 requires immense amounts of timing, which is almost impossible to obtain in practice.

In my experience, the best backgame is the 2-4, which combines ease of timing with the ability to generate a lot of shots early. Close behind is the 2-3. After those come the group of high backgames: the 2-5, 3-4, 3-5, and 4-5. These are relatively hard to prime and generate shots early. They don’t get as many shots as the deep backgames, but they don’t lose as many gammons either. The true deep backgames, the 1-3 and the 1-2, are very hard to time and lose lots of gammons and backgammons, but do generate lots of shots. Bringing up the rear are the 1-4 and the 1-5, which are little more than glorified ace-point games.

Note, by the way, that ranking backgames has only a little practical significance. Unless you roll a particularly opportune set of double-aces or some other small number, you mostly can’t upgrade your weak backgame to a stronger one. But knowing the rankings might help us avoid some bad backgames in the first place.

**Doubling in Backgames**

Once a backgame has been established and a containing prime has been built, we reach positions like 25a through 25c. Here and for awhile, the checker play for both sides is fairly simple.

White will bring his spares down on top of his prime, trying not to get hit in the process. If he throws a good number, he will make his 2-point. If he doesn’t make the 2-point naturally, he will need to decide if he wants to slot the 2-point, and pick a good time to do it. Eventually he will move all his spares into the home board and start to dismantle his prime from the back.

Black, meanwhile, will slot the front and back of his prime and try to build a strong position as soon as possible. If White leaves a shot somehow, Black in general will try to hit it and contain it. Rolls like 4-4 and 5-5 will crush Black’s timing. If he rolls 6-6, he will often have to abandon the 22-point anchor and play a well-timed ace-point game rather than a poorly timed backgame.

During this phase of the game, the doubling window is very narrow. “Doubling window” is simply a term used to describe the set of positions where double and take are the correct options. The doubling window is said to “open” when White has a marginal double, at which point Black will have an easy take. The window “closes” when White has an optimal double and Black has a close take/pass decision. Positions within the window are double and take, while positions outside the window are either no double and take or double and pass. In blitz positions, or positions with a lot of blots strewn around the board, the doubling window is very wide. Even a few variations where you vacuum all the blots and gammon your opponent will justify an otherwise early double. But in long races or backgames, the window is typically very narrow. The vast majority of rolls result in little or no fundamental change to the position, so the side with the edge has no need to rush. You can creep up to a double slowly, and double when your opponent just barely has a take.

These three positions illustrate exactly this idea. In (a), Black trails by just 49 pips in the race. That’s not enough timing, and the position is double-pass. In (b), Black has 55 pips of timing. That’s a little better, and Black just barely has a take when White doubles.

Position (c) shows the other end of the scale. Now Black trails by 65 pips, and he has an easy take, while White just barely has enough of an edge to turn the cube.

These last two numbers, 55 pips and 65 pips, are what I call the *characteristic numbers* for this particular backgame structure. By remembering those, you can handle the cube properly in these and a lot of related 1-3 backgame positions. However, let’s be clear that these numbers apply only to backgames of a very particular structure. The following conditions have to be satisfied:

(1) Black has a 1-3 backgame with no additional checkers behind White’s prime.

(2) White has a 5-prime from the 4-point to the 9-point.

(3) There is no significant contact in the outer boards.

(4) Black’s home board is structurally sound. (He doesn’t have a gap on his 5-point, he hasn’t made his ace-point, things like that.)

If we keep a 1-3 backgame but start changing some other features of the position, the characteristic numbers will change, sometimes dramatically. Here are a few examples.

> If we add a fifth checker back for Black, but on the edge of the prime (the 22-point), Black needs about 10 more pips of timing to take. So he’d need to trail in the pip count by about 65 pips for the position to be double and marginal take.

> If we add a fifth checker back, but not at the edge of the prime (say on the 24-point) then Black needs about 15 more pips of timing for a take.

> Breaking up Black’s home board a little, say by moving his checkers from the 5-point down to the 2-point and 3-point, has the effect of requiring 10-15 more pips of timing than in the basic position. The more easily he can fill in the 5-point with his remaining checkers, the less extra timing he needs.

In short, once you remember the 55 pip – 65 pip numbers for the edges of the doubling window in the basic structure of a 1-3 backgame, you can make some educated guesses for a lot of real positions and handle the cube much better than most.