Long backgammon tactics

Two resources: tempo and structure

Every turn you spend your dice either on tempo — progress in the race — or on structure: points that get in your opponent’s way. Strong play is seeing which of the two is worth more right now. Behind in the race, look for a block; ahead, keep it simple and run.

Inside the engine that balance is a number, not a metaphor. The registry of tactical concepts holds 11 entries, of which 10 carry weight in the position evaluation: checkers borne off, pips, blocking, the prime, containment, roll coverage, trapping, stacking, home readiness and home gaps. The eleventh — the awkward point six pips from the head — carries no weight on purpose: the engine does not measure it yet, and the number from the guides stays a hypothesis rather than a coefficient, so it works only as a mistake detector in the Academy.

Stacking: why a tall tower loses

Stacking is piling checkers onto one or two points instead of spreading them. It looks safe and quietly narrows your options: an extra checker on an already closed point adds no new legal move at all. The engine flags stacking when a point holds four or more checkers — taller than the tower the reference move would build.

The extreme case looks like this: instead of spreading a group across several points of the route, a player gathers eight checkers on one point two steps from home and leaves the remaining seven on the head. Two overloaded points instead of five or six working ones — every roll then has at most two directions to go.

Spare checkers: fuel for the block

A wall holds as long as you have something to move other than the wall. Strong players deliberately keep 2–4 free checkers in transit outside the block — spares that absorb awkward rolls. Without them the first bad roll forces you to break your own blockade.

There is an honest open question here. Classic guides count spares in pips — about five spare pips — while the ProNardy model counts free checkers, two to four of them. Different units, different numbers; which measure predicts wins better will be settled by statistics over many games, not by the authority of a source.

The opposite of keeping spares is running too far too fast and leaving emptiness behind. A naive evaluation that looks only at pips reads this as progress, because the checkers are closer to home. In fact the position loses exactly the slack that used to absorb bad rolls and turns rigid: the next roll has nowhere to go without damaging the structure.

The six-point wall: building it and keeping it

A wall is six consecutive points under your checkers, closing your opponent’s route completely. With no hitting, a point costs one checker rather than two: six points cost six checkers and leave the other nine in play.

All 36 combinations of two dice are equally likely — a principle set out by the Department of Mathematics at the University of Hawaiʻi. Within that space, a distance of 6 points is covered by 17 combinations: a straight six on either die gives 11, pairs summing to 6 give five more (1-5, 5-1, 2-4, 4-2, 3-3), and the double 2-2 covers the same distance in three of its four steps. That is 11 + 5 + 1 = 17. A distance of 7 points, by contrast, is covered by just 6 combinations, all of them pairs summing to seven — no double produces a seven.

Hence the practical rule: price a block by the opponent rolls it kills, not by the points it occupies. The point six pips ahead of your opponent’s mass is the most expensive square on the board for exactly this reason.

A solid wall is rarely built in one go, so the efficient route is a sieve: a sparse frame with one or two points skipped, later grown into a full block — filling the gaps is easier than seizing six points at once. Another device is duplication: a move after which your opponent needs the same die number for two different jobs. It halves their window without spending a single extra checker on blocking.

Sealing the wall is not always legal: the rules of long backgammon forbid it when no opposing checker is left ahead of the barrier. At the start of a game that is precisely the case, so a prime right in front of the opponent’s head is forbidden.

How to bear off in long backgammon

Greed loses the bear-off. If your home board has an empty higher point (a gap), the big dice keep falling into emptiness and burn: the six or five that should have taken a checker off goes into a worse move instead. The correct order has two steps:

1. Fill the gaps on the higher home points while the board is still uneven.
2. Only then bear off, no longer worrying about the order of points.

That is the exact opposite of the greedy “take off everything you can, right now” — and it is the difference the computer sees in a game review.

The awkward point six pips from the head

The point exactly six steps from your own head has a nasty property: a lone checker leaves it into the next quadrant only on a 6 — one number out of six. From the point five steps out it is already two numbers, and one step from the quadrant edge it is all six. So you keep two checkers there, or none.

The same point with two or more checkers is a strong holding: it appears in both canonical opening schemes, 1-4-6 and 2-5-6.

What not to do in long backgammon

After every game the ProNardy Academy looks for exactly four kinds of mistake and shows which move each one was played on.

What the 8-9-12 rule is

The “8-9-12 rule” belongs to doubling-cube theory, not to the choice of points to close. According to The Gammon Press, in a pure race with no contact the first double is justified from an 8 % lead in the pip count, a redouble from 9 %, and accepting an opponent’s double is worth it only while you trail by no more than 12 %.

None of those numbers apply to long backgammon: there is no doubling cube here at all, it belongs to the short game. The version of the same rule read as “the points to close” is not confirmed by any of the sources we worked through — it looks like oral folklore rather than a canonical rule.

Training tactics: the Academy and computer levels

Every one of these decisions can be tested against the computer at three levels inside the game. Easy looks one move ahead and sees the race only, with no understanding of blocking. Medium also looks one move ahead but uses the full evaluation, so it knows how boxed in the opponent is. Hard searches two plies: an expectimax, where the chance node returns the average weighted by the probability of each outcome (Carnegie Mellon University course notes). The engine takes its own top 10 moves by the fast evaluation and, for each, averages the result across all 21 distinct opponent rolls: 15 non-doubles weighted 2/36 and 6 doubles weighted 1/36.

That picks the move that is best not in the abstract but against the opponent’s best reply. After the game the Academy walks through every move you played and names the mistake from the table above if one occurred — which is where the difference shows between a move that felt fine at the time and a move that was actually throwing rolls away.