The Timmes Race Rule

By Henry Timmes · First published October 9, 2026 · Updated October 10, 2026

A pip-count method for doubling decisions in backgammon races, built on Axel Reichert's Isight count. Its new idea: the boost and the doubling window change with the length of the race. On Tom Keith's 51,502 rolled-out positions from real games it makes 23% fewer cube errors than Isight (whole-pip version) or 26% fewer (exact version), and about 35% fewer than the Keith count, measured on positions it was never tuned on.

The rule

Exact version (most accurate): in races of 30 pips or less use 1½ per extra checker; ½ per checker beyond 2 on the 3-point; ½ per checker beyond 4 on the 6-point; and in races of 12 pips or less double if the difference is 8 or less. Everything else is the same. The Backgammon Pip Trainer app lets you choose either version.

Short bear-offs: 12 pips or less, both sides home

In the last few rolls being on roll is worth so much that a plain count misleads. Count wasted pips instead, like an effective pip count. For each side:

Example. White, on roll: 2 on the 3-point and 1 on the 4-point (10 pips): 10 + 3 + 2 + ½ + 1½ (three checkers) = 17. Black: 2 on the ace point and 1 on the 2-point (4 pips): 4 + 3 + 4 + 1½ + 1½ = 14. Difference 17 − 14 = 3: no more than 7 − 1.7 = 5.3, so double; White is behind, so Black takes. The rollout agrees (example 1 below).

On Keith's short races (12 pips or less, both sides home) this cuts the error from 24.6 to 19.0 millipoints per decision on the half it was not tuned on. It is the same for both versions of the rule.

Worked example. White, on roll: 73 pips, one more crossover than Black, and an empty 5-point while Black holds his: 73 + 1 + 1 = 75. Black: 81. Over 60 pips, so the boost is 1/6: 75 + 12.5 = 87.5. Difference 87.5 − 81 = 6.5: 7 or less (double) and 2 or more (take), so double / take. GNU Backgammon agrees.

Results on real games

Seven methods were scored on Tom Keith's database of 51,502 rolled-out positions from real games, using Keith's and Reichert's error measure (equity lost on the double, redouble and take decisions). The positions were split in half: the Timmes rule was tuned on one half only, and the figures below for it come from the half it never saw.

Average loss per decision in millipoints (lower is better) · share of decisions wrong. Millipoints on the held-out half (25,751 positions); % wrong over the whole database.

Positions per band: 4,250 · 13,871 · 22,982 · 10,399. Our code reproduces the published totals for Keith (1,262) and Isight (1,064; 7.1% wrong). Isight was tuned on the whole database.

Other checks

Four real positions where it beats Isight

Each position comes from Tom Keith's database, from the half the rule was never tuned on, with White on roll and the cube in the middle. The equities are Keith's rollouts, shown for White per point of cube value. Doubling is right when Double/take beats No double; taking is right when Double/take is below +1.000, which is what White gets if Black passes.

These four were chosen because Isight's mistakes there are large; see sixteen randomly chosen positions, both ways. It isn't right every time: on the held-out half, the whole-pip version is right and Isight wrong on 1,256 double and take decisions, and Isight right and Timmes wrong on 811. For the exact version it is 1,179 against 677.

See 16 random positions, both ways: where Timmes wins and where Isight wins →

Effective pip count in the bear-off

In a bear-off the plain pip count understates how long you need, because some pips are wasted: a 6 that takes a checker off the 2-point wastes 4. Walter Trice's effective pip count (EPC) adds the waste back. It is the expected number of rolls to bear off, times 49/6.

Example. 1 on the 2-point, 2 on the 4, 1 on the 5, 2 on the 6 = 27 pips. 27 + 4½ + 1 (2-point) + 1 (gaps on the 1 and 3) = 33.5. The exact EPC is 33.5.

We computed the exact EPC of every possible bear-off position (54,263 of them; ours match Trice's and Matussek's published figures) and scored each rule on the bear-offs that actually occur in Keith's real games (75,616 sides).

The first column is the half of the positions the rule was not fitted on. With 8 checkers or fewer, Joachim Matussek's seven-number formula is more accurate; use it there if you know it. For a pure stack on the ace point use Trice's exact rule: 7 × rolls + 1.

Credit where it is due

The Timmes Race Rule refines earlier work. New here: the boost and window that change with race length, the heavier checker penalty in short races, the retuned stack penalties, the short bear-off count, the Timmes EPC rule, and the measurement behind them.

Still open

• More to remember than Isight: a table of four race lengths. The whole-pip version keeps the sums simple.
• Short bear-offs are still the hardest part: even with the short count the error there (19 millipoints) is several times the average. Exact tables remain better.
• Independent replication: code and data are available on request.

Comments and corrections are welcome: [email protected].

How to cite

The rule is built into Backgammon Pip Trainer, which shows the verdict and its sums after every race position.