The numbers to know
- Starting pip count: 167 per side (rules §3).
- An average roll moves 8.17 pips — the expected value including doubles. A normal turn is ~8 pips; doubles average 16-plus.
- Only the difference matters in a race — that, plus who is on roll. Being on roll is worth roughly half a roll (~4 pips).
Cluster counting
Count checkers in clusters — same-point stacks multiply, mirrored formations cancel. The opening position in clusters:
| Cluster | Arithmetic | Pips |
|---|---|---|
| 5 on the midpoint | 5 × 13 | 65 |
| 5 on the 6-point | 5 × 6 | 30 |
| 3 on the 8-point | 3 × 8 | 24 |
| 2 on the 24-point | 2 × 24 | 48 |
| Total | 167 |
Two speed-ups compound it: symmetry cancellation — regions where you and the opponent mirror each other contribute zero to the difference, so skip them — and reference shifts: count a messy stack as “all on the 5-point, plus 3, minus 1” rather than point by point.
The half-crossover method
Jack Kissane's tournament technique: count crossovers — quadrant boundaries each checker must still cross — instead of pips. Each crossover is worth ~3 pips (a half-crossover rounds to 1.5), giving a difference estimate accurate to 2–3 pips in a fraction of the time. Ideal for confirming “is this cube even close?” before doing an exact count.
Race formulas: turning counts into cubes
- Thorp-style rule of thumb: with a lead of about 8% of your count + 2 pips, double; the taker should be within about 12% + 2 pips of the leader.
- The 8-9-12 rule (Trice): in a medium race, take your own count as the base — a lead reaching +8% doubles, +9% redoubles, +12% is a pass.
- On-roll bonus: remember the roller effectively banks half a roll; formulas above assume you count before rolling.
When the raw count lies
Two positions with equal counts can have very different winning chances. The refinements:
- Keith count: penalizes stacked, gappy distributions before applying race thresholds — the practical standard for over-the-board race cubes.
- EPC (effective pip count): adds expected wastage to the raw count — essential in the bear-off, where a 3-stack on the ace-point “wastes” most of every big roll.
- Ward's formula: a refined Thorp variant for close redouble decisions.
The theme is always the same: smooth, even distributions race better than tall stacks — which is also why stacking the 6-point is a beginner leak.
Related: cube theory for what to do with the count, and the running game for playing the race itself. Boardgammon shows a live pip count at the table — practice estimating before you peek.