Backgammon race calculator
Paste a race position and get both pip counts, the Keith count and the 8-9-12 rule, each with its cube verdict, and ask the engine for its own answer beside them. It reads an XGID, a GNU Backgammon ID or an OGID, and the counting runs in your browser.
| Pips | Keith count | |
|---|---|---|
| White (on roll) | 72 | 73 |
| Black (opponent) | 79 | 80 |
- White: Checkers beyond one on the 2-point, +1
- Black: Checkers beyond one on the 2-point, +1
The cube is in the middle, so these are the initial doubling thresholds.
The engine runs in your browser, so asking it downloads the engine and a network (a few megabytes, once).
Counting pips
A checker's pip count is how far it has to travel to bear off: a checker on your 6-point needs 6 pips, one on the bar 25. Your pip count is the sum over all fifteen. Each roll moves you 8 1/6 pips on average, doubles included, so a lead of 8 pips is worth about a roll. In a race, where nothing can be hit any more, the pip count is most of the story, but not all of it: a checker stacked deep on the 1-point, or a gap on the 6-point, wastes pips that the raw count does not see. The two rules below are ways of correcting for that and turning the counts into a cube decision at the table.
The Keith count
Tom Keith built this count by testing it against computer analysis of many races, and it is one of the most accurate rules a player can work out at the table. Start from each player's pip count and add:
- 2 for each checker beyond one on the 1-point;
- 1 for each checker beyond one on the 2-point;
- 1 for each checker beyond three on the 3-point;
- 1 for each empty 4, 5 or 6-point.
Then add a seventh to the count of the player on roll. If that is more than the opponent's count by no more than 4, double (by no more than 3 to redouble). The opponent should take if it is more by at least 2, and pass if it is more by less than that, or lower.
The 8-9-12 rule
Work out the roller's lead as a share of the roller's own pip count. From 8% it is a double, from 9% a redouble, and the opponent can take up to 12%. It uses nothing but the two pip counts, so it is the quickest rule, and it is meant for long races. In a short race it misses how much the distribution matters, and the Keith count is the better guide.
When to trust the engine instead
Both rules are for money games and both are approximations; where they disagree with each other, the position is close. The engine does not approximate the race: it looks ahead over every roll, and in a short bearoff it reads exact tables rather than estimating. At a match score a double is worth what it does to your match winning chances, which neither rule knows, so there the take point comes from the match equity table, and the engine's verdict above already prices it.