About
The pippish race formulas are a simple way of calculating cube decisions (double or no double, take or pass) based on the pip count. They work when both sides have low wastage, meaning checkers are spread across multiple points without big pileups on low points. For positions where one or both sides has significant wastage, other methods like Keith count or EPC are more accurate.
These formulas are based on Art Benjamin's PrimeTime articles: "The Art of the Long Race" (Fall 2020) and "Short Pippish Races" (Summer 2022).
When to use
The pippish race formulas should only be used to make cube decisions when both sides have pippish positions. A position is pippish if it has very little wastage, meaning not too many checkers on the 1, 2, or 3 points.
The quick test for pippishness is the 1-2-3 rule:
Let a, b, c be the number of checkers on the 1, 2, and 3 points. A position is pippish if all three hold:
- a ≤ 1 (no more than 1 checker on the 1-point), AND
- a + b ≤ 2 (no more than 2 checkers between the 1- and 2-points), AND
- a + b + c ≤ 3 (no more than 3 checkers between the 1-, 2-, and 3-points)
Advanced refinement: Minimum checker counts
Don't worry about this until you've mastered applying the formulas. Technically, a position can be not-pippish even if meets the criteria above if there are too few checkers on the board. Positions with profiles 000, 001, 002, and 010 (where the digits are a, b, c) are always pippish regardless of checker count. Other profiles (e.g., 011) need enough total checkers for the wastage to stay low: at least 8 for profile 011, at least 10 when a = 1, at least 12 when a + b = 2 or a + b + c = 3, and at least 14 when both conditions hold.
If the position is not pippish, use an alternative like the Keith count or EPC for more accurate cube decisions.
How to use
Step 1: Count the leader's pips.
Use any method you prefer (half-crossover, cluster counting, or just playing online with pip count turned on).
Step 2: Calculate the point of last take (PLT).
The PLT is the largest pip count at which the trailer should still take a double. It depends on the length of the race.
Let X be the leader's pip count ("floor" means round down):
| Pips | Rule | PLT | Interpretation |
|---|
| 19–29 | Trice | X + floor((X−5)/7) | Subtract 5, divide by 7, round down, add to pips |
| 30–60 | Pippish 9 | X + floor(X/9) + 1 | Divide by 9, round down, add 1, add to pips |
| > 60 | Long race | X + floor(X/10) + 2 | Drop last digit, add 2, add to pips |
In longer races, the PLT is higher relative to the leader's pip count (the trailer has more time to catch up). In practice, the PLT works out to roughly X + 2 or X + 3 for short races, X + 4 to X + 7 for medium, and X + 8 or more for long.
In shorter races (less than 19 pips), use the 3-checker or 4-checker rules instead.
Step 3: Count the trailer's pips and compare to PLT.
Count the trailer's pips. The cube action depends on the trailer's pip count relative to the point of last take that was calculated in Step 2:
Let Y be the trailer's pip count:
| Condition | Cube action | Interpretation |
|---|
| Y > PLT | Pass | Pass beyond the point of last take |
| Y ≥ PLT − 3 | Double (initial) | Initial double within 3 pips of PLT |
| Y ≥ PLT − 2 | Redouble | Redouble within 2 pips of PLT |
For example, if the point of last take is 72 pips, we can double if the trailer's pip count is 69 or more, or redouble if the trailer's pip count is 70 or more, and in either case the trailer can take if their pip count is 72 or less. (The leader needs a bigger lead to redouble than to send an initial double because by redoubling they also give up the advantage of exclusive cube ownership. But the take/pass decision is the same for initial doubles and redoubles, since the trailer will own the cube after they take either way).
Tips
1. Remembering point of last take
While this order of operations minimizes the amount of numbers you need to mentally juggle simultaneously, you still need to remember the point of last take while calculating the trailer's pip count. Consider techniques like holding the digits of the point of last take on your fingers while counting the trailer's pips (most useful if you use sign language to represent 0-9 on one hand), or even pointing at points on the board (e.g., the 4 and 7 points to represent 47). Whatever you use, it's useful to practice this and have a reliable way of storing the point of last take, to avoid getting stuck in a loop where you keep forgetting numbers and needing to re-calculate.