About
The Keith count is a method for making cube decisions in races. It adjusts each side's pip count to account for wastage (extra checkers on low points or gaps on high points), then uses the adjusted pip counts to determine the point of last take and cube action.
It gives accurate cube decisions for a wider range of positions than the pippish race formulas, which only apply to low-wastage positions.
The Keith count was developed by Tom Keith (original article).
How this formulation differs from the original
The Keith count approach described on this page is equivalent to the approach in the original article, but recommends structuring the calculations in a way that (in my opinion) is simpler and results in fewer mental calculation errors. The original Keith count computes adjusted pip counts for both sides, then compares them to get the cube decision. This version calculates the leader's adjusted count first, derives the point of last take from it, then compares the trailer's adjusted count against the point of last take to get to the cube decision. Feel free to try the approach in the original Keith article and use this if you find this easier.
When to use
The Keith count is a reasonable choice for a "default" race formula or a first pass at the cube action for almost any racing position. It does a decent job at recommending the correct cube action in most bearoff positions, including ones that are not pippish.
If both sides have pippish (low wastage) positions, the pippish race formulas are simpler and equally (or more) accurate.
If one or both sides have rollish (very high wastage) positions with many checkers piled up on low points, even the Keith count starts to fail, and more complex methods like EPC are needed to calculate the cube action over the board.
How to use
Step 1: Count the leader's pips.
Use whichever method you prefer (half-crossover, cluster counting, or just playing online with the pip count turned on).
Step 2: Add Keith penalties to leader's pip count to get the leader's Keith count.
Add these penalties to the pip count to get the Keith count:
| Condition | Penalty | Interpretation |
|---|
| Each checker beyond 1 on the 1-point | +2 each | 1-point spares are very bad (+2 pips each) |
| Each checker beyond 1 on the 2-point | +1 each | 2-point spares are somewhat bad (+1 pip each) |
| Each checker beyond 3 on the 3-point | +1 each | 3-point stacks are bad (+1 pip each beyond 3) |
| Each empty point among 4, 5, 6 | +1 each | Empty high points are bad (+1 pip each) |
Step 3: Calculate the point of last take (PLT).
The point of last take (PLT) is the largest Keith count at which the trailer should still take a double:
Let K be the leader's Keith count ("floor" means round down):
| PLT formula | Interpretation |
|---|
| PLT = K + floor(K/7) − 2 | Divide by 7, round down, subtract 2, add to Keith count |
After calculating, remember this point of last take (either make a mental note or consider using your fingers), since we'll need to retrieve it after counting the trailer's pips.
Step 4: Count the trailer's pips and add Keith penalties to get the trailer's Keith count.
Use the same penalties as Step 2.
Step 5: Compare the trailer's Keith count to the PLT to get cube decision.
The cube action depends on the trailer's Keith count relative to the point of last take that was calculated in Step 3:
Let T be the trailer's Keith count:
| Condition | Cube action | Interpretation |
|---|
| T > PLT | Pass | Pass beyond the point of last take |
| T ≥ PLT − 2 | Double (initial) | Initial double within 2 of PLT |
| T ≥ PLT − 1 | Redouble | Redouble within 1 of PLT |
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 and Keith 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.