Neil's Numbers Developed by Neil Kazaross
The full Match Equity Table is roughly 600 cells of precise numerical equity, indexed by both players' away-scores. Holding all 600 values in working memory while also tracking the position on the board, the dice probability distribution, the gammon prices, and the cube context is not how any human plays — not even the world's strongest.
Neil's Numbers compress that table into one number per trailer score and one line of arithmetic. They are named after Neil Kazaross — the same Kazaross of the Rockwell-Kazaross MET — and they let a player estimate the leader's MWC in their head, in seconds, when both players are 3-away or more.
This page covers the numbers, the formula, the table values you still need at close scores, two worked examples, and the limitations.
For the full table the heuristics approximate, see /mathematics/match-equity/. For the cube-equity formulas that consume MWC values, see the same page.
Why a Mental System Is Needed
A tournament match is played under a clock. The standard match clock allocates each player roughly 12 seconds per move plus 2 minutes of reserve time per point of match length. A 9-point match gives each player about 18 minutes of reserve total. Meaningful cube decisions — the ones where a percentage point of MWC matters — must therefore be made in single-digit seconds, against full positional analysis, full gammon-and-backgammon-probability estimation, and current-game equity assessment.
The Janowski formula, covered on the match equity page, gives a closed-form approximation:
M=0.5+0.87×T+6D
(the pre-Crawford form — see the match equity page for the Crawford-specific variant). The formula is useful, but the arithmetic (a division by T+6, then a multiplication by 0.87, then an addition) is not instant under clock pressure. Memorised anchor values — Neil's Numbers — are.
Each trailer away-score has its own number: the extra match-winning chance, in percentage points, that one point of lead is worth to the leader at that score.
| Trailer away | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|
| Neil's number | 10 | 9 | 8 | 7 | 6½ | 6 | 5⅔ | 5⅓ | 5 | 4¾ | 4½ | 4¼ | 4 |
From 3-away to 6-away the number is simply 13 minus the trailer's away-score. Beyond that, three values carry the rest: 8-away = 6, 11-away = 5, 15-away = 4; the scores in between are interpolated.
The estimate is then:
Leader’s MWC≈50%+(difference in away-scores)×Neil’s number of the trailer
Table Values You Still Need
The formula only holds when both players are 3-away or more. When the leader is 1-away or 2-away it is inaccurate, and those values are memorised straight from the match equity table. The pre-Crawford Rockwell-Kazaross values most often needed (rounded to one decimal):
| Score (a / b) | Player a's MWC |
|---|
| 1 / 2 | 67.7% |
| 1 / 3 | 75.1% |
| 1 / 4 | 81.4% |
| 1 / 5 | 84.2% |
| 2 / 3 | 59.9% |
| 2 / 4 | 66.9% |
| 2 / 5 | 74.3% |
The mirror cells (e.g., 2-away/1-away) are simply 100% minus the player's MWC at the reversed score, and equal scores are always 50%.
Using the Numbers in a Cube Decision
A cube decision compares three outcomes: take and win, take and lose, and drop. With the cube at 2, taking and winning moves you two points closer to the target, taking and losing moves your opponent two points closer, and dropping gives your opponent one point. Read the MWC for each of the three resulting scores — from Neil's Numbers when both sides are 3-away or more, from the table otherwise — and compare.
Worked Example 1: Estimating a Score
Score: you are 3-away, your opponent is 8-away.
- Neil's number for the trailer (8-away): 6.
- Difference in away-scores: 8−3=5 points.
- Estimate: 50%+5×6%=80%.
The Rockwell-Kazaross table gives 80.5% — close enough for any decision made over the board.
Worked Example 2: A 7-Point Match Cube Decision
Position: 7-point match. Current score: 5-3 (you leading). You are 2-away; opponent is 4-away. Opponent doubles you to 2. Your current-game winning probability, estimated from the position, is 28%.
- Take and win: you win the match with the 2-cube. MWC: 100%.
- Take and lose: opponent gains 2 points and the score is 2-away vs. 2-away. MWC: 50%.
- Drop: the score is 2-away vs. 3-away. You are 2-away, so this comes from the table, not the formula: M(2,3)=59.9%.
Take: 0.28×100%+0.72×50%=64%. Drop: about 60%. Take, by roughly 4% match equity.
The Post-Crawford Free Drop
At 1-away vs. 2-away after the Crawford game, the trailer doubles at once:
- Take and win: 100% (match over).
- Take and lose: the opponent wins the match. MWC: 0%.
- Drop: 1-away vs. 1-away (DMP). MWC: 50%.
With an even game, take equity is 0.50×100%+0.50×0%=50%, exactly the same as the drop. This is the canonical free drop window in post-Crawford play: if the position is even slightly worse than 50% for the leader, the drop is correct.
Limitations
Neil's Numbers approximate the MET; they do not replace it. Three categories of decision where the heuristics fail:
- Gammon-rich positions. The Neil's Numbers system assumes "normal" gammon prices. In positions with extreme gammon distortion (e.g., late-game blitz positions with 60%+ gammon probability), MWC must be computed with the gammon multiplier built in, and direct MET lookup beats heuristic interpolation.
- Close scores. When the leader is 1-away or 2-away the formula is inaccurate; use the table values above or the full MET.
- Cube ownership asymmetry. When the cube is owned by one player at value 4 or higher, the doubling possibilities open up secondary recube decisions that the Neil's Numbers anchor values don't directly capture. Modern engine analysis (XG, Wildbg) is the only reliable resolution at these positions.
For the matches and score combinations that comprise the vast majority of competitive play, however — 5- and 7-point matches at common score asymmetries — Neil's Numbers is the standard mental toolkit, and is taught explicitly in most strong-player coaching programmes.
See Also
