Neil's Numbers: The Mental MWC Toolkit

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 is the mental compression of that table into a few dozen anchor values and a small number of derivation rules. Developed by Neil Kazaross — the same Kazaross of the Rockwell-Kazaross MET — and refined over years of his published lectures and clinics, the system gives tournament-level players a way to compute MWC to within 1–2% in their head, in seconds, at the score combinations that matter most.

This page covers the anchor values, the derivation rules, 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.

1. 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:

$M = 0.5 + 0.87 \times \frac{D}{T + 6}$

(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.

2. The Three Canonical Anchors

Kazaross's published "starting set" consists of three away-score combinations whose MWC values are deliberately spaced across the equity surface, so they can be used as reference points for interpolation:

Memorising just these three values is sufficient to anchor most of the in-match equity landscape for matches up to 9 points. The system extends with additional anchors for longer matches.

3. The Extended Anchor Set

Strong players memorise an extended set of approximately fifteen to twenty anchors covering the asymmetric scores from 1- to 5-away. The extended set:

The mirror cells (e.g., 2-away/1-away) are simply $100\%$ minus the player's MWC at the reversed score.

These eighteen values together cover essentially every reachable score combination in matches up to 7 points, which is the most-played match length in serious tournament play.

4. The Derivation Rules

For away-scores not in the memorised set, Kazaross's system uses three structural rules to derive intermediate values:

Rule 1: The Symmetry Rule

If the player and opponent are at the same away-score, MWC is 50%. This is a direct consequence of the conservation law $M(a, a) = 50\%$ derived on the match equity page.

Rule 2: The Trailing Decay

For a fixed leader-away $a$, the trailer's MWC at $b$-away decays approximately geometrically as $b$ grows:

$M(\text{trailer}, b) \approx M(\text{trailer}, b - 1) \times (0.7 \text{ to } 0.85)$

The decay coefficient is closer to 0.7 in the early-trailing region (small $a$) and closer to 0.85 in the deep-trailing region (large $a$). Memorise the 1-away column values and the rest of the trailing column is reconstructable.

Rule 3: The Cube-Turn Reduction

If the cube has already been turned to 2, the effective post-cube score is shifted by the cube-value. For practical mid-game cube decisions: