About

In backgammon match play, it is often useful to know a player's match-winning chances at a particular score. (Some specific examples where this is useful are discussed below). One way of doing this is to memorize a match equity table. This works, but requires more up-front memorization, and numbers can be forgotten over the board. Neil's numbers (named after Neil Kazaross) are a shortcut to approximately compute match-winning chances by memorizing just a few numbers instead of a whole grid of match-winning chances.

To use Neil's numbers, you will memorize calculate the trailer's away-score (how many points they need to win the match), remember Neil's number for this score, then multiply this number by the size of the lead (in points) and add to 50% to estimate the leader's match-winning chances.

When to use Neil's numbers

Neil's numbers only produce accurate match-winning chances when both players are 3-away or more (i.e., they are inaccurate when the leader is 1-away or 2-away). To estimate match-winning chances at those scores, you will need to memorize the values directly from the match equity table.

When is it useful to know match-winning chances in the first place?

One direct (and high-stakes) application of the match equity table is deciding whether to take a large cube. Say you are leading 5-3 in a match to 11 points, and your opponent has just redoubled to 8. Should you take or pass? If you take and lose 8 points, you lose the match. If you pass, the score will be 5-7 in an 11-point match, where (thanks to Neil's numbers) you know you have 36% match-winning chances. Therefore, you should only take the cube if you win this game more than 36% of the time. Deciding whether you win more or less than 36% game-winning chances is a separate skill, but it's enough to notice that this is much higher than the normal money takepoint (25%), so if it would be anywhere near a reasonable double for money you should probably pass.

Game-winning chances at various scores are also a useful input into more subtle match-score-based checker and cube decisions. See Kit Woolsey's article Five Point Match for an introduction. Learning match play is a useful skill to help move from the intermediate to advanced or open level.

How to use

Step 1: Recall Neil's Number for the trailer's away-score.

Step 2: Multiply the score difference by Neil's number, and add to 50% to get the leader's match-winning chances.

Example

Leader is 3-away, trailer is 8-away.

1. Neil's Number for 8-away: 6%/pt
2. Score difference: 8-away − 3-away = 5 pts
3. Leader matching-winning chances ≈ 50% + (5 pts) × (6 %/pt) = 80% (actual MET: 80.5%)