Last updated on April 4, 2025
In this Deluxe Backgammon post for beginners, we take a look at the concept of Match Equity in backgammon. It can be quite an intimidating concept for newcomers to the game. However, it is important to understand the concept to advance to an intermediate level and beyond. It only applies to match play as opposed to money play or single games.
Match equity is a concept in backgammon that refers to the likelihood of winning a match, which is a series of games played between two players. In a match, each player begins with a target of a certain number of points. The first player to reach the predetermined number of points wins the match. Typically, matches are played to 5 or 7 points. However, this can be as high as 25 points in tournament play. This is in contrast to money play, where players simply play individual games for agreed stakes. In match play, scores are typically referred to in terms of the number of points each player is away from victory. For example, if a player is leading 5-4 in a 7-point match, this is referred to as “2-away, 3-away”.
Formula
The match equity formula is a way of determining the likelihood that a player will win a given match. This is based on the current score and the number of points required to win the match. The formula takes into account the probability of winning each individual game, as well as the probability of winning the match from a given score. It can be quite complex and is typically calculated using computer programs or tables.
Although the formula is complex, it is important for players to understand it in order to make informed decisions during a match. The match equity formula is as follows:
Match Equity = (P / (1 – P)) ^ (S / (M – S))
Where P is the probability of winning a single game, S is the current score, and M is the number of points needed to win the match. The formula calculates the probability of winning the match from the current score.
The Crawford rule is a rule in backgammon that applies to match play. This applies when one player is within one point of winning the match. Under the Crawford rule, the player who is behind is not allowed to use the doubling cube for the next game. The rule is designed to make match play more equitable for the player in the lead. Once the game after the Crawford game is completed, normal doubling cube rules resume.
Strategy and tactics
Match equity has a significant impact on strategy and tactics in backgammon. In general, players will adopt more aggressive tactics when they have a high match equity, meaning they are likely to win the match regardless of the outcome of any individual game. Conversely, players will adopt more conservative tactics when they have a low match equity, meaning they need to win a higher percentage of the remaining games to have a chance of winning the match.
For example, if a player is leading a match 7-5 and needs one more point to win, their match equity is very high. They can afford to take more risks, such as leaving blots or making more aggressive plays. This is because even if they lose the next game, they still have additional opportunities to win the match. In contrast, if a player is behind 5-7 and needs to win three more points, their match equity is low. They may adopt more conservative tactics, such as playing more defensively and avoiding leaving blots, in order to try and win the required games without giving up too many points to their opponent.
Rockwell Kazaross match equity table
The “Rockwell-Kazaross” table is the most widely recognised match equity table in backgammon. It was developed by David Rockwell and Neil Kazaross through extensive rollouts on eXtremeGammon. The table shows the probability of a player winning the match based on the number of points each player needs to complete the match. For example, the entry E(-3,-5) represents the probability of a player winning the match when they need three points to complete the match, and their opponent needs five points. This is different from the standard backgammon notation.
The entries where one player is only one point away are known as “pre-Crawford” probabilities. This is because they assume the next game is played under the Crawford rule. The rule prevents either player from doubling their opponent and winning the match in a single game. Pre-Crawford probabilities are typically used to calculate take points, while post-Crawford probabilities are rarely used in practice.
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Rockwell Kazaross match equity table at Backgammon Galore.
Interesting concept, is it needed for social play? We play simple one off games in local cafes, the loser bows out and joins the end of the queue.
Hi Niki, you don’t need to understand match equity if you are playing money (single) games. You don’t even need to use the doubling cude in backgammon (but we recommend you do!). Maybe try a Backgammon chouette for something different? Thanks for taking the time to comment, enjoy your backgammon!