Notation on suit variables

In competitive and defensive bidding, combinations of calls grow factorially. It is convenient to replace unknown suits with variables, just like how algebra brings computation to a higher level.

This book usually follows principles introduced in BML and CSS.

Ordered suit variables

X, Y, Z are suit variables that satisfy X < Y < Z. They are also distinct from the other suits in the same auction. For example:

(1Y)-2X matches (1♥)-2♣ but not (1♥)-2♠.
(1Y)-2Z matches (1♥)-2♠ but not (1♥)-2♣ or (1♥)-2NT.
(1M)-2X matches (1♥)-2♣ but not (1♥)-2♥.

Precedence

Multiple rules may match the same auction. The rule with the highest precedence applies.

Precedence of strain symbols

Concrete strain > suit class > suit variable

Concrete strain: ♣, ♦, ♥, ♠, NT
Suit class: M, m, R, B
Suit variable: X, Y, Z

Juxtaposition of strain symbols

Juxtaposition of strain symbols produces multiple rules, similar to | in regular expression. For example, 2MNT is a valid expression that matches 2♥, 2♠, and 2NT.

Specificity is determined like CSS specificity. The rule with the most concrete strains wins. Then we compare the number of suit classes. Note that juxtaposition expands to multiple rules instead of one. For example:

1♥-2X > 1R-2B
Comparing 1MNT-2X and 1X-1R:
- 1M-2X = 1X-1R
- 1NT-2X > 1X-1R

Precedence of rules

The most specific rule applies. If there are multiple rules with the same specificity, compare specificity lexicographically. For example, 1M-2X > 1X-1R because 1M is more specific than 1X. If there are still multiple rules with the same specificity, the last rule applies, like CSS and laws but not BML.