Competing to the Three Level: The Law of Total Tricks
In a part-score battle, bid to the level of your combined trumps: eight trumps, the two level; nine, the three level.
The Law of Total Tricks is a guide for competitive auctions. It says the total number of tricks available on a deal, in both sides' best fits, is roughly equal to the total number of trumps in those fits.
The practical rule
In a part-score battle, bid to the level that matches your combined trump length:
Eight trumps: compete to the two level (eight tricks).
Nine trumps: compete to the three level (nine tricks).
Ten trumps: the four level may be right.
Example
You open 1♥, partner raises to 2♥ and the opponents compete with 2♠. You hold five hearts; partner's raise promises at least three. That is at least eight trumps. With only eight, defend 2♠ or bid 3♥ only with extra values. With six hearts, you know of nine trumps: bid 3♥.
Why it works
If both sides have nine trumps, there are about 18 tricks in total. If the opponents can take nine in spades, you can probably take nine in hearts. Either you make 3♥ or 3♠ would have made for them.
Adjust for these
Vulnerability: be more careful vulnerable.
Double fits: a second fit makes extra tricks.
Honours in their suit: queens and jacks in their suit are better on defence, so lean towards defending.
Flat shape: 4-3-3-3 hands take fewer tricks than the Law predicts.
Key takeaways
Compete to the level of your combined trumps.
Nine trumps: the three level.
Adjust for vulnerability, shape and values in their suit.