The granddaddy (and simplest) of them all is Mathe. Invented by Lew Mathe several decades ago, it just goes like this:
When the opponents open a big club on your right or they open a big club on your left, partner passes, and they bid a "little diamond" on your right, double shows both majors, and one notrump shows both minors. That's all there is to it.
The first big club defense I learned was CRASH. This is a quick mnemonic for Color, RAnk, SHape. CRASH uses one more bid than Mathe: 1D. So it doesn't quite work over (1C!) P (1D!).
Playing CRASH, when the opponents open a strong club on your right,
- Double shows two suits of the same Color.
- One Diamond shows two suits of the same RAnk (minors or majors).
- One Notrump shows two suits of the same SHape (look at the tops: pointed [spades and diamonds] and rounded [clubs and hearts].)
- Anything else is natural.
When your partner makes a CRASH (or SHARC) bid, it's your job to preempt as high as you can. Much of the time you don't know that you have a fit, but sometimes you're assured of one. For example:
LHO opens a strong club, partner bids 1D (RAnk), and RHO passes. You hold:
AJ652 74 T9742 4
Since partner either has the minors or the majors, you know there's a big pointed-suit fit somewhere. So you bid... 3D! Partner has at least four cards in one pointy suit, so you have at least nine trumps somewhere. The three level shouldn't be too high. Partner will pass (or maybe raise!) holding both minors, and will correct to 3H holding both majors. You'll correct 3H to 3S, and you've found your fit and your level!
This is very important. Playing CRASH, SHARC, Suction [which I'll get to soon], or many other big club defenses, responder's actions are all pass or correct. So if you hold:
T4 J2 73 QT98532
and pard overcalls with 1NT (SHape), don't bid 3C! He'll correct to his cheapest suit (because he almost certainly has spades and diamonds). Start with 2C, and when partner corrects to 2D, he'll get the message that all you have is clubs when you rebid 3C.