Early in our bridge careers, we noticed that something was wrong when the bidding went 1-1N-2-2. The 1N response apparently denied 4+ spades, so how could partner be bidding them now? As a result, good players decided that 2 was artificial. The usual approach was to play that it shows a “serious” raise of clubs, while a direct 3 is a “courtesy” raise. This is certainly better than having no understanding at all about 2, but it is not the best use for the bid.

The best use for the impossible 2 depends on what 1N is. In some partnerships, it is forcing; in others it is semi-forcing; and in still others it is not at all forcing. If it is forcing, then opener might fairly often have to rebid 2 on a doubleton (e.g., if he is 4=5=2=2). If it is semi-forcing, then it depends on what “semi-forcing” means. If it means that opener may not pass with 13+ hcp, then he will still have to bid 2 on a doubleton occasionally. If it is not at all forcing, then he will usually have real clubs when he bids 2 (although he might be 4=5=1=3).

Another consideration is what opener does with 3=5=3=2 hands when he doesn’t have the option systemically to pass. Nowadays, many partnerships take the sensible approach to bid 2 with this pattern, so that 1-1N-2 shows real diamonds (although opener could be 4=5=3=1). This is beneficial because it exchanges two ambiguous rebids for one fairly descriptive and one very ambiguous rebid (this also the basic concept behind the so-called "short club", in which the opening bid with 4=4=3=2 hands is 1 rather than 1).

We can boil all this down to two systemic situations: (1) opener might fairly often have only a club doubleton to bid 1-1N-2, and (2) opener will usually have real clubs when he bids this way. The optimal use for the impossible 2 is different for (1) and (2).

In situation (1), the impossible 2 should show a hand with 4 or 5 clubs, invitational values, and lacking the stoppers to bid 2N. Raising to 3 with such a hand is dangerous, because we might have only a 7-card fit (in the extreme, a 6-card fit). After this kind of 2 bid, opener can sign off in either 2N or 3; he can accept the invitation by rebidding 3N or even 5; if he happened to bid 2 with a non-minimum-range hand, hoping that responder wouldn't pass, he can bid something else, which is natural and game-forcing.

In situation (2), the impossible 2 should be a relay to 2N, after which responder can rebid three of a minor or 3. Direct rebids generally show weaker hands than indirect rebids. This is especially important when you play bergen raises or strong jump shifts. 1-1N-2-3 would show a weak jump shift in diamonds, while 1-1N-2-2-2N-3 would show very long diamonds and invitational values. You would still have your serious and courtesy raises of clubs. 1-1N-2-2-2N-3 would show a sound 3-card limit raise, while 1-1N-2-3 would show a light, often distributional, 3-card limit raise (e.g., x QJx Axxxxxx xx).

The impossible 2 arises in two other sequences: 1-1N-2-2 and 1-1N-2-2. These are situation (2) because opener’s length in the suit he rebids is pretty well defined. So 2 is a relay to 2N, with direct rebids at the 3-level being weaker than belated rebids. 1-1N-2-2-3 should be a 3-card limit raise, while 1-1N-2-2-2-2N-3 should be a 2-card invitation; this is consistent with the idea that direct 3-level bids are weaker than belated 3-level bids because with 3-card support, you need fewer hcp to invite than you do with only a doubleton in support.