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Checkback is a simple convention used when responder shows a 4+ card major, and opener rebids 1NT. The rewards are two-fold. In the first place it discovers whether opener has 3-card support for responder's major or not at a low level. Secondly, it allows natural non-forcing rebids at the 2-level (except in clubs).
a) 1 - 1;
1NT - 2
After opening 1
In sequences (a) and (b) the opening is 1. Opener therefore hasn't actually shown a real suit yet. Opener cannot have a 6-card minor or 10 cards in two suits, but many balanced hands are possible and, in (b), even a minor 2-suiter with 5 diamonds and 4 clubs is not ruled out.
The Checkback bid is 2, over which opener bids:
So the rules are:
After a fit is shown
After a response which shows a fit, normally the responder knows what to do. A new suit is forcing to game and searches for a 4-4 fit for an eventual slam. The system, in fact, encourages, once slam is found improbable, rapidly signing off in game.
The only sign-off is 3, bid with long clubs, a 4-card major only, and a weak hand that can only play in clubs.
The cheapest available bid (often 2NT) is an asking relay to determine more of opener's distribution. The responses:
After a misfit is shown
In the case of a misfit 3 is always to play, but repeating the major and 2NT are natural, non-forcing, and suggest a contract (with rebidding the suit discouraging 2NT). The forcing bids after the response of 2, are therefore:
Follow-up asking bids
So there are two sequences where responder can, after having bid checkback and having received a misfit response, inquire further. These are:
In these cases opener rebids:
After opening 1
When the opening is 1 the response 2 to the asking bid 2 shows 5 hearts and 3 spades, minimum or maximum.
Because of this treatment, the sequence 1 - 1; 1NT - 2 shows 5 spades and 3 hearts too weak for Checkback, but the sequence 1 - 1; 2 - 2; 2 shows 5 spades and 3 hearts, but is forcing, and at least invitational to game.
Note! Unlike when opening 1, the sequence 1 - 1; 1NT - 2; 2 - 2NT shows 4 spades, 3 hearts, and invitational strength. An immediate 2NT denies 3 hearts.