Flannery is a bridge convention using an 2♦ opening bid to show a hand of minimal opening bid strength (11-15 high card points) with exactly four spades and five (or sometimes six) hearts. It was invented by American player William L. Flannery.
This convention was introduced because of the awkwardness of describing such a holding, especially with four-card major systems. For example, with the hand ♠ KQ82 ♥ AJ643 ♦ KJ ♣ 54, if the bidding starts 1♥ - 1NT (denying four spades), the opener cannot rebid 2♠, as it would be a reverse bid showing a stronger hand, 2♥ would show a six-card suit, and two of a minor would show four or at least three good cards. Thus, the opener cannot easily explore for a 5-3 fit in hearts. Five-card major openers are somewhat better placed, because 1NT denies both three hearts and four spades, so opener may pass more safely but is nevertheless at risk of missing a potential optimum 4-3 Moysian fit in spades. Flannery is also useful when playing five-card majors in conjunctions with forcing notrump, to prevent opener from having to respond in a nonsuit after 1♥ - 1NT when not strong enough to reverse.
Responder's only forcing bid is 2NT; all other bids are natural. The responses are:
"Anti-Flannery" is a variation used in systems which use canapé approach, where shorter suit is opened first. It is used in some variations of Blue Club and Lancia systems. With canapé in effect, hands with 4=5 in majors are naturally opened 1♠ with 2♥ rebid, however, hands with 5 spades and 4 hearts are the ones that present a problem. So, the bid of 2♦ shows 5 spades and 4 hearts. Continuations are similar to basic Flannery.