Stayman is a convention used after partner opens the bidding with one no-trump (1NT). Its purpose is to locate a 4-4 fit in hearts or spades. A response of two clubs is Stayman, asking "Partner, do you have four hearts or four spades?" To use Stayman, responder must hold at least one four-card major suit (hearts and/or spades), and 7 high card points or more (the equivalent of an ace and a king).
The purpose of Stayman is to use hearts or spades as trumps, if the hands will play better than in a no-trump contract.
If partner does not have four hearts or four spades, he should rebid two diamonds. With a four-card heart suit, he should rebid two hearts. And with four spades, he should rebid two spades. Note that with 4-4 in both major suits, partner should bid two hearts. After hearing partner's bid, responder can bid naturally.
Stayman can also be used after an opening bid of two no-trumps (2NT). A three clubs response is then Stayman.
The Stayman convention was popularized by Sam Stayman, a wealthy businessman and bridge expert in the mid-20th century.
Blackwood is a convention for bidding slam contracts. It is used when a trump suit has been agreed and a player thinks that a small slam or grand slam is possible. A bid of four no-trumps (4NT) asks partner how many aces he holds.
Partner should bid five clubs with 0 or 4 aces; five diamonds with 1 ace; five hearts with 2 aces; and five spades with 3 aces. A five no-trumps follow-up bid asks partner how many kings he holds. Partner should bid six clubs with 0 or 4 kings; six diamonds with 1 king; six hearts with 2 kings; and six spades with 3 kings. The five no-trumps bid should only be used if there is a possibility of a grand slam.
After hearing partner's responses, the Blackwood bidder's subsequent bids are natural.
There are certain times when 4NT is not Blackwood. The most common example is when partner opens the bidding with one, two or three no-trumps. In those cases, then a 4NT response invites opener to bid a slam slam (6NT) with maximum strength.
Blackwood has a reputation for being an abused convention; it should only be used when there are no other good bids available for probing for slam.
Blackwood is named for Easley Blackwood, a bridge expert and contemporary of Sam Stayman.