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The Kokish Convention is a way of distinguishing between strong hands after an opening bid of 2 in a standard bidding system. In standard methods after a 2 response opener rebids 2NT with 22-24 HCP and 3NT with 25+. The range for 2NT is extremely wide, and the 3NT rebid crowds the auction for slam exploration. Eric Kokish proposed a solution to this problem using a rebid of 2 by opener to show either hearts or a strong balanced hand. This is how it works:

2       2 (waiting or positive)

2 - Ambiguous forcing responder to rebid 2 , then opener continues:
2NT - forcing, 24+ balanced, stayman and transfers apply. Could have 5 hearts.
3 new suit - natural, unbalanced hand
3 - 6 card suit, unbalanced hand
3NT - balanced with 5 hearts and minimum values
2 - 5 card spade suit, may be balanced or unbalanced
2NT - 22-23 HCP, no 5 card major, stayman and transfers
3 minor - 10+ trick hand with 5+ suit. Step bid by responder neutral if 2 was waiting.
3/ - solid suit, requests immediate cue bidding
3NT - Long solid minor and 8-9 tricks, at least partial stopper in all suits. Minimal slam interest, responder will need at least three controls to continue.

  Qx AKJx 2 2  
  AKJx x 2 (kokish) 2 (forced)  
  AKQJ 9xxxx 2NT (24+) 3 (stayman)  
  AQx Kxx 3 3 (4 card suit)  
      3NT 4 (suit)  
      5 (cue for diamonds) 6 (grand slam try)  
      7 (or 7NT) P  

The precise details of how to continue are a matter of partnership agreement. My own preference is to use 2 as an immediate game force response, this works well with the Kokish convention.

2     ?

2- 7+ points, or two kings or one ace, game forcing
2/NT/3/ - "positive negative response" showing a topless 6+ card suit with no side card
(e.g.)QJ10xxx xxx Q xxx. 2NT is the positive negative with hearts2 - negative response, auction may end below game. Opener continues:2 - 5+ suit, unbalanced hand, forcing, responder continues:2NT - either clubs or balanced, game force, some useful value(s)
3 - second negative, responder may pass any rebid by opener
3/- decent 5 card suit that will provide a stopper at least if opener continues with 3NT
3- 3+ support, including either a top honour or a side king, some possibility of two cover cards
4 bids - splinter with top trump honour or 5 card length
4 - good fit but lacking singleton or two possible cover cards

2NT - 22-24, not forcing, may have a 5 card heart suit, optional puppet stayman or stayman rebid and transfers
3- one round force, responder bids a 5 card major, or raises with at least one trick and fit, or rebids 3 neutral
3- one round force, responder bids 3(5), 3(4+), 3NT- no major unless exactly 4324
3/ - solid suit, asking for cue of king. An alternative is to use this to show a 4 card major with 6 diamonds, to avoid the clumsy rebid structure after a 3 rebid.
3NT - to play, may be good 24+ balanced or long minor and stoppers, either way responder is expected to pass