Two-way checkback, introduced by Kit Woolsey in an article in Bridge Today, uses the rebids of two of either minor by responder after opener's 1NT rebid as artificial and forcing. In the Woolsey style, 2 puppets to 2 to play 2 or 3 or to invite game in various strains. 2 over 1NT is artificial and game forcing.
Two-way is super if playing weak notrumps, so that a 1NT rebid by opener shows extra values. With those methods, responder will often have a game forcing hand; indicating that at the level of 2 is quite helpful. Two-way also is nice when playing Walsh-style responses to 1, because responder can play 2 without fear of correction back to his short major.
Details are below with a few interesting tinkers.
"Purish" means "most of the high cards in the long suits. "m" means a minor suit; "M" means a major suit; "OM" means the other major; "om" means the other minor.
- 2 = relays to 2
- 2 = game forcing, asks for shape
- 2M = to play
- 2OM = if hearts, no game interest if spades, 4-4, invitational, not forcing
- 2NT = natural invitational
- 3m = game forcing, purish 5-5
- 3om = game forcing, purish 5-5
- 3M = game forcing, purish 6+ 3OM = if hearts, game forcing, purish 5-5 if spades, game forcing, purish 6-5
- 3NT = to play
- 4 = Gerber (RKC?)
- 4 = usually 6331 with stiff, very good suit, slam interest
- 4M = to play
- 4oM = stiff, same as 4, I guess
- 4NT = natural, invitational (what's 2...4NT?)
1m-1M; 1NT-2; 2
- 2M = 5 card suit, invitational, nonforcing
- 2OM = if hearts, 5-4 or 5-5, invitational, nonforcing if spades, 4-5 invitational, nonforcing
- 2NT = invitational, shows clubs
- 3 = to play
- 3 = invitational, natural
- 3M = strong invite, 6+
- 3OM = if hearts, strong invite, 5-5 if spades,
1m-1M; 1NT-2; Priorities:
- bid 4 of the other major
- bid 3 of responder's major
- rebid a six-bagger
- show 2-2-4-5 or 2-2-5-4?
- rebid 2NT
This set of choices is due to Woolsey, probably mostly intended for weak NT systems; this is most likely to get the partnership to play the hand from the strong NT's side. He claims that it doesn't really matter which of the first two is highest priority, and some others prefer to show 3-card support first, while others prefer to bid hearts first.