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Non-forcing 1NT

Responder bids 1♠ with any 4+♠, and the transfer raise takes the 3-card limit raise out of 1NT. Thus, 1NT denies most major fits. Opener passes 1NT with any balanced minimum, just as over 1♠ - 1NT. A balanced medium still has to bid 2♣ on a doubleton, and 2♦ can be 4531.

1♥ - 1NT -
2♣(11–16, 4+♣) or BAL 13–14
2♦(11–16, 4+♦) or (13–14, 4531)
2♥11–14, 6+♥
2♠15–16, 4+♠
2NT!15–16, 6=♥, ≤ ♥AJ9
3♣♦15–16, 5+#
3♥15–16, ((6+♥, AJT+) or 7+♥)
3♠15–16, 4+♠, 6+♥
3NT!Gambling, 7+♥ AKQ, no outside A/K

Just like 1♠ - 1NT, the threshold of suit quality is based on Binky Points.

Impossible spades

Spades that responder rebids must be artificial because 1NT already denies spades. Over 2♣ the impossible 2♠ is the traditional invitational club raise: opener signs off in 2NT or 3♣ or bids game.

1♥ - 1NT -
2♣ -
2♦NF, 5+♦
2♥NF, 2–3♥
2♠!INV, 4+♣
2NTNAT INV
3♣NF, 5+♣
3♦INV, 6+♦

Over 2♦♥ there are two or more invitations to carry, so 2♠ becomes a puppet to 2NT. The following 3-bid is then the invitational version of the same call, while the direct 3-bid is to play.

1♥ - 1NT -
2♦ -
2♥NF, 1–3♥
2♠!ART INV, PUP
2NTNAT INV
3♣NF, 6+♣
3♦NF, 4+♦
1♥ - 1NT -
2♦ - 2♠! -
2NT -
3♣INV, 6+♣
3♦INV, 4+♦

Over 2♥ opener has shown 6+♥, so the direct minor bids are signoffs out of the misfit. The puppet carries the limit raise and invitations in either minor. The direct 3♥ is the weaker raise with 3 trumps.

1♥ - 1NT -
2♥ -
2♠!ART INV, PUP
2NTNAT INV
3♣♦S/O, 6+#
3♥NF, 3+♥
1♥ - 1NT -
2♥ - 2♠! -
2NT -
3♣♦INV, 6+#
3♥INV, 2+♥