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Non-forcing 1NT

Opener is free to pass 1♥-1NT with a balanced minimum. The best major fit at 1♥-1NT-P is balanced 5-3. Opener can judge when to pass quite safely.

1♥-1NT-Usually 7–11, 0–3♠, 0–3♥
2♣11–17, 3+♣
2♦11–17, 4+♦
2♥11–14, 6+♥
2♠15–17, 4+♠
2NT!15–17, 6=♥, ≤ ♥AJ9
3♣♦15–17, 5+#
3♥15–17, 6+♥, AJT+ or 7+♥
3♠15–17, 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. The impossible 2♠ is the invitational raise of opener’s last suit — clubs after 2♣, diamonds after 2♦, hearts after 2♥ — forcing for one round, so opener accepts game with a maximum or signs off in three of the suit. The direct three-level raise is the weaker, to-play version.

1♥-1NT-2♣-NF, 3+♣
2♦NF, 5+♦
2♥NF, usually 2–3♥
2♠!INV, 4+♣
2NTBAL INV
3♣NF, 4+♣
3♦INV, 6+♦
3♥INV, 3=♥
1♥-1NT-2♦-NF, 4+♦
2♥NF, usually 2–3♥
2♠!INV, 4+♦
2NTBAL INV
3♣INV, 6+♣
3♦NF, 4+♦
3♥INV, 3=♥
1♥-1NT-2♥-NF, 6+♥
2♠!INV, 2+♥
2NTBAL INV
3♣♦INV, 6+#
3♥NF, 3+♥

Precision 2NT

Like 1♠-1NT-2NT, opener has pinned a narrow hand — a maximum with a weak six-card suit — so responder simply places the contract. Here the spade puppet has nothing to find: 1NT denied spades, so there is no second major, and the escape suits ♣♦ straddle hearts rather than sitting below the trump suit. Every call is therefore a natural sign-off — pass with a balanced minimum, retreat to a long minor, or take the 6–3 heart fit at the level your strength buys.

1♥-1NT-2NT-15–17, 6=♥
3♣S/O, 6+♣
3♦S/O, 6+♦
3♥S/O, 3=♥
3NTS/O, 0–2♥
4♥S/O, 3=♥