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Competitive bidding

1NT (X)

I suggest Terrorist’s runout regardless of what (X) means. This runout also applies to a conventional double, yet responder can also pass balanced hands more often.

1NT (X)-
XXPEN
2!P/C, 5+ or 4+ 4+
2!P/C, 5+ or 4+ 4+
2MNF, 5+#
2NT!CUE, good unbalanced hand
3XPRE, 6+#

Opener often runs with clubs because it is hard for responder to do so.

1NT (X) P-
XX5+ suit
2!4+, 4+ another suit

1NT (2)

Systems on is a decent approach over 1NT (2︎). The overcall is somewhat ignored, and X replaces the stolen bid of 2. Since continuations to 1NT is major suit oriented, it is crucial if (2) shows a major suit.

(2) shows both majors

This kind of 2︎ requires extra care. I recommend BTU vs Unusual.

1NT (2)Both majors
XPEN for either major
2NF, 5+
2!FG, 5+
2!INV+, 5+
2NT!LEB, PRE 6+ or FG (xx)45
3INV, 6+#
3!Ask for stopper in this suit

(2) specifies one major

This position is analogous to (1M) 1NT. X replaces the Gladiator 2.

(2) specifies no major

Ignore the (2) overcall. X replaces the Stayman 2 as usual.

1NT (2)

Rubinsohl covers these auctions.

1NT (2NT)

BTU vs Unusual suffices.

1NT (2NT)5+, 5+
XPEN
3!INV+, 5+
3!INV+, 5+
3NF, 5+#
3NTS/O
4!Choice of games, 4+, 5+