Strong 2♣

The strong 2♣ shows 21–23 points not suited to a 2NT opening, or 22–23 HCP with 2NT distribution. The openings chapter tells it apart from 1 of a suit, 2NT, and 2♦. Opener’s rebid is natural, and a 2NT rebid continues as a 2NT opening.

The 2♣ opening is forcing for one round only. Responder never passed 2♣ in the probes, but after 2♣ - 2♦ responder may pass a simple rebid with a bust.

Every row in this chapter comes from probing Wbridge5 5.12, which shows that 2♣ is opened with 19–23 HCP. Ranges in HCP are as probed; the program counts length and shortness as well (see hand evaluation), so shapely hands go positive with fewer HCP.

Vulnerability hardly matters. At unfavorable vulnerability, the same 300 hands with 19–26 HCP made the same openings, and 300 responders with 6–12 HCP made the same responses at unfavorable and both vulnerable. The few changes are in responder’s and opener’s game decisions below.

Responses

The positive suit responses are by points. A 5-card major goes positive at about 10 points counting shortness and length, with as few as 7 HCP, while a flat 10 HCP hand has to choose between 2♦ and 2NT.

A 6-card minor needs quality for a 3-level response, as the official help says: 2 of the top 3 honors. A poorer 6-card minor responds 2NT with 10+ HCP, or 2♦ with less. 2NT may also hold a 5-card major: 33 of 132 hands with 10–13 HCP and 5+♥ responded 2NT.

• ♠92 ♥AQ10864 ♦Q64 ♣108: 2♥. Only 8 HCP but 6 hearts.
• ♠86 ♥A10653 ♦K965 ♣103: 2♦. 7 HCP and two doubletons fall short of 10 points.
• ♠Q2 ♥J753 ♦J ♣AKJ872: 3♣ with a good suit.
• ♠10 ♥842 ♦AKQ ♣Q106542: 2NT. The clubs are too poor for 3♣.

A strong responder makes the same positive as a minimum one. There is no jump response for strength, and 2♦ was never bid with 16+ HCP. Of 300 hands with 16–24 HCP, 187 responded 2NT, 47 2♠, 38 2♥, 13 3♣, 9 3♦, 4 3♠, 1 3♥, and 1 7♥. The rules above hold at 16–22 HCP. A 5-card major bids 2♥ or 2♠ (256 and 258 of 300 hands), or 2NT with a poor suit holding at most one of the top 3 honors. A 6-card minor bids 3♣ or 3♦ (267 and 275 of 300), or 2NT with only one of the top 3 honors. A 7-card major with 2 of the top 3 honors bids 3♥ or 3♠ (14 hands each). The only slam jumps were 2 grand slams with a long suit and a void.

• ♠AK ♥AK3 ♦K76 ♣Q10432: 2NT with 19 HCP.
• ♠K10964 ♥KQ2 ♦AKJ ♣108: 2NT. The spades are too poor for 2♠.
• ♠A5 ♥AKQ8432 ♦— ♣AKJ8: 7♥.
• ♠— ♥A2 ♦AQJ97543 ♣AQJ: 7♦.

Responses over interference

Over an overcall, pass is weak and double shows values without a natural call. The double is not penalty; it is the usual call when the overcall took responder’s own suit.

• ♠8732 ♥96 ♦K85 ♣KQJ7: Double. 9 HCP, no heart stopper.
• ♠92 ♥AQ10864 ♦Q64 ♣108: Double. The 2♥ response was taken away.
• ♠AK8 ♥K1073 ♦KQ932 ♣9: 2NT.

A takeout double of 2♣ hardly changes Wbridge5’s responses. It bids 2♦ with most hands, including 42 of the 57 hands that would respond 2♥ or 2♠. The probes never saw pass or redouble.

Opener’s rebids

After 2♣ - 2♦

The 2NT rebid is a delayed 2NT opening, mostly with 22–23 HCP. Probing Wbridge5 5.12 shows 14 of 62 such rebids with 21 HCP, and some 4-4-4-1 hands with a small singleton.

Rarer rebids:

• 3♠ or 4♥: 7+ cards in the major (1 and 2 hands).
• 3NT: 5-5 in the majors (3 of the 4 such hands). The fourth rebid 2NT.

For example,

• ♠AK ♥Q1073 ♦AK107 ♣AK5: 2NT.
• ♠A4 ♥K10854 ♦A10 ♣AKQ4: 2♥.
• ♠AK2 ♥QJ ♦KQ10952 ♣AQ: 3♦.

After a positive response

Opener raises responder’s suit with 3+ cards ahead of anything else. Otherwise, opener bids a new 5+-card suit, a 6+-card minor, or notrump with 21–23 HCP. The jump rebids for a 7-card suit in the 2011 writeup were not seen.

The probes do not explain the choice between 3NT and 5 of responder’s minor with a balanced hand. Neither fit length nor stoppers tell them apart.

• ♠AQJ72 ♥AKJ9 ♦J7 ♣KQ: 2♣ - 2♥ - 3♥. The heart fit comes first.
• ♠AK32 ♥AQJ43 ♦A3 ♣J9: 2♣ - 2♠ - 3♠ with only 4 spades.
• ♠AK42 ♥A ♦AQJ4 ♣A876: 2♣ - 2♥ - 2NT with a singleton ace.

Over interference

Opener’s double after 2♣ - 2♦ is takeout and shows a 4-4-4-1, as the 2011 writeup says. Pass shows a balanced hand without a stopper. Partner has another chance to act.

When the overcall is passed around, the meanings change: double is the balanced hand without a stopper, and pass is a penalty pass with hearts.

• ♠AQ7 ♥653 ♦AKQ6 ♣AK7: Pass over 2♣ - 2♦ - (2♥), but double over 2♣ - (2♥) - P - (P).
• ♠AK42 ♥A ♦AQJ4 ♣A876: Double over 2♣ - 2♦ - (2♥), but 2NT over 2♣ - (2♥) - P - (P).
• ♠Q ♥AK10876 ♦KJ ♣KQJ7: Pass over 2♣ - (2♥) - P - (P).

Vulnerability does not change this table. At unfavorable and at favorable vulnerability, 2 and 1 of the same 245 calls differed from none vulnerable. The penalty pass came up on 28–30 boards each time.

Responder’s second call

After 2♣ - 2♦ - 2♥♠

With support, the fast 4M is weak and the slow 3M is the good raise. The splinters show shortness with 3+ cards in opener’s major. With nothing, responder passes.

• ♠A42 ♥K52 ♦8654 ♣Q43: 2♣ - 2♦ - 2♥ - 3♥, the good raise.
• ♠K42 ♥972 ♦984 ♣A652: 2♣ - 2♦ - 2♥ - 4♥.
• ♠10853 ♥987 ♦82 ♣J753: Pass any simple rebid.

Vulnerable, a few more hands raise to game. After 2♣ - 2♦ - 2♥, 3 of the 24 hands (of 264) that passed at none vulnerable bid 4♥ at unfavorable vulnerability, and 2 with both vulnerable, all with 1–4 HCP and 3–4♥, e.g. ♠Q32 ♥953 ♦Q9732 ♣53. One of them, ♠106 ♥8754 ♦98542 ♣J3, had only 1 HCP, below the 2 HCP floor at none vulnerable, but one board is too few to move the range. No other call changed.

After 3♥, opener never passed or signed off in 4♥ in the probes. Opener makes control bids up the line instead. It never bid 4NT either, not even with all five keys (7 of 226 boards), since every hand had a spade or club control to show.

After the 2NT denial, opener shows a second suit or settles in a game.

• ♠54 ♥AKQJ4 ♦A9 ♣KQ62: 2♣ - 2♦ - 2♥ - 3♥ - 4♣ without a spade control, but pass over 2NT.

At unfavorable vulnerability, 4 of the 7 hands that passed 2NT bid 3NT instead, including the example above, and one 3NT hand passed. Seven boards are too few for a rule, but vulnerable opener passes 2NT less often.

After 2♣ - 2♦ - 2NT

Opener’s 2NT rebid shows a 2NT opening with about 2 HCP more, and Wbridge5 plays systems on: Stayman, transfers, and their answers are those after a 2NT opening. Only responder’s ranges move down by 2 HCP.

Opener answers as after a 2NT opening. Over 3♣ it bids 3♦ without a 4-card major, 3♥ or 3♠ with one, and 3NT with both. The transfers are accepted, with super acceptances and a 3NT rejection over 3♥ with a doubleton spade. Over 3♠, opener bids 4♣ with 3+♣ or 3NT with a doubleton.

• ♠AK ♥Q1073 ♦AK107 ♣AK5: 2♣ - 2♦ - 2NT - 3♣ - 3♥, and 2♣ - 2♦ - 2NT - 3♥ - 3NT with only 2 spades.

After 2♣ - 2♦ - 3♣♦♥

The 3♥ rebid is almost always raised. 4NT is presumably RKCB, but opener’s answer cannot be probed, because Wbridge5 never rebid 3♥ itself: not on any of 245 boards after 2♣ - 2♦, nor on 20 hands with 6+♥ and 19–23 HCP, which rebid 2♥ or 4♥.

Responder’s second call after a positive 2♥

After 2♣ - 2♥, responder has 5+♥ and about 8–11 HCP, the range probed.

• ♠QJ86 ♥KJ654 ♦A52 ♣7: 2♣ - 2♥ - 2♠ - 4♣ splinter, but 2♣ - 2♥ - 2NT - 3♠.
• ♠Q94 ♥AJ1096 ♦85 ♣K32: 2♣ - 2♥ - 2NT - 4NT.

Responder’s second call after a positive 2♠

The probes gave responder 5+♠, 0–4♥, and 9–15 HCP. As after 2♥, a fit for opener’s suit comes first. Without one, responder shows 4 hearts, then 6 spades, then a 4-card minor. Over 2NT, a 4-card minor usually comes first, even with 6 spades (21 of 25 hands).

After the raise to 3♠, responder makes control bids up the line on 182 of 197 hands, and 4NT without any side control. It signed off in 4♠ on only 5 hands, all with 9 HCP and no shortness.

The heart fit outranks 6 spades: with 3+♥ and 6♠, responder raised over 3♥. Over 3♦, a 4-card heart suit and 6 spades usually come before the diamond raise. The 6NT jumps are few (8 and 4 hands), and so is 3NT over 2NT (5 hands).

• ♠AKJ95 ♥K10 ♦865 ♣Q85: 2♣ - 2♠ - 3♠ - 4♥, 2♣ - 2♠ - 2NT - 4NT, 2♣ - 2♠ - 3♥ - 6NT, and 2♣ - 2♠ - 3♦ - 4♦.
• ♠KJ6543 ♥AK104 ♦9 ♣53: 2♣ - 2♠ - 3♠ - 4♦ with the singleton, 2♣ - 2♠ - 2NT - 3♥, and 2♣ - 2♠ - 3♥ - 4NT.
• ♠KQ9762 ♥10 ♦K9 ♣K843: 2♣ - 2♠ - 2NT - 3♣, but 2♣ - 2♠ - 3♥ - 3♠.
• ♠AKQJ4 ♥Q93 ♦J87 ♣J7: 2♣ - 2♠ - 3♠ - 4NT without a side control.

Responder’s second call after a positive 2NT

The probes gave responder 10–15 HCP with 2–4 cards in each major and 2–5 in each minor. Responder raises opener’s suit with 3+ cards, even a minor, and even with a 5-card minor of its own. With a doubleton, it shows a 5-card minor, or bids 3NT with 10–12 HCP and 5NT with 13–15 HCP. A 4-card major is never shown.

The major raise to game is the minimum: 4♥ and 4♠ came only with 10–11 HCP (25 and 27 hands), and 4NT with 10–15 HCP (196 and 182 hands).

Over 3NT, responder bids a 5-card minor at the 4 level. Otherwise it passes or bids 4NT, and probing Wbridge5 5.12 shows that aces weigh more than strength. It passed on 32 of 39 hands with 10 HCP. With 13–15 HCP, it passed on 36 of 43 hands with 2 or more aces, but bid 4NT on 28 of 33 with 0–1 ace. With 11–12 HCP, it mostly bid 4NT (64 of 90 hands).

• ♠KQ4 ♥842 ♦1093 ♣AJ72: 2♣ - 2NT - 3♠ - 4NT, but 2♣ - 2NT - 3♥ - 4♥. Over 3NT, pass. Over 3♣ and 3♦, raise.
• ♠AQ102 ♥852 ♦KJ83 ♣A6: 2♣ - 2NT - 3♣ - 5NT, and 2♣ - 2NT - 3NT - pass with 2 aces.
• ♠AKQ10 ♥972 ♦Q2 ♣K1087: 2♣ - 2NT - 3NT - 4NT with 1 ace, and 2♣ - 2NT - 3♦ - 5NT.

Responder’s second call after a positive 3♣♦

The probes gave responder 6+ cards in the minor, 0–4 in each major, and 9–15 HCP. Over opener’s 3♥ or 3♠, responder bids 4NT with 3+ cards in the major. Without a fit, it shows a 4-card suit or a 7-card minor, or bids 3NT with about 9–10 HCP and 6NT with more.

A 4♠ raise over 3♠ came on only 5 hands in each line, with 9–10 HCP. The 4♥ raise over 3♥ came on 9 hands, 8 of them with 9 HCP. A few 4NT bids held only 1–2 cards in opener’s major with a strong minor: 3 of 79 over 2♣ - 3♣ - 3♥, 5 of 81 over 2♣ - 3♣ - 3♠, and 3 of 78 over 2♣ - 3♦ - 3♠.

Over opener’s 3NT, responder bids 4NT with 6 cards in the minor and mostly 4 of the minor with 7. It passed on only 3 and 5 hands, all with 9–10 HCP. A 4-card major was bid at the 4 level on a handful of hands with 9–10 HCP.

After opener raises to 4 of the minor, responder makes control bids up the line, as after the raise to 3♠. 4NT denies a control in the side suits after 3♣ - 4♣, but only in the majors after 3♦ - 4♦, where it is bid even with the ♣A.

The rarer calls over 4♦ were 5♣ with a club void (2 hands) and 5♦ with 9–10 HCP and no control (3 hands).

Opener’s jump to 5 of responder’s minor shows a balanced 21–23 HCP, and responder takes it as a slam invitation. It bids the small slam with most hands, and 7NT only with 13–15 HCP. With 2 aces and the top 3 honors in the minor, it bid 7NT on 12 of 16 hands. It passed on only 2 and 5 hands, with 9–10 HCP.

• ♠K762 ♥Q8 ♦2 ♣AKJ1084: 2♣ - 3♣ - 3♥ - 3♠, 2♣ - 3♣ - 3♠ - 4NT, 2♣ - 3♣ - 3NT - 4NT, 2♣ - 3♣ - 4♣ - 4♦ with the singleton, and 2♣ - 3♣ - 5♣ - 6♣.
• ♠J8 ♥532 ♦K8 ♣KQ8532: 2♣ - 3♣ - 3♠ - 3NT, 2♣ - 3♣ - 3♥ - 4♥, and pass over 3NT and 5♣.
• ♠6 ♥Q3 ♦AKJ10854 ♣A42: 2♣ - 3♦ - 3♠ - 4♦, 2♣ - 3♦ - 3NT - 4♦, 2♣ - 3♦ - 4♦ - 4♠, and 2♣ - 3♦ - 5♦ - 7NT.

Not probed

• Vulnerability for the responses over interference, opener’s rebid after 2♣ - 2♦ or a positive, and responder’s second call other than after 2♣ - 2♦ - 2♥. Favorable vulnerability, except for 2♣ - (2♥) - P - (P).
• Responder’s second call with 16+ HCP, or with fewer HCP than the probed ranges (9–15 after 2♠, 3♣ and 3♦; 10–15 after 2NT).
• Responder’s second call after 2♣ - 2♠ - 3♣, 2♣ - 3♣ - 3♦, 2♣ - 3♦ - 3♥ or 4♣, and after 2♣ - 3♥ or 3♠.
• What responder’s 4NT asks or shows after a positive, and opener’s answer to it or to a control bid. North is scripted, so the probes cannot tell RKCB from a quantitative 4NT.
• The rarest second calls, each on 5 or fewer boards: 4♠ after 2♣ - 2♠ - 3♠, 3NT after 2♣ - 2♠ - 2NT, 4♠ after 3♠ and pass after 3NT or 5 of the minor following a 3♣ or 3♦ response, and 5♣ or 5♦ after 2♣ - 3♦ - 4♦.
• Opener’s third call except after 2♣ - 2♦ - 2♥ and 2♣ - 2♦ - 2NT.
• Overcalls other than 2♥, and responder’s call when the opponents bid after opener’s rebid.
• The 2011 writeup’s support double after 2♣ - 2♥ - (new suit), and its double of an overcall of 2♣ - 2NT or 2♣ - 3x showing 4+ support and 4+ in both other suits.