Strong 2♦

The strong 2♦ is forcing to game. See Openings for when to open it. Besides balanced blockbusters, Wbridge5 opens 2♦ with 19–22 HCP and a long suit, such as ♠A5 ♥AKQ8432 ♦- ♣AKJ8.

Probing Wbridge5 5.12 shows that a 2♦ opening holds at least two aces. No 2♦ opening in the probes held fewer, and none of 300 hands with 19–26 HCP and at most one ace opened 2♦. They opened 1 of a suit, 2♣, or 2NT instead.

The 2♦ opening does not depend on seat or vulnerability. See later seats.

Since game is certain, the first question is slam. Responder shows aces right away, and opener is the captain.

Responses

Strength does not matter once responder holds an ace. The 2♠ response covers 4–18 HCP in the probes, and 3NT covers 8–22 HCP.

The 2011 writeup puts the 2♥ / 2NT boundary at 8 points. Probing Wbridge5 5.12 shows that 8 HCP with one king usually bids 2♥, as with ♠KQ86 ♥72 ♦Q76 ♣J854. From 9 HCP on, a hand with no ace bids 2NT, as with ♠J104 ♥QJ ♦KQ65 ♣J982.

A suit response needs a good suit but little else. It takes priority over 2NT, holding up to 12 HCP.

• ♠K7 ♥10987 ♦J109 ♣QJ98: Bid 2♥. One king is not two.
• ♠82 ♥A53 ♦K943 ♣10532: Bid 2♠ with any one ace.
• ♠K105 ♥1087 ♦K10532 ♣96: Bid 2NT with two kings.
• ♠Q83 ♥KQ8763 ♦63 ♣64: Bid 3♥.
• ♠A6 ♥A103 ♦J8752 ♣J75: Bid 3NT.
• ♠A754 ♥A986 ♦873 ♣A2: Bid 4♣.

There is no response for four aces. Probing Wbridge5 5.12 shows that it passes 2♦ with all four aces, as with ♠AJ ♥A87 ♦AKJ ♣AK962 (100 of 100 boards).

A few hands with one ace and a solid 7-card suit jump to the 4-level instead, as with ♠93 ♥AKQJ975 ♦10 ♣874 bidding 4♥. Such a 4♣ would clash with the three-ace response, and only one board showed it.

Opener’s rebids

Opener describes shape naturally. All suit rebids show 5+ cards.

Over 2♥ or 2♠

The rebids are the same after either response.

The 2NT rebid includes 4-4-4-1 and a 5-card minor. The 2♠ rebid over 2♥ and the 3♠ rebid over 2♠ are both the cheapest spade bid.

A 7-card major usually jumps with 19–21 HCP. Stronger hands with 7 cards, and some minimum ones, bid the major at the cheapest level.

The 2011 writeup has any jump show 7+ cards. Probing Wbridge5 5.12 shows that a 7-card minor never jumps: it bid the cheapest level on all 488 boards over 2♥ and all 288 over 2♠. Some 8-card minors jump, and no single rule sorts them:

• Over 2♥: 285 of 531 boards with 8 cards jumped, holding 19–23 HCP, mostly 19–20.
• Over 2♠: Only 68 of 531 jumped, all with 19–20 HCP, and all but one with exactly two aces.
• 9 cards: 7 of 32 boards jumped over 2♥ and none of 32 over 2♠.

The same hand can jump over one response and not the other.

• ♠AJ ♥A87 ♦AKJ ♣AK962: Bid 2NT.
• ♠AKQJ9 ♥- ♦AJ10 ♣AKQ106: Bid 2♠.
• ♠A ♥AKQJ643 ♦Q ♣AK104: Bid 3♥ over 2♥.
• ♠K7 ♥AKQJ632 ♦AQ4 ♣A: Bid 4♥ over 2♥.
• ♠AK ♥7 ♦AK5 ♣AQ109642: Bid 3♣ over 2♠. A 7-card minor does not jump.
• ♠AJ ♥A106 ♦AKQJ7543 ♣-: Bid 4♦ over 2♥, but 3♦ over 2♠.
• ♠92 ♥A ♦AKQJ9875 ♣KQ: Bid 3♦ over 2♥, but 4♦ over 2♠.
• ♠A ♥10 ♦AKQ ♣KQJ107654: Bid 4♣ over 2♥, but 3♣ over 2♠.

Hands 5-5 or longer in the majors open 2♣ instead, even with 24 HCP.

Responder’s second round

After the 2NT rebid, systems are on. Responder bids as over a 2NT opening, taking opener’s extra 4 HCP or so into account. See delayed 2NT openings and systems on.

• 2♦ - 2♥ - 2NT: 3♣ Stayman, 3♦♥ transfers, 3♠ for clubs, 4♣ for diamonds, and 4♠ for 5-5 minors, all with 0–5 HCP. 3NT is to play.
• 2♦ - 2♠ - 2NT: The same, and the notrump raises are 3NT with 4–6 HCP, 4NT with 6–10 HCP, and 5NT with 11 HCP.

After a suit rebid over 2♥, responder is very weak.

• ♠KQ4 ♥9 ♦6432 ♣87432: Bid 3♠ over 2♠.
• ♠J9752 ♥954 ♦KJ73 ♣4: Bid 4♣ over 2♠.
• ♠10853 ♥987 ♦82 ♣J753: Bid 4♠ over 2♠.

Probing Wbridge5 5.12 shows that the 2♦ opening is not absolutely forcing to game. Responder passes 3♣ with a bust and club tolerance, as with ♠J654 ♥542 ♦53 ♣9853 (9 of 250 boards).

After a suit rebid over 2♠, responder with one ace and a fit takes over.

• ♠K42 ♥972 ♦984 ♣A652: Bid 4♥.
• ♠KQ4 ♥842 ♦1093 ♣AJ72: Bid 4NT.

Responder’s 4NT is plain Blackwood, and the ♥K does not count. Opener holds at least two aces, so only two answers occur.

Probing Wbridge5 5.12 shows 5♣ with three aces, with or without the ♥K (52 boards), and 5♥ with two aces even when opener holds the ♥K (15 boards).

• ♠A5 ♥AKQ8432 ♦- ♣AKJ8: Bid 5♣ over 4NT.
• ♠K10 ♥KQ1075 ♦AK4 ♣AK10: Bid 5♥ over 4NT.

Over 2NT

As over 2♥ and 2♠, a 7-card minor bids 3♣♦ (488 of 488 boards). With 8 cards, 194 of 531 boards jumped, as with ♠92 ♥A ♦AKQJ9875 ♣KQ bidding 4♦.

Responder’s 2NT promises no ace, so opener’s 4NT asks for kings, as over 3NT. The 2011 writeup does not list it. Probing Wbridge5 5.12 shows that responder answers with its kings and never passes or bids 6NT (252 boards).

• ♠8732 ♥96 ♦K85 ♣KQJ7: Bid 5♥ over 4NT.
• ♠J104 ♥QJ ♦KQ65 ♣J982: Bid 5♦ over 4NT.
• ♠K7 ♥K1063 ♦72 ♣K10764: Bid 5♣ over 4NT.

• ♠AQ62 ♥AK63 ♦AK ♣AJ2: Bid 4NT over 2NT.
• ♠8732 ♥96 ♦K85 ♣KQJ7: Pass 3NT.
• ♠J104 ♥QJ ♦KQ65 ♣J982: Bid 4NT over 3NT.

Over a suit

With 2+ cards in responder’s suit, opener raises. A raise has priority over a 5-card major of opener’s own.

The 2011 writeup has 3NT deny a 5-card major or 6-card minor. Probing Wbridge5 5.12 shows that a balanced opener raises instead, and 3NT shows a singleton in responder’s suit, as with ♠KQ5 ♥K ♦AK92 ♣AKJ62 over 3♥.

The raise of a minor is 4♣ or 4♦. After a major, there are two raises.

• 4♥♠: 2+ cards, usually balanced, 23–26 HCP
• 4NT: 2+ cards, stronger or more shapely, asking for kings

Responder has already denied an ace, so 4NT asks for kings, and the king of responder’s suit counts. Probing Wbridge5 5.12 shows the same steps as over 2NT on 207 boards after 3♥ and 3♠. Four kings were not seen.

• ♠AKQ6 ♥A95 ♦AKQJ43 ♣-: Bid 3♦ over 3♣.
• ♠AJ4 ♥AK973 ♦AK3 ♣KQ: Bid 4♣ over 3♣. Raise rather than show hearts.
• ♠AKJ10 ♥AQJ ♦AK9 ♣K63: Bid 4♥ over 3♥.
• ♠AKQJ106 ♥AJ6 ♦A ♣AKJ: Bid 4NT over 3♥.
• ♠Q83 ♥KQ8763 ♦63 ♣64: Bid 5♦ over 2♦ - 3♥ - 4NT, with one king.
• ♠KJ105432 ♥7 ♦KQ2 ♣106: Bid 5♥ over 2♦ - 3♠ - 4NT, with two kings.

Over 3NT

Responder holds two aces and opener at least two, so opener holds exactly two.

Probing Wbridge5 5.12 with exactly two aces in opener’s hand (117 boards) confirms the table. One balanced 24 HCP hand, ♠AK ♥KQ63 ♦AKJ ♣KJ109, bid 7NT directly in the 1st seat, but 4NT in the 3rd seat.

• ♠AKQ10 ♥KQJ5 ♦AJ ♣KQ9: Bid 4NT over 3NT.
• ♠A6 ♥A103 ♦J8752 ♣J75: Bid 5♣ over 4NT.
• ♠965 ♥AK1095 ♦K84 ♣A9: Bid 5♥ over 4NT.

The 2011 writeup also lists 5x for a 7-card suit. Probing Wbridge5 5.12 shows that a 7- to 9-card minor bids 4♣♦ on all 446 boards, as with ♠3 ♥K2 ♦AK2 ♣AKQ7432 bidding 4♣. A 7-card major also bids at the 4-level, as with ♠KQJ8763 ♥AK ♦AKJ ♣K bidding 4♠ (3 of 3 boards with 7 cards in a major).

Over 4♣

Responder holds three aces, but a 2♦ opener holds at least two, so this auction never arises from a real deal. The 2011 writeup’s rebids cannot come up: new suit for 5+ cards, 4NT for a balanced hand, and a jump for 7+ cards. The probes forced 4♣ anyway on openers with 2–4 aces, and they mostly bid 4NT. That was the call on 219 of 220 boards with 23+ HCP and on all 241 boards with 7+ clubs. With 7+ diamonds, 220 of 255 boards bid 4NT, and the rest bid 4♦ (13), 5♣ (18), or 5♦ (4). None of these hands can face a real three-ace response, so the book gives no rebid table.

Competitive bidding

Over a double, the responses stay the same. A pass shows a hand that would bid 2NT, usually with diamond honors to defend 2♦ doubled.

• ♠J104 ♥QJ ♦KQ65 ♣J982: Pass.
• ♠K7654 ♥KJ6 ♦8642 ♣10: Bid 2NT.
• ♠AQ64 ♥AJ ♦J8543 ♣A6: Bid 4♣ with three aces (100 of 100 boards).
• ♠AJ ♥A87 ♦AKJ ♣AK962: Pass with four aces, as without the double (100 of 100 boards).

Over an overcall of 2♠, only 3NT and 4♣ still show aces.

• ♠8732 ♥96 ♦K85 ♣KQJ7: Double.
• ♠KQ4 ♥842 ♦1093 ♣AJ72: Bid 2NT.
• ♠AJ ♥A87 ♦AKJ ♣AK962: Bid 2NT with four aces (100 of 100 boards).

Three aces bid 4♣ on all 100 boards probed. Other overcalls were not probed.

Later seats

Probing Wbridge5 5.12 shows that seat and vulnerability change neither the 2♦ opening nor the responses. The probes dealt the same hands board for board in each seat, so each call can be checked against the same hand’s 1st-seat call.

Responder shows aces the same way after passing. The responses matched the 1st-seat ones on all 1,425 boards opposite a 2♦ in a later seat: 300 boards with 8–12 HCP opposite a 2nd-seat 2♦, and passed hands with 0–7 HCP (271 boards in each of the 3rd and 4th seats), 8–11 HCP (203 boards in each), and 4–10 HCP with 6+♦ (177 boards, 3rd seat). A passed hand still usually bids 2♥ with 8 HCP and one king (4 of 5 boards in each seat), as with ♠KQ86 ♥72 ♦Q76 ♣J854, and bids 3NT on all 207 boards with two aces and 8–11 HCP. Both vulnerable, 300 of 300 responses with 8–12 HCP matched.

A passed hand with a good 6-card major has usually opened a weak 2, so only one example was probed. Vulnerable, ♠75 ♥KQ8642 ♦943 ♣72 passes as dealer and bids 3♥ over a 3rd-seat 2♦, as it does over a 1st-seat 2♦. Not vulnerable, ♠75 ♥943 ♦KQ8642 ♣72 passes and then bids 3♦, also as over a 1st-seat 2♦.

A 3rd- or 4th-seat opener facing a passed partner rebids as in the 1st seat on 994 of 997 boards: with 23+ HCP over 2♥ in the 3rd and 4th seats and over 2♠ and 2NT in the 4th seat, and with two aces and 22+ HCP over 3NT in the 3rd seat. The three exceptions were single boards. Only the first was probed in two later seats, and it differed in the 3rd seat but not the 4th:

• ♠A ♥AKQJ643 ♦Q ♣AK104: Bid 4♥ over 2♥ in the 3rd seat, but 3♥ in the 1st and 4th.
• ♠A3 ♥AKQJ832 ♦A ♣AQ2: Bid 4♥ over 2♠ in the 4th seat, but 3♥ in the 1st.
• ♠AK ♥KQ63 ♦AKJ ♣KJ109: Bid 4NT over 3NT in the 3rd seat, but 7NT in the 1st.

Not probed

• Opener’s rebids after a 2nd-seat 2♦
• After a 2♦ in the 2nd, 3rd, or 4th seat: opener’s rebids over a suit response, and the later rounds (4NT king asks, responder’s second round, competition)
• A passed hand’s suit responses in the majors beyond the one example hand
• Vulnerability for opener’s rebids and the later rounds