Public Access

# Solution to Opening Bids

by Diana Tenery and joon pahk

Each of the 11 deals is a declarer play problem in bridge. In each one, the auction is given, except that the opening bid has been obscured. The deals are ordered by final contract, lowest to highest.

Using bridge logic and the bidding system (Bridge World Standard) indicated in the flavortext, figure out the opening bid in each case (as per the puzzle title). The play is given up to the point where declarer (always South) needs to make a key decision; cards are given in the order they are played within each trick, with the winning card highlighted. You need to figure out what card to play next on each deal. The images at the end of the puzzle provide rebus-style hints (in alphabetical order) to the cardplay techniques that are used.

The correct card to play on each of the eleven deals is a different rank (as hinted in the flavortext) from ace down to 4; this gives an ordering mechanism to the hands. Converting the opening bids into letters (where 1♣, the lowest opening bid, corresponds to A, 1 = B, etc.) and reading off in ace-to-four order gives THECBOFACBL. This is a clue phrase; in the context of bridge, ACBL is the American Contract Bridge League, so THE CB OF ACBL is CONTRACT BRIDGE.

Board # Opening bid Contract Letter Card Technique
11 4NT 7NT T ♣A Unblock
7 2 5 H ♣K Scissors coup
2 1NT 3NT E ♠Q Endplay
3 1 4 C J Safety play
1 1 3NT B 10 Percentage play
10 3NT 6NT O 9 Double squeeze
4 2♣ 4♠ F 8 Ruff a loser in dummy
9 1♣ 6♠ A 7 Morton's Fork coup
8 1 6 C ♣6 Trump coup
5 1 4♠ B 5 Dummy reversal
6 3 4♠ L 4 Loser-on-loser

### Full solutions:

Board: 1
Dealer: North
• ♠ J 6 3
• K 5
• A K J 10 7 4
• ♣ 6 2
• ♠ Q 10 5 2
• J 8 4
• 5 3
• ♣ A K 8 3
N
S
E
W
West North East South
1 (B) Pass 1♠
Pass 2 Pass 2NT
Pass 3NT Pass Pass
Pass

Tricks:

1. 2 5 10 J
2. 3 2 10

The North hand opens 1. 1 is the second-lowest opening bid, so this corresponds to B.

Your heart stopper has been removed, so the opponents can cash at least three hearts and two spades as soon as you let them in. That means you need to run 9 tricks right now, so you need 6 diamond tricks. There are three possible lines: 1) play diamonds from the top, hoping the queen is singleton or doubleton; 2) finesse twice against the queen in West; and 3) play one top diamond, then finesse on the second round. Option 1 is the worst, as the queen will be onside 50% of the time but singleton or doubleton only about 30% of the time. Comparing lines 2 and 3, cashing one high diamond first gains against singleton queen in East, but finessing twice gains against a small singleton in East (if you cash one high honor, you'll lose to Qxxx with West). A small singleton is four times as likely as a singleton queen, so the 10 is the percentage play.

Board: 2
Dealer: East
• ♠ 8 4 3
• Q 8 5
• A 10 4
• ♣ A Q J 4
• ♠ Q J 6
• A J 4
• K J 5
• ♣ K 10 9 3
N
S
E
W
West North East South
Pass 1NT (E)
Pass 3NT Pass Pass
Pass

Tricks:

1. ♠5 ♠3 ♠A ♠6
2. ♠9 ♠J ♠2 ♠4
3. ♣10 ♣2 ♣4 ♣5
4. ♣3 ♣8 ♣J ♣6
5. ♣Q ♣7 ♣K 2
6. ♠Q

South has a balanced 15-count and opens 1NT.

From the first two tricks, West appears to have five spades (having led a fourth-best 5-spot followed by the deuce at trick 2). If you take a heart finesse and it loses, West will cash three more spades and down you go. A diamond finesse into East is safer, since if it loses, you can still try the heart finesse later, bringing your chances up to about 75%. But the best play is just to endplay West by leading your ♠Q. West can cash up to two more spades (you can discard two hearts from dummy, and a heart and a diamond from hand), but then West has to play either hearts or diamonds for you, either of which will present you with your ninth trick. (You should keep the ♣A in dummy in case West exits a low diamond, since you'll need to unblock the K and then go back to dummy to cash the A.)

Board: 3
Dealer: South
• ♠ K 8 5 2
• 9 5 3
• 9 6 2
• ♣ K 7 5
• ♠ -
• A K J 8 7 4
• K 8 4
• ♣ A Q J 10
N
S
E
W
West North East South
1 (C)
1♠ 2 2♠ 4
Pass Pass Pass

Tricks:

1. ♠Q ♠2 ♠3 4
2. A 6 3 2
3. ♣10 ♣2 ♣K ♣4
4. 5 10 J

The South hand, with plenty of high cards and long hearts, is a clear 1 opening bid.

With nine combined trumps, playing for the drop is slightly better than playing for the finesse here, but if you play for the drop and are wrong, you will go down if the diamond ace is offside. However, if you finesse, you guarantee the contract: if the finesse wins, you get 6 trump tricks and 4 clubs; if it loses, West can't hurt you in diamonds, so will have to exit passively in a black suit. With trumps 2-2, you can pitch a diamond from dummy on the fourth club and later ruff a diamond in dummy for your tenth trick. So taking the finesse is a safety play—even if it loses, you'll still make your contract.

Board: 4
Dealer: West
• ♠ 9 4 2
• 8 7 5 2
• J 2
• ♣ 9 8 4 2
• ♠ A K Q 8 5
• A K
• 10 9 8
• ♣ A K 6
N
S
E
W
West North East South
Pass Pass Pass 2♣ (F)
Pass 2 Pass 2♠
Pass 3♣* Pass 3NT
Pass 4♠ Pass Pass
Pass

* double negative

Tricks:

1. Q 2 6 K
2. 8

With 23 high-card points, South's opening bid is 2♣, strong, artificial, and forcing.

You have 9 tricks if trumps break 3-2. (If trumps break badly, you're toast.) By far your best chance of a tenth is by ruffing a loser in dummy. In order to ruff your diamond loser before the opponents play trumps, you need to play diamonds right now. (Playing even one round of trumps gives the defense time to draw dummy's trumps; playing either hearts or clubs risks a defensive trump promotion.)

Board: 5
Dealer: North
• ♠ Q J 10
• Q 7 2
• A 7 6 5
• ♣ A 8 3
• ♠ A K 9 5 4
• 9 6 5
• 3
• ♣ K Q 5 2
N
S
E
W
West North East South
1 (B) Pass 1♠
Pass 1NT Pass 2*
Pass 2♠ Pass 4♠
Pass Pass Pass

* artificial game force

Tricks:

1. K A 4 3
2. 5

With a balanced 13-count, North opens their longer minor.

You have 9 tricks on top: 5 spades, 3 clubs and 1 diamond. The best chance for a 10th trick is a dummy reversal: ruff three diamonds in hand and use dummy's three spades to draw trump. This is safer than hoping clubs break 3-3, or that both ace and king of hearts are onside; all you need is a 3-2 break in trumps (and for the defense not to lead trumps right away, which they thankfully haven't). You'll need to use all four of your dummy entries for this: three for diamond ruffs and one more to finish drawing trump. Since you've just been forced to use one dummy entry already, you must start with a diamond ruff. The play will continue: club to dummy, diamond ruff high, trump to dummy, diamond ruff high, trump to dummy, draw the last trump pitching a heart from hand, cash two more clubs (and if they happen to break 3-3, you can score an overtrick).

Board: 6
Dealer: East
• ♠ A 10 5 4
• 6 5 2
• Q 10 2
• ♣ A Q J
• ♠ K Q 9 8 3
• A 4
• 9 7
• ♣ K 8 6 5
N
S
E
W
West North East South
3 (L) 3♠
Pass 4♠ Pass Pass
Pass

Tricks:

1. 3 10 J 7
2. A 9 7 2
3. K 4

A 3-level preempt by East is the only explanation for South's 3♠ bid, and the play to the first two tricks reveals that East started with AKJ8654.

If you ruff low, West can overruff and you still have to lose a heart later. If you ruff high, you'll have to guess whether to try to drop the ♠J or finesse against Jxx in West, and you might go wrong. You can ensure the contract by discarding your heart loser on this trick, a loser-on-loser play. Dummy can overruff West if East continues diamonds, and otherwise you can just draw trumps and claim.

Board: 7
Dealer: East
• ♠ J 5
• A 7 5 2
• 8 6 4 2
• ♣ K J 5
• ♠ A K Q 10 7
• 8 4
• K Q J 9 5 3
• ♣ -
N
S
E
W
West North East South
2 (H) 4*
Pass 5 Pass Pass
Pass

Tricks:

1. 6 A K 4
2. ♣K

South's first bid is "leaping Michaels", which is a defense used against an opponent's weak two-bid in a major: a leap to four of a minor shows that suit and the other major, and is forcing one round. Thus East's opening bid must have been 2.

Board: 8
Dealer: South
• ♠ A 8 6
• 5 4
• A 10 6
• ♣ A 9 8 7 6
• ♠ Q 4 3
• A K Q 10 7 6
• K Q J
• ♣ 4
N
S
E
W
West North East South
1 (C)
Pass 2♣ Pass 3
Pass 3♠ Pass 4NT
Pass 5♣ Pass 5NT
Pass 6 Pass Pass
Pass

Tricks:

1. ♠J ♠6 ♠K ♠3
2. ♣K ♣4 ♣2 ♣A
3. ♣6

South has a normal 1 opening bid.

If trumps behave, you have 12 tricks: 2 spades, 6 hearts, 3 diamonds and a club. What if trumps don't behave? If West has four or five hearts to the jack, there's nothing you can do. But if East has four to the jack, you're still alive. Finessing against the jack on the first or second round is unwise; you could go down on a totally normal break if West produces the jack. But if you cash two top trumps and East shows up with Jxxx, you can still succeed via a trump coup—if you took the precaution of ruffing a club at trick 3. The key is that you need to come down to trick 12 with the lead in dummy, and you holding Q10 of trumps over East's Jx. The only way to do that is to reduce your trump length to the same as East's (otherwise you'll be in your hand after trick 11, not in the dummy). The play will go (starting from trick 3): club ruff, two top trumps. If trumps break, draw the last trump and claim. If West shows out on the second round, cross to dummy with a spade and ruff another club. Then cash winners ending in dummy after trick 11 for the trump coup. You'll need East to follow suit a lot, so it might not work against every distribution, but it will work if East is 3=4=3=3.

Board: 9
Dealer: North
• ♠ K J 9 2
• A 8 7
• 8 3
• ♣ K Q 7 2
• ♠ A Q 10 8 7 5 4
• -
• A 10 9 6
• ♣ J 6
N
S
E
W
West North East South
1♣ (A) Pass 1♠
2 2♠ 4 5
Pass 6♠ Pass Pass
Pass

Tricks:

1. Q 7

North, with a balanced 13 count, opens their longer minor.

You seem to have an inescapable loser in both diamonds and clubs, but you have recourse to a delightful play called a Morton's Fork Coup. West, with the bulk of the defensive high cards but evidently neither of the top heart honors, is likely to hold the ♣A. What happens if you lead your low club through West? If West grabs the ace without capturing one of your club honors, you can later discard two diamond losers from hand on clubs and one on the A. But if West ducks the club, you can simply discard your ♣J on the A, concede a diamond, and then ruff two diamonds in dummy; the defense will score a diamond but not their club ace. However, the play only works if you preserve dummy's A, since you don't yet know which suit you'll need to discard on it. If you pitch a club from hand at trick 1, West can play the ace on your jack; and if you pitch a diamond at trick 1, West can duck the ♣A safely because you will have no way of getting rid of your ♣J. So ruff trick 1 in hand, draw trumps, and then put West on Morton's Fork.

Board: 10
Dealer: South
• ♠ A K 3 2
• A J 10 3
• A 9
• ♣ 9 5 3
• ♠ 5 4
• 7
• 8 5 2
• ♣ A K Q J 10 7 4
N
S
E
W
West North East South
3NT* (O)
4 Double 5 Pass
Pass 6NT Pass Pass
Pass

Tricks:

1. 10 9

Bridge World Standard uses the gambling 3NT, a seven-card solid minor with little or no strength outside. That's precisely what South has, and North's bidding doesn't make any sense if South's opening bid had been any number of clubs.

The bidding has been quite informative. West surely has long hearts, probably six or seven headed by the KQ. East has no tolerance for hearts and long diamonds, apparently headed by the KQJ based on West's lead. You have 11 top tricks. If you win the opening lead and attempt to establish a second heart trick, you will go down (in fact, down a lot) if West started with two diamonds. The contract is, in fact, secure on a double squeeze if everybody has what they say they have, but you need to rectify the count for a double squeeze, and that can only be done safely by ducking trick one. Then win whatever suit they play at trick 2, cash both red aces (and, optionally, one round of spades) if they are still unplayed, and run the clubs. As you lead the last club, the position will be:

• ♠ A K 3
• J
• -
• ♣ -
• ♠ 5 4
• -
• 8
• ♣ 4
• ♠ ???
• K
• -
• ♣ -
• ♠ ???
• -
• K
• ♣ -
N
S
E
W

If East had as much as honor-doubleton in hearts, they surely would not have run from 4 doubled, so West is the only defender who can guard hearts. So West must pitch down to a doubleton spade on the last club lead. Now the J can be discarded from dummy (having done its duty), and the squeeze operates on East. East is the only one who can guard diamonds, so must also pitch down to a doubleton spade. Then you lead a spade to dummy and take the last trick with dummy's low spade.

Board: 11
Dealer: South
• ♠ J 9 8 7 6 5 2
• 5
• A
• ♣ K 7 5 3
• ♠ A
• A K Q J 6
• K Q J 10 9 6
• ♣ A
N
S
E
W
West North East South
4NT (T)
Pass 5 Pass 7NT
Pass Pass Pass

Tricks:

1. ♠K ♠2 ♠3 ♠A
2. ♣A

A 4NT opening is actually not defined in Bridge World Standard, but the 5 response makes no sense except as a response to an ace-asking bid (and South has the kind of hand that is only interested in one card). Does 5 show one ace, or does it show specifically the diamond ace? In this case, it doesn't matter.

You have thirteen top tricks here (1 spade, 4 hearts, 6 diamonds, and 2 clubs), but you need to make sure you unblock the ♣A before you use your one dummy entry to cash the ♣K and discard your low heart. If you don't get two club tricks, you'll need to hope hearts break 4-3, about a 61% chance. But cashing the ♣A is a 100% play. (If the opening lead had been a diamond, you'd be forced to fall back on the hearts breaking.)

## Author's Note

This was one of the first puzzles we started writing and one of the later ones to be finalized. As soon as the Reference meta was approved with CONTRACT BRIDGE as a feeder answer, joon claimed it for a bridge puzzle and enlisted Diana—a long-ago bridge teammate much more recent trivia and puzzle teammate—to help construct it. Bridge puzzles in previous Hunts had been more puzzly and less bridgy (e.g. using bridge terminology as a data set), so we aimed for a puzzle that would reward bridge expertise, and settled on declarer play problems. The rebus elements were added in as a possible back channel: if you wouldn't be able to solve a deal on your own but could read up on, say, Morton's Fork Coups and figure out where to fit that in, you'd still have a chance. The additional unique rank constraint (and, in some cases, the very limited options for what card to play next based on the requirements to follow suit and play the lowest of equals) further constrained the options, but we still wanted solvers to think deeply about the hands.

The idea of using the missing opening bids to stand for letters in the extraction was suggested by the title of the puzzle (which in turn was constrained by the Reference meta). Plenty of puzzles involving playing cards have previously based an extraction on 52 cards being exactly twice the alphabet, but we thought it might be frustrating to have to disambiguate among all the different ways you could map cards onto letters, none of which quite makes sense for bridge ordering. Normally in bridge, you'd order the cards from ace=1 down to deuce=13, but that causes the spot cards to not stand for their own number; conversely if the spot cards do stand for their own number, ace isn't A, and it doesn't really make bridge sense to either start with deuce, or make aces low. So using the cards as an ordering and the bids to stand for letters stood out as a cleaner choice. In the end, the clue phrase is basically unrecognizable until you have at least 9 or so out of 11 letters correctly placed, and certainly running the 11 letters through Nutrimatic (or equivalent) is not going to turn up the right result, so having the mapping to letters be ambiguous on top of all that would just be mean.