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Chasing Rainbows

Being a problematist by nature, I’ve always been fascinated by unusual bridge deals. Most of my puzzle creations have been inspired by the construction or discovery of a bizarre layout. In the old days these puzzles had a special aura, in that a solution might elude the human mind forever; and even if a solution were found, proving it unique was difficult. Nowadays, much of the mystique is lost, because computer software is capable of exact double-dummy analysis in a short time.

One of my longest quests has been to construct a deal in which all four players can make one of the same suit against any defense. This may seem trivial — after all, it’s just a one-bid — but if you consider the implications of such a feat, you begin to realize how unusual it would be. Indeed, it has proved to be as elusive as squaring the circle or trisecting an angle in geometry. For years I wondered if such a deal even existed, fully expecting that I might be chasing rainbows.

The logical start was to consider symmetric deals, those with four identical hands except for suit rotation; i.e., West’s spades are the same as North’s hearts, East’s diamonds and South’s clubs, and analogously in every other suit. I wanted to create a database of every possible symmetric deal, but there were just too many to be practical. To reduce the size, I treated the two through six in each suit as indistinguishable, and eliminated any redundancies caused by rotation and suit order. This left a workable size of 344,064 symmetric deals.

Alas, a complete double-dummy analysis of the symmetric deal database found none where all four players could make one of the same suit. Actually, considering the symmetry, this would translate to each player making one of every suit, so my disappointment was predictable. There were, however, many cases (9458 to be exact) where 1 NT makes around the table. For example:

1. All make 1 NT (symmetric)

S 8 2
H A K Q 6
D J 9 7 5
C 10 4 3
S A K Q 6
H J 9 7 5
D 10 4 3
C 8 2
TableS 10 4 3
H 8 2
D A K Q 6
C J 9 7 5
S J 9 7 5
H 10 4 3
D 8 2
C A K Q 6

Makes NSWENT 7777S 6677H 7766D 6677C 7766

Whichever side is defending can easily cash six tricks, but doing so establishes a seventh trick for declarer. Further, if the defense leads either of its weak suits, declarer can win a fourth trick in that suit. Note that even a seemingly safe eight lead (dummy covers) allows partner’s holding to be captured. Like the Zugzwang in chess, whoever makes the first move loses.

While everyone can make 1 NT, note that results of suit contracts (summarized in the “Makes” bar) are as ordinary as one could expect. North or South make seven tricks in either of their 7-card fits, as do West or East in theirs.

For the past five years or so, I have also been building a database of random deals, solved at double-dummy for each player and each strain (thus requiring 20 solutions per deal). For convenience I use an old computer, which just chugs away; well, except when I forget to restart after a power failure (a Florida feature). Despite the occasional down time, my untiring workhorse has just passed the 8 million mark — a good-sized database to continue my quest.

Out of 8 million deals I had great expectations, but there was no pot of gold (at least for what I wanted) at the end of my rainbow. Surprisingly, there was only one deal where everyone makes 1 NT — evidently quite a rarity without symmetry. Here it is:

2. All make 1 NT (nonsymmetric)

S J 9 5 4 2
H A J 8 7 6
D J 6 5
S K 7 6
H 10 9 4
D A 10 3
C K 8 4 3
TableS A 10 8
H Q 5 3
D Q 9 8
C J 7 5 2
S Q 3
H K 2
D K 7 4 2
C A Q 10 9 6

Makes NSWENT 7777S 8855H 8855D 8855C 7766

The appearance of this deal hardly suggests that anyone, much less everyone, makes 1 NT; but looks don’t matter to a double-dummy solver. Computers are hard to argue with — kind of like the old Hans & Franz line, “Believe me now, or believe me later.” Therefore, I tend to save my efforts for causes I might win. A complete analysis will be left to the reader; or more specifically, to any reader who’s more of a nut case than I am.

Surprisingly, all the suit makes favor North-South (8:5 in spades, hearts and diamonds, 7:6 in clubs) and there is no gain or loss for being on lead (trick counts in each suit always total 13) — yet everyone makes 7 tricks in notrump. Go figure. Considering this was the only such deal out of 8 million, I could see that my task of finding an equal-all-around suit make would be daunting.

Speaking of equivalent notrump makes, there is no known layout where everyone makes 2 NT; and after searches and construction attempts, I believe it’s impossible. Amazingly, there is one symmetric layout (unique except for hand rotation and suit swaps) where everyone makes 3 NT. Hard to believe, but here it is:

3. All make 3 NT (symmetric)

H A 8 7 6 5 4 3 2
C Q 10 9
S A 8 7 6 5 4 3 2
D Q 10 9
TableS Q 10 9
D A 8 7 6 5 4 3 2
H Q 10 9
C A 8 7 6 5 4 3 2

Makes NSWENT 9999S 22BBH BB22D 22BBC BB22

The key to this extraordinary layout is that every long suit is blocked. Whoever is on lead must allow declarer to unblock his or dummy’s suit, else lead from his K-J and lose that stopper. For example, if West leads a low spade, dummy pitches a club; then declarer can duck a club to establish clubs. Note that West’s spade suit, while established, remains hopelessly blocked.

Although I “discovered” the above deal in my symmetric deal database, I had first learned of it from Thomas Andrews, whose obsession for the bizarre may exceed my own (see “Everybody Makes” at History suggests the deal has earlier discoverers as well.

The Quest Continues

Meanwhile, back to my search for the pot of gold. While my database of 8 million random deals had none where each player can make one of the same suit, I did notice a related characteristic. I found three deals — count ‘em, three in 8 million — in which 28 total tricks could be made in one suit around the table. Curiously, these were all in hearts, but that’s just a coincidence. This deal came the closest to my goal:

4. Hearts total 28 tricks

S A 8 7 4
H K J 9 5 4
C J 9 3 2
S K 5 2
H A Q 8 7
D A 8 7 5
C 10 4
TableS J 3
H 10 6 3 2
D J 6 4 2
C K Q 5
S Q 10 9 6
D K Q 10 9 3
C A 8 7 6

Makes NSWENT 8855S AA33H 8866D 8855C AA33

Note the unusual makes in the heart suit: North or South can win 8 tricks, while West or East can win 6 — a full two tricks beyond the norm — which essentially means that no matter what is led, being on lead costs a trick. Curiously, every other suit or notrump is perfectly normal (26 total tricks), so the anomaly in hearts shows how strange and unpredictable this game can be.

Aha! Maybe I could change a card or two without disturbing the essence of the deal, converting the “8866” results into four 7’s. Alas, this was easier said than done. Obviously, I had to weaken the North-South hands somehow to send a trick to the other side. First I attempted to revise the trump layout; then I tried weakening South’s diamonds; then various spade and club modifications. All to no avail — and frustrating, as I spent several days trying this. It was like dropping coins into a slot machine; the reels would spin, but I never hit four 7’s. I gave up.

About a week later, I looked at it again. Maybe something new would occur to me. There were some black-suit holdings I hadn’t tried, so I fiddled around some, not very hopeful. More disappointment, but at least I was expecting it now. I even tried changing two suits at a time but quickly abandoned that when the deal began to lose its magic. About ready to quit again, I tried a few more spade layouts including:

S K 8 7 4
S Q 5 2S A 10
S J 9 6 3

I checked North… makes 1 H; then South… makes 1 H; West… makes 1 H; and East… [I’m sweating]… Yes! East makes 1 H! For a brief moment I felt like Christopher Columbus or Jonas Salk — then the truth sank in how useless this really was. In my own little world at least, perseverance had paid off. What I thought might be impossible finally came to fruition.

For my final exhibit, it seemed prudent to switch the major suits. I mean, who wants to make only 1 H when you can make 1 S? Spades rule! So here it is, folks. Guard this deal with your life:

5. All make 1 S

S K J 9 5 4
H K 8 7 4
C J 9 3 2
S A Q 8 7
H Q 5 2
D A 8 7 5
C 10 4
TableS 10 6 3 2
H A 10
D J 6 4 2
C K Q 5
H J 9 6 3
D K Q 10 9 3
C A 8 7 6

Makes NSWENT 7766S 7777H 9944D 6676C 8845

I won’t go into the many play intricacies (I’d be writing for a month), but 1 S by East seems to be the toughest. South can safely lead the D K (ducked) then shift to a low club, giving nothing away. Even so, East can keep South off lead (else gain a club trick) and endplay North repeatedly. The fact that East cannot achieve the same result if on lead (or if West leads) is truly remarkable.

Although the deal allows 28 total tricks in spades, no other denomination allows more than the usual 26. In fact, each minor allows only 25, which indicates an advantage for being on lead. Weird, when leading is a disadvantage in spades.

Also strange is the makeup of the deal itself. When I first tackled this problem many years ago, I expected some kind of balanced distribution: suits 4-3-3-3 around the table (especially trumps) and 20 HCP for each side. Now a solution comes along with no suit being 4-3-3-3, trumps 5-4-4-0, a side-suit void, and HCP split 22-18. Incredible. Another curio is that North-South makes the odd trick in notrump despite holding fewer HCP.

Crazy game, this bridge. The more I study it, the more I realize how much more there is to learn.


© 2008 Richard Pavlicek