Main   Puzzles 8K03 by Richard Pavlicek  

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 only a one-bid — but if you consider the implications of such a feat, you begin to understand how extraordinary it would be. Indeed, it has proved to be as elusive as squaring the circle or trisecting an angle in geometry. For many 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: 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 too many to be practical. To reduce the size, I treated the two through six in each suit as indistinguishable, and eliminated 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 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:

All make 1 NT (symmetric)

1. 1 NT
South (WNE)
S 8 2
H A K Q 6
D J 9 7 5
C 10 4 3
Makes
North
South
West
East
Deal
NT
7
7
7
7
28
 S
6
6
7
7
26
 H
7
7
6
6
26
 D
6
6
7
7
26
 C
7
7
6
6
26
S A K Q 6
H J 9 7 5
D 10 4 3
C 8 2
Table S 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

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 weaker 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 moves first loses.

While everyone makes 1 NT, note that results of suit contracts 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. TopMain

For the past three 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 the end of my rainbow. In fact there was only one deal where everybody makes 1 NT — evidently quite a rarity without symmetry. Here it is:

All make 1 NT (asymmetric)

2. 1 NT
South (WNE)
S J 9 5 4 2
H A J 8 7 6
D J 6 5
C
Makes
North
South
West
East
Deal
NT
7
7
7
7
28
 S
8
8
5
5
26
 H
8
8
5
5
26
 D
8
8
5
5
26
 C
7
7
6
6
26
S K 7 6
H 10 9 4
D A 10 3
C K 8 4 3
Table S 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

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 26) — 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. TopMain

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:

All make 3 NT (symmetric)

3. 3 NT
South (WNE)
S
H A 8 7 6 5 4 3 2
D K J
C Q 10 9
Makes
North
South
West
East
Deal
NT
9
9
9
9
36
 S
2
2
11
11
26
 H
11
11
2
2
26
 D
2
2
11
11
26
 C
11
11
2
2
26
S A 8 7 6 5 4 3 2
H K J
D Q 10 9
C
Table S Q 10 9
H
D A 8 7 6 5 4 3 2
C K J
S K J
H Q 10 9
D
C A 8 7 6 5 4 3 2

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 come across it at the web site of Thomas Andrews, whose obsession for the bizarre may exceed my own. History suggests the deal has earlier discoverers as well. TopMain

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. Coincidentally, these were all in hearts. This deal came the closest to my goal:

Hearts total 28 tricks

4. 1 H
South (WNE)
S A 8 7 4
H K J 9 5 4
D
C J 9 3 2
Makes
North
South
West
East
Deal
NT
8
8
5
5
26
 S
10
10
3
3
26
 H
8
8
6
6
28
 D
8
8
5
5
26
 C
10
10
3
3
26
S K 5 2
H A Q 8 7
D A 8 7 5
C 10 4
Table S J 3
H 10 6 3 2
D J 6 4 2
C K Q 5
S Q 10 9 6
H
D K Q 10 9 3
C A 8 7 6

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 a variety of 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 could never hit four 7‘s. I gave up. TopMain

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 idea when the deal began to lose its magic.

About ready to quit again, I tried a few more spade layouts including West S Q-5-2, North S K-8-7-4, East S A-10 and South S J-9-6-3. I checked North… makes 1 H. Then I checked South… makes 1 H. Next I checked West… makes 1 H! Oh my god! Could this really be it? Sweating profusely, I was almost afraid to check East but had to do it: Yes! East also makes 1 H!

For a brief moment I felt like Christopher Columbus or Jonas Salk, until the truth sank in about how useless this really was. In my own little world at least, perseverance had paid off. What I thought might be impossible had finally came to fruition.

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

All make 1 S

5. 1 S
South (WNE)
S K J 9 5 4
H K 8 7 4
D
C J 9 3 2
Makes
North
South
West
East
Deal
NT
7
7
6
6
26
 S
7
7
7
7
28
 H
9
9
4
4
26
 D
6
6
7
6
25
 C
8
8
4
5
25
S A Q 8 7
H Q 5 2
D A 8 7 5
C 10 4
Table S 10 6 3 2
H A 10
D J 6 4 2
C K Q 5
S
H J 9 6 3
D K Q 10 9 3
C A 8 7 6

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 repeatedly endplay North. The fact that East cannot achieve this 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 with spades trump is a disadvantage.

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

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

© 2008 Richard Pavlicek