Main     Puzzle 8F23 by Richard Pavlicek    

Yarborough Fair

Could a Yarborough win all 13 tricks in notrump? Yes, with cooperation. Imagine you hold the South hand on the following deal, playing in a fantasy world:

NT win 13
in 1 hand
S
H A K Q J 10 5 4 3 2
D
C K 10 7 3
S A K Q J 10 5 4 3 2
H
D
C Q 9 6 2
Table S
H
D A K Q J 10 5 4 3 2
C A J 8 4
Lead: S 2 S 9 8 7 6
H 9 8 7 6
D 9 8 7 6
C 5

South wins four spade tricks as West obligingly ducks, while North and East toss red honors. Similarly, South wins four heart tricks as North ducks, and four diamond tricks as East ducks. Somewhere in the process South leads the C 5 to fetch the two, three and four! Unreal, but the issue is not what would happen in practice; only what is possible via legal plays. A puzzle for you:

What is the weakest hand that could win all 13 tricks in notrump?

Assume South is declarer (though it doesn’t matter) and must win all 13 tricks in the South hand. You can dictate the play of all four hands to achieve the goal. Weakness is judged as the sum of South’s cards. The above sum is 95. How low can you go?

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Tim Broeken Wins!

In December 2010 and January 2011 this puzzle was presented as a contest, with 66 participants from 29 locations. Thanks to those who entered, and congratulations to the 11 solvers who produced the absolute weakest hand to win 13 tricks. Also listed (places 12-17) are those who missed perfection by a single pip. Everyone listed below submitted a valid complete deal, so the ties among equal sums are broken by date and time of entry.

Except for a few token Americans, it was a European sweep — mainly England and Netherlands — and I’ll tell you why. The Yarborough was named after the Earl of Yarborough, a British nobleman. How the Dutch got in the picture I’m not sure, but I vaguely remember an Earl of Holland. Maybe the two got together for lunch with the Earl of Sandwich. Or was he a Duke? No, I seem to have landed in a 1960s time warp with Duke of Earl blaring from the jukebox, but I digress.

RankNameLocationSum
1Tim BroekenNetherlands54
2Hendrik NigulEstonia54
3Pavel StrizCzech Republic54
4Charles BlairIllinois54
5Audrey KuehEngland54
6Howard LiuIllinois54
7Dan BakerTexas54
8Ufuk CotukEngland54
9Jim MundayCalifornia54
10Jonathan MestelEngland54
11Julian WightwickEngland54
12Mike WenbleEngland55
13Reint OstendorfNetherlands55
14James LawrenceEngland55
15Perry GrootNetherlands55
16Jan KuipersNetherlands55
17John AuldEngland55

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Solution

How low can you go? It was easy to improve on my example Yarborough (sum 95) at the introduction of this puzzle, but most reduced the sum only to the low 60s or high 50s. Anyone with experience at the game of Hearts, or the French game Misere, would have an edge here. Or as one of my regulars noted:

Charles Blair: “Anyone can raise a cheap cheer by chucking an ace. The true master shows his worth in the manipulation of twos and threes.” –Victor Mollo

Charles was one of our token American solvers, not quick enough to stem the European tide. Perhaps if he changed his name to Tony?

Before showing the perfect solution, let’s look at a few that came within a hair:

NT win 13
in 1 hand
S
H J 10 9 6
D 10 9 8 7
C 10 9 8 7 3
Trick
1. W
2. S
3. S
4. S
5. S
6. S
7. S
8. S
9. S
Lead
S 6
S 5
S 3
H 8
H 5
H 4
H 3
H 2
C 4
2nd
H J
4
2
D 6
C 6
C 5
S A
S K
S Q
3rd
H A
H 10
H 9
6
D 10
D 9
D 8
D 7
3
4th
7
H K
H Q
7
D A
D K
D Q
D J
2
S A K Q J 10 9 8 6 4 2
H
D 6
C 6 5
Table S
H A K Q 7
D A K Q J
C A K Q J 2
Mike Wenble
England

S 7 5 3
H 8 5 4 3 2
D 5 4 3 2
C 4

After nine tricks, South’s D 5-4-3-2 are high. Note that the West, North and East hands are interchangeable. For instance, if you swap North and West, the H 6 lead would just reorder the first four tricks.

The 55 sum can also be attained with a balanced South hand, and the highest card a seven:

NT win 13
in 1 hand
S
H 10 9 8 7 6
D 9 8 7
C 10 9 8 6 3
Trick
1. W
2. S
3. S
4. S
5. S
6. S
7. S
8. S
9. S
10. S
Lead
S 2
S 5
S 7
C 7
C 4
D 6
D 5
D 4
D 3
D 2
2nd
D 9
4
6
D Q
D J
H 5
S A
S K
S Q
S J
3rd
D A
D 8
D 7
6
3
H 10
H 9
H 8
H 7
H 6
4th
3
D K
D 10
5
2
H A
H K
H Q
H J
C A
S A K Q J 10 9 8 6 4 2
H 5
D Q J
C
Table S
H A K Q J
D A K 10
C A K Q J 5 2
Reint Ostendorf
Netherlands

S 7 5 3
H 4 3 2
D 6 5 4 3 2
C 7 4

After 10 tricks, South’s H 4-3-2 are high. Here also, the West, North and East hands are interchangeable.

Hand 54, where are you?

The absolute weakest hand that can win 13 tricks has a sum of 54, and is unique except for suit identity. South must hold suits of 7-5-3, 7-5-4-3-2, 5-4-3-2 and a singleton 4. Note that this is the same as the first example (sum 55) except the eight is reduced to a seven.

The following solution from our winner plays out like a broeken record:

NT win 13
in 1 hand
S
H A K Q J 10 3
D K 9 8 6
C 8 7 6
Trick
1. W
2. S
3. S
4. S
5. S
6. S
7. S
8. S
Lead
S 2
S 5
S 7
H 4
D 7
D 5
D 4
D 3
2nd
D K
4
6
D A
C 10
C 9
S A
S K
3rd
D Q
D 9
D 8
3
6
C 8
C 7
C 6
4th
3
D J
D 10
2
C A
C K
C Q
C J
S A K Q J 10 9 8 6 4 2
H
D A
C 10 9
Table S
H 9 8 7 6 5 2
D Q J 10
C A K Q J
Tim Broeken
Netherlands

S 7 5 3
H 4
D 7 5 4 3 2
C 5 4 3 2

After eight tricks, South’s D 2 C 5-4-3-2 are high. Once again the other three hands are interchangeable.

Earning style points were Howard Liu, Dan Baker and Julian Wightwick. Each not only produced a perfect solution (sum 54) but also made North as weak as possible. In the above layout, swapping the North-East hearts and the D K/10 effects their solution. Dan and Julian also correctly noted that a second Yarborough is impossible if South has a sum of 54, but close with North requiring one 10.

Howard Liu: Next time I will open 7 NT with the South hand.

Jim Munday: This is a lot of fun. With the way I bid, this is a technique I need to master.

A new bridge Law?

Considering that the worst possible bridge hand, S 4-3-2 H 4-3-2 D 4-3-2 C 5-4-3-2, has a sum of 41, it is curious that adding 13 to get 54 allows all the tricks to be won — exactly one trick per pip. Move over, Jean Rene Vernes! The LOTT is hereby superseded by Pavlicek’s LOTP (Law of Total Pips) which states that the sum of the pips less 41 equals the number of tricks the hand can win against lunatics. Of course you ask, is there enough lunacy in the bridge world for the Law to be practical? While I can speak only for my own ward, evidence to the affirmative is mounting. To wit:

Jonathan Mestel:
Tell her to make me a notrump grand;
Parsley, sage, rosemary and thyme.
With barely a seven held in her hand,
She will ever be a true love of mine.

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© 2011 Richard Pavlicek