Puzzle 8K65 Main

The Law of Total Trash

by Richard Pavlicek

A popular catchphrase of the times is “The Law of Total Tricks” which states: If each side were to play in its longest trump fit, the combined number of trumps is approximately equal to the combined number of winnable tricks. Unfortunately, the Law has dubious value because of its high degree of variance. Consider this deal:

N or S	J 7 6 3
win 3	3 2
	K Q 7 6
	Q J 2
4		A K Q 10
A K 10 9 8 7		6 5 4
10 9 8		J 3 2
9 8 3		K 7 4
	9 8 5 2
	Q J
W or E	A 5 4
win 7	A 10 6 5

North-South have eight spades and East-West have nine hearts, or 17 total trumps. With best defense, N-S win only three tricks and E-W win seven, or 10 total tricks. This deviation of seven puts quite a strain on “approximately equal,” which brings me to the puzzle:

What is the greatest possible deviation in the Law of Total Tricks?

Construct a deal that deviates from the Law by at least eight tricks (the more the better). The longest trump fit must be distinct (no ties) as spades for N-S, and hearts for E-W.

Winnable tricks are determined at double-dummy, using the more productive declarer (if it matters)
for each side. For example, if North wins more tricks than South in spades, North’s result counts.

Dan Dang Wins

After almost a year of European domination, the winner has returned to American soil, at least continentally. Dang, we have a winner, eh? I learned to appreciate our northern neighbors back in the heyday of Rick Moranis and Dave Thomas with their “Great White North” skits. Indeed, my first contest in this series may have been a subconscious side effect, eh? And I might have increased participation this time if I had followed Rick’s footsteps with the title “Honey, I Shrunk the Law.”

Winner List

Rank	Name	Location	Deviation
1	Dan Dang	British Columbia	-12
2	Hendrik Nigul	Estonia	-12
3	Ed Barnes	Australia	-12
4	Tim Broeken	Netherlands	+10
5	James Lawrence	England	-10
6	Tim Bentley	Michigan	-10
7	Edouard Bonnet	France	-10
8	Reint Ostendorf	Netherlands	-10
9	Leigh Matheson	Australia	+10
10	Licai Yeo	Singapore	-10
11	Tony Norris	Massachusetts	-10
12	Richard Stein	California	+10
13	Manuel Paulo	Portugal	-9
14	Jim Munday	Mississippi	-9
15	Wes Eldred	Minnesota	+9
16	Wayne Somerville	Northern Ireland	-8
17	Jean-Christophe Clement	France	-8

Puzzle 8K65 Main

Top The Law of Total Trash

Solution

In this contest the longest trump fit for each side had to be distinct; i.e., a deal was not allowed if two suits tied for a side’s longest fit. Besides simplifying the task, this eliminated the trivial case of 14 trumps, 26 tricks, based on each side having two 7-card fits and a pat hand like A-K-Q-J-10-9-8 A-K-Q-J-10-9. This restriction does not alter the solution, since the trivial case (+12) must be the greatest positive deviation, and negative deviations can produce the same (-12).

A few respondents overlooked “by more productive declarer if it matters” and submitted a deal that required a
specific declarer to achieve a high deviation. Sorry, but just as in real life, it would be unfair to force a contract
to be played from the wrong side. For more insight on this check out my latest puzzle, Right-Sided Spades.

Three respondents produced deals with a negative deviation of 12, curiously based on entirely different layouts — or maybe that should be expected, since they live on three different continents. Let’s begin with our winner, who was not only first in the clubhouse but brought a touch of deja vu:

N or S	6 5 4 3		Trick	Lead	2nd	3rd	4th
win 2	A K Q J 2		1. W	7	8	A	J
	10 9 8		2. E	2	Q	2	9
	7		3. W	A	3	7	7
A K Q J 2		—	4. W	K	4	8	8
6 5 4 3		10 9 8 7	5. W	Q	5	9	9
7		A 6 5 4 3 2	6. W	J	6	10	10
10 9 8		K Q J	7. W	8	7	J	A
	10 9 8 7		8. S	2	9	2	Q
	—		9. E	3	K	3	10
W or E	K Q J			Lose the rest
win 2	A 6 5 4 3 2

Dan Dang: North or South plays in spades, East or West in hearts, each with an 8-card fit (total trumps = 16); but any declarer is held to two tricks (total tricks = 4) so the Law is off by 12. The same result could be achieved if South held x-x-x-x -- A-K-Q J-x-x-x-x-x, and East -- x-x-x-x J-x-x-x-x-x A-K-Q.

Yes, and other holdings as well. My own construction, which inspired this silly contest, has the same deal pattern but with South holding x-x-x-x -- Q-J-10 A-K-x-x-x-x, and East analogous.

Dan’s construction is also aesthetically pleasing with each hand having one card of each rank — a far cry from the next deal, where a hail storm just wiped out the northeast.

Stoned in Estonia

Two nine-card fits are exploited by Hendrik Nigul in this version of the minus-12 genre, with each side being able to win only three tricks. Pretty weird, but the bridge world can’t hide from a composer gone amok:

N or S	9 8 7 6 4 3		Trick	Lead	2nd	3rd	4th
win 3	—		1. E	2	A	J	5
	5		2. W	A	3	2	2
	8 7 6 5 3 2		3. W	K	4	4	5
A K Q J		—	4. W	Q	6	5	10
10 9 3		8 7 6 5 4 2	5. W	A	2	4	9
—		8 7 6 4 3 2	6. W	K
A K Q J 10 9		4		Win 3 trump tricks
	10 5 2
	A K Q J
W or E	A K Q J 10 9
win 3	—

Hendrik Nigul: Total trumps = 18; total tricks = 6; so the Law is off by 12. [No matter who declares], the defense can take the first four tricks with trumps (trick one is a ruff if the trump void is on lead) and then six side-suit winners.

Twelve the hard way

The creativity award this month must go to Ed Barnes (Australia) for the following exhibit, which bolsters the concept of its source “Down Under.” While North-South have the predictable 4-4 spade fit, the East-West heart fit is 8-0! Remarkably, the 8-bagger is blessed with a 3-2 trump break yet can win only three tricks. On second thought, maybe “blessed” should be replaced by “screwed.”

N or S	9 8 7 6		Trick	Lead	2nd	3rd	4th
win 1	A Q 10		1. N	A	7	8	2
	A K Q J 10 9		2. N	K	2	2	3
	—		3. N	Q	9	3	4
—		A K Q J 10	4. N	J	10	4	5
9 8 7 6 5 4 3 2		—	5. N	10	J	5	6
6 5 4 3 2		7	6. N	6	10	J	2
—		A K Q J 10 9 2	7. S	3	3	10	Q
	5 4 3 2		8. N	7	J	K	4
	K J			Lose 2 trump tricks
W or E	8
win 3	8 7 6 5 4 3

Ed Barnes: This looks like minus 12, but it can’t be the optimal solution, as I’ve failed to squeeze anyone out of a trick or two, or three.

A stylish comment, too. Hmm. Do I see a new puzzle brewing? Trash the Law with a three-trick-gaining squeeze? Yes! And I see a perfect prize for the winner: one week with Ed in the outback. (Losers get two weeks.)

Richard Stein: Following the Law at the table has gotten me into more trouble than I care to admit, so it might be time, after 15 years or so, to put the Law to pasture. I’m sure the contest entries you choose to show will confirm that idea.

To bid or not to bid

As this contest was running I received a note from Larry Cohen, who was amused by my title. When I invited him to submit an entry, he confided that the best he could come up with is a deal off by one. I’m kidding of course, as Larry is sharp as a tack, to which I can attest first-hand from my playing days. More importantly, however, he is one of the most good-natured guys in the game.

Thirteen, anyone?

Considering the variety of winning solutions, there are probably other deal patterns as well, so I am not convinced that 12 is the greatest possible negative deviation. For the time being I will consider the contest still open. Show me 13 and I’ll star you in my next documentary “The Beerhunter.” A sure hit, eh?

As you exit, please put your empty bottles in the trash can.

Puzzle 8K65 Main

Top The Law of Total Trash

© 2011 Richard Pavlicek