Puzzle 8M55   Main

# When in Doubt

by Richard Pavlicek

Professor Freebid and Timothy Tenace boarded their return flight from Chennai after a disappointing finish in the Transnational Teams. “The cards were stacked against us,” Timothy sighed, “like Board 2 against that hopeless Guadeloupean team. I knew your bid was weak, but how could I not double four hearts with a singleton in your suit and all that stuff behind declarer? Amazingly unlucky layout, I must say.”

The Professor jotted down their two hands from memory on his clipboard:

 4 × South ?  ?  ?  ? 6 K J 10 9 K J 10 9 K J 10 9 K Q J 10 9 8 6 8 7 8 7 6 5 Lead: 6 ?  ?  ?  ?

“Your double was reasonable but you led like a puppet. Yes, I bid spades, but you have to visualize. With both minors bottled up, how is declarer going to make tricks? Ruffing, that’s how. I realize you’ll never understand the intricacies of my boson deflection theory, but common sense dictates a trump lead. Even the old cliche ‘When in doubt…‘ is right more often than not.”

“But I had a broken sequence,” Timothy argued. “It would usually cost me a trump trick.”

“Cost works both ways,” the Professor explained. “You might win one fewer trump tricks, but that will often break even by stopping a ruff. In all probability you’ll get in for a second trump lead to show a profit, and maybe a third time for a bonanza.”

“I guess,” Timothy reluctantly conceded. “I just hate to lead from a tenace.”

“Hard to believe with your name. Have you ever seen me reject a free bid?”

The intercom interrupts, “We are next in line for takeoff. Please turn off all electronic devices, return tray tables to their upright and locked position, and stow all personal items… [15-second pause] …and to the dinosaur in Row 7, this includes clipboards.”

Construct the North-South hands so that only a trump lead will defeat 4 .

A further goal (tie-breaker for the January 2016 contest) is for the South hand to be as strong as possible, judged by the sum of all card ranks: Ace = 14, King = 13, Queen = 12, Jack = 11, etc.

## Dean Pokorny Wins

In January 2016 this puzzle was presented as a challenge, inviting anyone who wished to submit a solution. The new year got off to a fair start with 42 persons offering a try, of which the 14 listed produced valid constructions. A diverse crowd from 10 different countries — and thanks to the Peacock for keeping our homeland on the chart.

Congratulations to Dean Pokorny, Croatia, who was the first of five to submit the optimal solution (strongest possible South hand). Dean doesn’t enter very often, but when he does he’s usually spot on. Previous wins include Queens Around in the current series, Dead Man's Deal in my 2011 series, and a long way back to my play-contest days, Distribution Most Foul with 838 participants. Let’s see… 838/42 means I’ve only faded 20-fold in 12 years. Not bad, as I comfortably avoid division by zero.

Winner List
RankNameLocationSouth Total
1Dean PokornyCroatia124
2Tim BroekenNetherlands124
3Leif-Erik StabellZimbabwe124
4Dan GheorghiuBritish Columbia124
5Marcin KrawczykPoland124
6Jamie PearsonOntario116
7Jean-Christophe ClementFrance115
8Jonathan MestelEngland113
9Tom SlaterEngland113
10Tina DenleeQuebec111
11Jurijs BalasovsLatvia109
12Grant PeacockMaryland104
13Nicholas GreerEngland100
14Gary LeungHong Kong100

 Puzzle 8M55   Main Top   When in Doubt

## Solution

During the contest run, several people inquired if it were necessary for both distinct trump leads ( K and J) to defeat 4 , or if either one would suffice. Grammatically, I think this is answered by the condition stating “only a trump lead,” which would be true if either or both were successful. Curiously, every correct entry but one made no difference which heart was led; either produced the same result. Below is the odd man out, our British Agent 006 (not quite ready for Goldfinger) who earns style points by defeating 4  with only one card:

 4 × South 2 Q 5 4 3 2 4 3 2 Q 4 3 2 Trick1 W2 S3 S4 W5 N6 S7 N8 S Lead K! A 3 J 2 4 3 5 2nd26 9Q5 96 10 3rd62 2 10A 3 8 4 4thA8979J10Q W-LW1W2L1W3W4W5W6W7 6 K J 10 9 K J 10 9 K J 10 9 K Q J 10 9 8 6 8 7 8 7 6 5 Lead: K A 7 5 4 3 A 8 7 A Q 6 5 A

Tom Slater: After a spade lead, declarer cashes the A and begins crossruffing, overruffing if necessary; West gets endplayed and declarer wins six hearts and four side tricks. The  J lead looks better, as after winning the Q, declarer cannot overruff in dummy; but by preserving the A entry, he can still make all the low trumps en passant, and depending on West’s defense, produce some sort of squeeze or endplay. Leading specifically the K ruins the timing, as it cuts down the ruffs while removing an entry from South.

In the play shown above, West ruffs in early (optional) to lead a second trump but must not ruff again to reach the ending:

 win 3Failure — 5 4 3 Q 4 Trick9 N10 W11 W Lead 5 K J 2nd 74Q 3rd 778 4th10 5 6 W-LL1L2W1 — 10 K J K J K — 8 7 8 7 North leads 7 — A Q 6 5 —

Declarer’s only hope is to exit with a trump, but West simply cashes the K and gives dummy the Q to await the setting trick in diamonds.

### Viva la difference!

Another curiosity is that every successful entry had declarer winning 10 tricks with a spade lead, and nine with a trump lead, as minimally required by the puzzle. Except one! The Professor would have reveled in the following layout, with his sage advice hitting a high note: Nine tricks with a trump lead; eleven with anything else. Additional style points to Jamie Pearson for this two-trick differential:

 4 × South 4 3 2 7 3 2 Q 6 5 4 3 2 2 Trick1 W2 S3 S4 S5 N6 S7 N8 S9 N10 S Lead 6 A A 3 3 4 4 Q 5 5! 2nd299108J 6K 8 3rd1022 2 4 3 8 7 5 4thA756107J8K W-LW1W2W3W4W5W6W7W8W9 6 K J 10 9 K J 10 9 K J 10 9 K Q J 10 9 8 6 8 7 8 7 6 5 Lead: 6 A 7 5 A Q 8 5 4 A A Q 4 3

Jamie Pearson: On a non-heart lead, win the A, A and A, then crossruff three rounds of clubs and diamonds (overruffing East if needed). Eliminating clubs and diamonds collapses the spade losers into West’s good hearts [so he is endplayed when forced to ruff Trick 10]. With a heart lead only two rounds of crossruffing are possible, and declarer must eventually lose two trumps and two side tricks (West can continue hearts to avoid any endplay).

### All points South

For tie-breaking purposes the object was to construct the strongest South hand, and it is possible for South to have all the high cards. Superficially this seems unlikely, particularly in real life, as I digress to reveal the Guadeloupean stars in action. On Board 2 (below) the Professor opened 3 , and South overcalled 3 NT. North correctly judged this contract to be hopeless, so he tried 4 . South was clueless what this meant — natural? Gerber? Stayman? — but guessed to bid 4 , which Timothy whacked. Trust me on this. (I would produce the hand records, except the Guadeloupean court considers me a security threat and won’t release them.)

Each of the five top solvers produced the following optimal layout, identical to every spot card, packing South to the hilt. Watch this magical make after Timothy blindly leads the Professor’s suit.

Marcin Krawczyk: I’m almost sure this solution gives South the highest card-rank sum.

Dan Gheorghiu: Looks like the ultimate card count!

 4 × South 4 3 2 7 4 3 2 6 5 4 3 2 2 Trick1 W2 S3 S4 N5 S6 W7 S Lead 6 A 3 2 Q! J 4 2nd29107K4J 3rd82 2A3 7 3 4thA5698 58 W-LW1W2W3W4L1W5W6 6 K J 10 9 K J 10 9 K J 10 9 K Q J 10 9 8 6 8 7 8 7 6 5 Lead: 6 A 7 5 A Q 8 5 A Q A Q 4 3

Note the key play at Trick 5, exiting in diamonds, rather than depleting dummy of entries with another club ruff. Timothy cannot benefit by leading a trump now (too late) so he exits with a diamond hoping for an uppercut with the 8. Not this time. Declarer ruffs, then ruffs a club to reach this ending:

 win 4Success 4 3 7 4 6 5 — Trick8 N9 S10 N Lead 5 Q 3 2nd 9KJ 3rd 8 75 4th10 10 9 W-LW1W2L1 — K J 10 9 10 K K Q J 10 9 6 — — North leads 7 5 A Q 8 — Q

Ruff a diamond in hand, then ruff a club with the heart seven — a necessary card for North to have, as declarer would fail with 5-4-3-2 in dummy. Finally just exit with a spade. West is obliged to ruff his partner’s trick and is endplayed in trumps.

An original trump lead, of course, spoils the fun and declarer is down one.