8765 opposite AKJ2

My phone buzzed at 1:20 am on Monday morning: it was Tom Townsend asking "How do you play 8765 in hand opposite AKJ2 in dummy for four tricks?". Not because he wanted to be told the answer, which he'd already worked out (and checked with SuitPlay), but because I was the only conscious person he could find who might be interested in such esoterica.

First, suppose you lead to the ace, LHO follows small, and RHO plays the nine. Then you come back to hand and lead the six, LHO playing small again. The queen and ten are still out, and there are three options: play the king, succeeding against RHO's Q9; play the jack, succeeding against 109; or play the three, succeeding against singleton 9. Q9 or Q10 are two distributions, so are 9 or 10, 109 is one distribution. So apparently one shouldn't finesse the jack, but it's roughly a toss-up between playing for the drop and playing the deep finesse. (It's relevant that RHO can't afford to play the Q from Q9 even if he knows you need four tricks from the suit, because he doesn't know you've got the spots for the deep finesse.)

Second, on any other combination of cards (unless the queen has dropped or someone has discarded), the normal and sensible line is to finesse the jack on the second round (detailed analysis, of the sort I've laid out here before, shows that some unlikely defensive strategies can make a different approach better, but they can't make this approach worse).

However, if one chooses to play for the drop in the first case, there's a problem: LHO can deflect you from this line into a losing finesse by playing high on the second round with 1043 (or 943). So the right thing to do is to take the deep finesse.

This does have some practical relevance: almost the exact combination came up on board 118 of the 120-board US teams trials final. At the time Diamond was leading Nickell by 5 IMPs, and the last two boards were to be flat, so this hand decided the match.

NS Game
Dealer East

• A983
• 8763
• Q1084
• 9

• K7
• KJ4
• AJ53
• AKJ3

N

W

E

S

• QJ62
• AQ
• K96
• 8765

• 1054
• 10952
• 72
• Q1042

West

North

East

South

Weinstein

Greco

Levin

Hampson

—

—

1¹

Pass

2²

Pass

3³

Pass

4⁴

Pass

4⁵

Pass

4⁶

Pass

5⁷

All pass

1. Three or more clubs
2. Natural and forcing
3. Minimum, three or four clubs
4. RKCB for clubs
5. One ace
6. Queen of clubs?
7. No

In the closed room, Levin-Weinstein were playing strong no trump, 5-card majors, and three-card minors. When Levin opened one club, Weinstein chose to agree clubs: Levin showed a minimum then one ace and no queen of clubs, so Weinstein gave up in five clubs. The trouble with that was that Levin could easily have had only three clubs (unless the system is no longer as described here). But he had four this time, and five clubs made easily enough, losing the ace of spades and a club.

West

North

East

South

Moss

Meckstroth

Bathurst

Rodwell

—

—

1¹

Pass

2²

Pass

2³

Pass

4⁴

Pass

5NT⁵

Pass

6⁶

Pass

6NT

All pass

1. Precision: 11-15, no 5-card major
2. Usually denies a 4-card major
3. 11-13 balanced
4. Intended as a slam invitation with 4-4 in the minors
5. Pick a slam - Bathurst didn't know what 4 meant, but he was a bit better than minimum, so...
6. Moss knows what he intended by this

In the open room, Bathurst and Moss had a murky auction to a poor 6NT, and Rodwell led the ten of hearts. Bathurst won with the ace and led a spade to the four, king and ace. Meckstroth returned the three of spades to the queen and five. Now declarer led the five of clubs to the two, ace and nine, came back to the queen of hearts, and led the six of clubs. Rodwell played the four, and Bathurst was looking at the situation as discussed above. (I'm sparing you my thoughts on the difference between AKJ2 and AKJ3.)

So, giving expert consideration to the arguments, he ran the six? No he did not, he played the jack, and with good reason. Suppose you run the six and it holds. Now you have eleven tricks, and the best chance for a twelfth seems to be the diamond finesse. But if you're going to take the diamond finesse anyway, putting the jack in may well not cost even when clubs are 4-1: If South has three diamonds you've got four tricks in the suit once the finesse succeeds, if he has four or more he'll get squeezed in the minors, and if he's got two North may get squeezed in the pointed suits.

North discarded a heart on the jack of clubs, so declarer cashed the king of hearts throwing his club, and the king of clubs, crossed to the king of diamonds, and cashed the jack of spades throwing dummy's club. Evidently there had been no squeeze, but the diamonds could still be 3-3. Declarer led a diamond towards dummy's AJ5, and North, holding a spade winner and Q8 of diamonds, claimed two off. That was 13 IMPs and the match to Nickell.

That's a reasonable line, but Bathurst could have made his contract by running the six of clubs, then squeezing North in spades and diamonds - worth considering once South shows four clubs and probably some heart length. South, on the other hand, could have prevented this by covering the six of clubs: it's unimaginable that he would do that since he can't know that declarer needs to do more than make four clubs tricks (QJ9x of spades would be enough). East, on the third hand, could have made by cashing a top club at trick two then playing the king of spades from dummy, saving an entry, before getting everything else right. And South, on the fourth hand, could have beaten to contract at trick one by leading a diamond to break up the squeeze. "It's poor that they're still playing single dummy in such a big event", as my correspondent remarked.

Alarm clock

E-W Game
Dealer East

• Q4
• J73
• AQ1075
• J76

• 103
• AK85
• K832
• A83

N

W

E

S

• A2
• Q10642
• 6
• 109542

• KJ98765
• 9
• J94
• KQ

West

North

East

South

Paul

Tony

Jon

Peter

—

—

Pass

1

X

2

3

3

Pass

Pass

4

4

X

All pass

I played in the EBU simultaneous last night, and very much enjoyed the defence on this deal.  The bidding was aggressive by both sides - South may have reasoned that with both opponents suggesting spade shortage, his partner was likely to have a little something to help.

I led the king of hearts, and, as the competition booklet points out, needed to switch to a diamond at trick two to secure four tricks for the defence.  There are good reasons to get this right after the revealing auction, and many Easts would have played the ten of hearts, explaining to West after he'd done the wrong thing that this was an obvious suit preference for diamonds.  Not so Jon, who played the queen.

The traveller showed spade contracts making eleven tricks once, ten tricks four times, and nine tricks once.

Intrafinesse - this time with the eight

But what, I hear you ask apropos of my previous post, if the suit is A852 opposite J943, also to be played for one loser.  The odds are a bit different, because declarer can succeed against either 107 or 106 in front of the J9.

As before, let's suppose that when declarer leads from his Axxx, the next hand plays the king from K10 with probability p, similarly from Q10; he plays the 10 from 107 or 106 with probability q, and the king from KQ with probability half.

The critical holdings for second hand are KQ, K10, Q10, 107, 106, and 1076.

Declarer's options are:

a) LHO plays the king or queen.  (a0) declarer tries to pin the ten: for every six times there's a critical layout this succeeds 2p times. (a1) declarer tries to drop the other top honour: this succeeds 1 time.

b) LHO plays the ten, and the jack loses to the queen or king.  (b0) declarer finesses against the remaining honour: this succeeds 2q times.  (b1) declarer tries to drop the other honour: this succeeds 2(1-p) times.

c) LHO plays low, and the nine loses to the queen or king.  (c0) declarer tries to pin the ten: this succeeds 2(1-q) times.  (c1) declarer tries to drop the other honour: this succeeds 1 time.

So the combined successes per six critical layouts are:
a0b0c0: 2 + 2p
a0b0c1: 1 + 2p + 2q
a0b1c0: 4 - 2q
a0b1c1: 3
a1b0c0: 3
a1b0c1: 2 + 2q
a1b1c0: 5 - 2p - 2q
a1b1c1: 4 - 2p

If the defender adopts p = q = 0.5, each of these combinations succeeds three times.  If he adopts some other strategy, declarer can do better than that by making the appropriate choice.  If the declarer wants to save his energies for something other than divining the defender's habits, he can lock in three chances of success by adopting a0b1c1 or a1b0c0.

In my previous post, with the defence holding the eight, I recommended rising with K10 or Q10 at least half the time.  Since the defender cannot tell whether declarer has the eight, he should in practice rise exactly half the time.

How do you make this sort of choice?  It's easy to come up with ways to do it: my method is to look at the sum of dummy's spot cards in the suit and the board number; I rise if the sum is even.  But now I've told you all, I'll have to change it to something else.

Intrafinesse

How do you play A752 opposite J943 for one loser?

The technician will advise you to take an intrafinesse by leading towards dummy's jack.  If LHO has K10 he will win the trick with the king, and you can subsequently run the jack, pinning his ten.  Similarly if he has Q10.  Or if he has 108, you can cover his eight (or ten) and subsequently pin his ten (or eight).  (There is no winning line if he has 106, this is different from a combination where declarer or dummy has the eight.)

However, against expert opponents life is harder.  They may play the ten from K10 or Q10 or 108 or 1086. and they may play the eight from 108 or 1086.  So what is the correct combination of plays?

I'll attempt a game-theoretic analysis.   Assuming that declarer starts with a low card towards the jack, there are five, equally likely, holdings for LHO where a successful play is available but might not be found - the four I listed above, plus KQ.  Let's suppose that the defender follows a mixed strategy: he plays the king from K10 with probability p, similarly from Q10; he plays the ten from 108 with probability q; and the ten from 1086 with probability r (and otherwise the eight: it's a mistake to play the six, which gives declarer no losing option).  And he plays the king from KQ with probability half (other approaches may be as good, but symmetry considerations say they can't be better).

To start with, let's assume that the values p, q, r are all known to declarer, who follows a pure strategy - this assumption is unjustified, but it's a useful starting point.

a) LHO plays the king or queen.  (a0) declarer tries to pin the ten: for every five times there's a critical layout this succeeds 2p times. (a1) declarer tries to drop the other top honour: this succeeds 1 time.

b) LHO plays the ten, and the jack loses to the queen or king.  (b0) declarer tries to pin the eight: this succeeds q times.  (b1) declarer tries to drop the other honour: this succeeds 2(1-p) + r times.

c) LHO plays the eight, and the nine loses to the queen or king.  (c0) declarer tries to pin the ten: this succeeds (1-q) times.  (c1) declarer tries to drop the other honour: this succeeds (1-r) times.

So the combined successes per five critical layouts are:
a0b0c0: 1 + 2p
a0b0c1: 1 + 2p + q - r
a0b1c0: 3 - q + r
a0b1c1: 3
a1b0c0: 2
a1b0c1: 2 + q - r
a1b1c0: 4 - 2p - q + r
a1b1c1: 4 - 2p

We can simplify this somewhat by putting s = q - r, getting:
a0b0c0: 1 + 2p
a0b0c1: 1 + 2p + s
a0b1c0: 3 - s
a0b1c1: 3
a1b0c0: 2
a1b0c1: 2 + s
a1b1c0: 4 - 2p - s
a1b1c1: 4 - 2p

We note that by making the appropriate choice from each pair, declarer can make the value of s irrelevant, and that it can't help the defender to choose a value other than 0, but may hurt him.

Putting s = 0, we see that a0b1c1 succeeds 3 times,  but a1b1c1 will be better if p < 1/2 .   So overall a sound strategy for the defender is to rise with K10 or Q10 at least half the time, and to choose between the ten and the eight on the same basis with either 108 or 1086.   If the defender follows this strategy, a sound strategy for declarer is to play for the pin if LHO plays the king or queen, but for the drop if LHO plays the ten or eight.
___

This morning I was watching the final round of the World Championship round robin stage on BBO, when the following deal came up:

Board 4         ♠ K 10 9 5
Game All        ♥ 4 2                
Dealer West     ♦ Q 9 8 7
                ♣ Q 8 6
♠ Q J 4                         ♠ A 8 2
♥ K J 8 3                       ♥ A Q 10 6
♦ 6 3                           ♦ A 10
♣ J 9 4 3                       ♣ A 7 5 2
                ♠ 7 6 3
                ♥ 9 7 5
                ♦ K J 5 4 2
                ♣ K 10

Robson          Fritsche        Forrester       Rohowsky       
West            North           East            South
Pass            Pass            1♣              Pass
1♦ (hearts)     Pass            4♥              All pass
                                         

Rohowsky for Germany led a diamond to the queen and ace. Forrester drew trumps and exited with a diamond, won by South who played a spade. Three rounds of spades put North on lead to concede a ruff and discard, which did the defence no harm. Declarer now needed to play clubs for one loser, so he led towards dummy, South playing the ten, and North beating dummy's jack with the queen. North returned a low club. The Vugraph commentators thought declarer would have to get it right, apparently not seeing the possibility of playing South for 108.  But Forrester got it wrong.

Tony Forrester and Andy Robson - it's an old and successful partnership, but the two were selected primarily to play with David Gold and Alexander Allfrey respectively - have been England's leading pair in the Butler rankings, so Tony won't mind my saying that I think he was wrong in theory as well as in practice on this one - strategies including b0 are never best.

One interesting aspect of this is that the same hand was played 22 times in the Bermuda Bowl, 22 times in the Venice Cup (for women), and 22 times in the d'Orsi Trophy (for over-60s).  In the Bermuda Bowl, 4♥ was played 21 times: four declarers went off; it was played all 22 times in the Venice Cup where five declarers went off; in the Seniors only 18 pairs reached 4♥ and six of them went off.  Perhaps it matters which hand is dummy: in the Bermuda Bowl all twelve West declarers, with A752 in dummy, made the contract, but only four out of nine Easts.  In the Venice Cup, fourteen out of seventeen West declarers made the contract, and three out of five Easts.  But in the d'Orsi Trophy four out of eight Wests succeeded, eight out of ten Easts.  Overall, West was 30/37 (81%), East 15/24 (63%).

BBO's vugraph archive (in the future you may need this link) records the play at fourteen tables, including the one above: alternatively one can find a record of the play at the same matches by following links from the results tables I linked to above (apparently play is recorded in seven of the 33 matches in each round).

This lets us see how two other declarers went off.  Multiple world-champion Lorenzo Lauria played the hand as East on a trump lead,  He drew trumps in three rounds and played ace and another diamond.   North overtook his partner's jack to switch to the ten of spades, won in dummy.  Declarer now unexpectedly played ace and another club and went off.  However, this surprising line is not much worse than the recommended intrafinesse strategy - it makes against KQ doubleton in either hand and K or Q singleton with North.  And perhaps there's some chance of success if North has king doubleton.

Furuta Kazuo played the hand as East for Japan on a spade lead to the nine and ace.  He drew trumps, knocked out the king of spades, won the diamond exit, and led a club towards dummy.  South rose with the king, cashed the king of diamonds, and exited with a spade.  Declarer now played for the drop in clubs.  This might be right in theory if South would play the ten from K10 sufficiently often, but having gone off I wouldn't want to advance that argument too loudly in the post mortem.

We have the play in 4♥ at nine other tables (both pairs in the Seniors match on record went off in 3NT).  Interestingly, whereas all three East declarers above went off, the nine declarers who played the hand as West all made it.  Usually the play involved leading a club off dummy in the middle of the play, won by South's king, and later leading the jack to pin the ten.  One notable exception was in Netherlands v Monaco: Verhees ducked the diamond lead, won the continuation, and immediately led a club off dummy.  Geir Helgemo, arguably the world's best player of the cards, won with the king and continued with the ten of clubs.  Two other Souths also continued clubs when in with the king, but much later in the play.  Paul Thurston, South for Canada, put the ten in when a club was played off dummy at trick ten, but Kevin Bathurst for USA1 dropped his king.  And the play went wrong when France declared against England in the Venice Cup: North led a spade to declarer's queen, declarer drew trumps and played ace and a diamond, won by South who played a second spade to dummy's ace.  Declarer now cashed dummy's ace of clubs, apparently a horrible line since unlike Lauria she didn't have the entries to take advantage of a singleton honour with North, but in practice an easy way to succeed because South dropped the king.

Most of the declarers fiddled about in diamonds and spades, hoping to learn something, but it seems to me that all they achieved was making it easier for the defence to read the position - a couple induced North to switch to a club, but that didn't help.  I like Verhees' line.

1850

Game all
Dealer West

• 76
• Q75
• J
• K986532

• AK109843
• 94
• 65
• Q7

N

W

E

S

• 5
• AK10832
• K1094
• J10

• QJ2
• J6
• AQ8732
• A4

West

North

East

South

Paul

 

Jonathan

 

Julian

 

Cath

3

Pass

Pass

3NT

Pass

Pass

X

?

My team guessed much better than our opponents on this board from the Pachabo (where the scoring is an unusual mixture of aggregate and point-a-board).

Holding the South cards, you view to try 3NT when left-hand opponent's pre-empt is passed round to you. This gets doubled on your right, now what?

Click here to show (or hide) the answer

The auction started the same way at both tables. Against us, South decided to run to 4, but unluckily she found East at home in diamonds, and lost 1100 (she could have got out for 800 if she'd ruffed the third heart with a middle trump). For us, Cath bravely stood the double, and the contract turned out to be unbeatable. Julian passed too (which looks right to me). West led a heart, which would have taken nine tricks if East had had a second spade. But he had only one of them, so he ducked at trick one and Cath cashed her nine tricks, reasonably refusing the diamond finesse.

Simply but difficult to see

E-W Game
Dealer East

• AQ6
• AQ8
• QJ8765
• 8

• 1053
• 42
• 103
• AJ10643

N

W

E

S

• 74
• K109765
• A92
• Q7

• KJ982
• J3
• K4
• K952

West

North

East

South

Jonathan

 

Paul

 

-

-

2^Multi

2

Pass

4

All pass

 

Cath

 

Julian

-

-

2^Weak

Pass

Pass

3

Pass

3

Pass

4

All pass

This weekend I played in the Pachabo - a competition for the winners of English county teams-of-four events. The format is all-play-all with three-board matches, using an unusual mixture of point-a-board and aggregate scoring (the aggregate uses a rather rum ratio method to convert to Victory Points).  The scoring method contributes to the fun, and the dealing computer helped with a lot of interesting hands.  I got several of them wrong, and so did my team-mates, so I was surprised when we took the lead at about noon on Sunday and held on to win.

This deal was an early play problem.  If I've remembered the auction at our table correctly, South's overcall was aggressive but North gave her some latitude (he may have been unclear about what slam tries were available - note to self: discuss this with partners).

But it's a play problem.  At both tables, West led the four of hearts to East's king and East returned the ten of hearts, suit preference for diamonds, won in dummy (one day I'll play in a game where East gives false suit preference, reasoning that West can't be ruffing the trick or declarer wouldn't have ducked.  But not yet.) Once you've placed the ace of diamonds, the ace of clubs has to be with West, so you know the hand is pretty much as in the diagram.  How do you play?  If you like this sort of problem, think about it before reading on.

At my table, declarer, fearing club forces if she played on diamonds, cashed one trump then tried the effect of playing a club herself.  I didn't cover, so Jonathan won the trick with the ten of clubs.  He read me for the ace of diamonds, but could see no fourth trick for the defence if he played a diamond - declarer could afford to ruff a heart return high - so he defended well by returning a trump.  Declarer won in hand and played the king of diamonds, which I ducked, and a second diamond to the jack and my ace.  I knew enough about the hand now to lead the queen of clubs: in desperation declarer tried covering it and went two off.

At team-mates' table, declarer played a diamond off dummy at trick two.  East rose with the ace, so declarer unblocked the king, ruffed the heart return high, drew trumps and made eleven tricks.

Well played, but what if East ducks the diamond?  You continue the suit, knocking out the ace, but East switches to a club (it needn't be the queen) and again you can't enjoy dummy's red cards. So what's the right line?

It's strangely difficult to see, but when the king of diamonds holds, declarer should change tack by playing a trump to dummy and discarding his remaining diamond on the ace of hearts.  If West ruffs, declarer has two trump entries to dummy to ruff down the ace of diamonds and run the suit (or one trump entry and a club ruff, if he's carelessly blocked the spades).  If West discards a diamond instead of ruffing, he'll have the same losing option when declarer next runs the queen of diamonds.  And if he declines that one too, declarer ruffs out the ace of diamonds, draws trumps ending in dummy, and makes an overtrick.

Too safe?

N-S Game
Dealer West

• 97
• Q6
• AKQJ106
• K104

West

North

East

South

Pass

Pass

1

2^Multi

3^{fit jump}

Pass

Pass (!)

?

You are South. Your call?

Love all
Dealer West

• KJ6542
• 4
• A75
• Q53

West

North

East

South

1

Pass

1

Pass

2

Pass

2

?

You are South. Would you have bid 2 directly over 1 if that were natural? Would you bid 2 now?

These hands come from last Saturday's Garden Cities Trophy Final.  On the first one, either East has passed by mistake, or, much more likely, his opening bid was a misrepresentation.  Partner is therefore likely to have a few high cards, making double a reasonable call.  But no one has much experience of this position, and the player at the table elected to pass, scoring +150 instead of the +500 or +600 (in 3NT) which were available, and losing 11 imps.

On the second, there's no particular reason to suspect anything afoot, but as it happens East, the redoubtable Gunnar Hallberg, has introduced a diversion on a 3325 5-count, and found his partner with 1543.  Each side can make nine tricks in its major suit fit.  But the spade spots were too few for me, so I lost 6 imps.

It's unusual to see two outright psyches like this in one afternoon: they're rather rare nowadays because they're more dangerous than the once were - the modern partner will often compete to what he thinks is the level of the fit.  Norberto Bocchi, the Italian world champion, wrote an article recently decrying a different sort of psyche - a safer and therefore more common one - in which a player asks a question in the bidding without having any real interest in the answer, in order to deceive his opponents about the nature of his hand: Bocchi's example is a long-suit game try on a hand which is always going to bid game anyway and hence need not have the long suit it represents.  In Bocchi's opinion, this sort of "controlled psych" should be banned.  I respectfully disagree; there's no need to ban anything, all we need is full disclosure: if a bid is simply an asking bid then it should be explained as such.  If it shows something - the game try presumably promises at least game-invitational values, and partner can double on that basis if opponents bid - then that should be explained also.  Players have got used to saying whether a Stayman enquiry promises a 4-card major, then can cope just as well with specifying whether a long-suit game try actually promises a holding in the suit bid, or if, more precisely, it asks partner to evaluate his hand opposite an invitational hand with such a holding.

I'm against banning things, and in favour of fair play.

Incidentally, the 1 psyche above is a bit safer if you're playing fit jumps.  Does anyone object to fit jumps on that basis?