Which squeeze? 2

Another installment in "which squeeze should you play for?"

		♠	K 10 7 3
		♥	Q 3 2
		♦	Q J 9
		♣	A K 8
		♠	A 8
		♥	A K 7 6 4
		♦	A K 8 4 3
		♣	10

Contract: 7♦
Lead: ♦10

You draw trumps (East pitches a club), cash 2 hearts (West pitches a club). Now what?

Answer below the fold.



You could play for a compound squeeze: cash another diamond (pitching a spade) to get to a 7 card ending. East must keep 2 hearts and can't keep 3 of both black suits. Whichever suit he unguards, cash those winners ending in hand (crossing back in spades if needed) then play the last trump. This will squeeze East out of the other black suit, then the final heart honor will squeeze West in the blacks.

The problem with this line is that you'll not see many pitches before guessing which suit East unguarded. Basically, he'll pitch one from each black suit, and you'll have a near 50-50 guess as to which one he started with 4+ of and still guards.

The alternative line (suggested by Jonathan Weinstein) is to ruff a spade. If someone shows out, you'll have either a marked major suit squeeze (vs East) or a marked double squeeze pivoting around clubs. If everyone follows to 3 rounds, you'll still have a guess for which of those 2 squeezes to play for. But, you'll be able to use restricted choice to make that guess -- whichever player shows up with a spade honor will be more likely to be out of spades than to have started with QJxx (about 3:2 for West, and about 3:1 for East). The odds of success are definitely higher.

And, occasionally the ♠10 will just set up.

Perhaps testing hearts early is a mistake. Too complicated for me today, though.

[This hand was taken from a recent post & slightly disguised to make a cleaner entry in this series]

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Another Maastricht Challenge

I found another problem from _Maastricht Challenge_ where I disagree with the book's solution:

♠	A J 7 2
♥	A 5 4 3
♦	A Q J 10 6
♣
♠	K 10 9 6
♥	K 9 2
♦	K 2
♣	9 6 4 3

East overcalls 2♣ on your way to 6♦. The problem specifies that West leads a 3rd highest ♣2, so you can take as given that clubs are 3=6. It also points out that finding the trump queen or ruffing 2 clubs is sufficient, but warns of a trap.

I've put the book's solution and my own below the fold.



Say you play a trump to the ten. If it loses, it's relatively straightforward to ruff another club and draw trumps.

If it holds, then what? The book points out that against a tricky defender, you might play a spade to the Ace and see East show out. It asserts that Qxxx/x is a 38% chance and xx/Qxx is only 29%, so against someone who is up to ducking the queen you should finesse the jack. A pretty cute play, finessing one way and then the other.

I agree that those are the relevant holdings. I get that their odds are 56:45 (12c6 * 4 : 12c4 * 6), which is very close to their numbers (not quite within rounding but I'm going to ignore that). But, it seems that after the ♠A and East shows out, you still have play: ruff a 2nd club and try shaking your other 2 on diamonds. The chance of West having 2 or fewer diamonds (which is required for this backup plan to fail) is under 30% (of the 38%), so the winning case for ♠J is more like 11%, a clear loser.

More generally: this sort of defensive play, ducking when declarer takes a loosing finesse, comes up from time to time. There was a nice hand in an early daily bulletin from San Diego with a similar theme. What should I look for so as to better recognize such situations on defense in the future?

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Remembering suit division odds

I always struggle to remember suit division odds. Rubens had one suggestion I liked: remember the probable ones and back out the improbable ones. If you can remember 3-3 and 4-2 are 36 & 48, then you can probably figure out that of the 16 left most of it is 5-1 and a small amount is 6-0. Similarly, 3-2 and 4-1 are 68 & 28, that leaves 4% for 5-0.

I also found that re-ordering the tables from most probable to least probable, as below, reveals some obvious patterns, many of which I hadn't noticed before (perhaps this shows how unobservant I am). I omitted 2 card suit divisions for 2 reasons: they break the pattern, and you should be able to calculate them on the fly.

1. x-y divisions are grouped by the difference between x&y:

1 off (e.g. 3-2, 4-3) is around 2/3.
2 off is around 50-50.
Even is 1/3+.
Off by 3 around 30%, etc.

(this is increasing except for exactly even)

If you forget 4-3, it's going to be closer to 3-2 than any other number you remember. Also, these groups don't overlap (excluding 2 card suits or 11+ card suits, and 5-5 is barely less likely than 6-3)

2. For the close divisions (not more than 2 off), the more cards there are the more likely you are to be off by more than 2, so the groups go from short suits to long suits (e.g. 4-2 is more likely than 5-3). After that, longer suits are more likely than shorter suits (e.g. 5-2 is more likely than 4-1).

3. As suits get longer, the odds become more similar. For example, 6-3 is virtually the same odds as 5-2. In contrast, 2-1 is 10% more likely than 3-2. If you remember 2 or 3 odds for same difference combinations, you can generally extrapolate the others. Generally, the differences cut about in half each time. For example, 3-2 / 4-3 are 68 / 62, so 5-4 is probably around 62 - 1/2 (68-62) = 59% (in fact it is).

Some more stuff below the table...

2-1	78%
3-2	68%
4-3	62%
3-1	50%
4-2	48%
5-3	47%
2-2	41%
3-3	36%
4-4	33%
5-2	31%
4-1	28%
3-0	22%
6-2	17%
5-1	15%
4-0	10%
7-2	9%
6-1	7%
5-0	4%

4. Void probabilities are relatively easy to derive from one another just by using open spaces:

1-0 is 100%,
2-0 is 12/25 of that, 48%,
3-0 is 11/24 of that 22%,
4-0 is 10/23 of that, a bit under 10% (9.6%),
5-0 is 9/22 of that, 3.9%,
6-0 is 8/21 of that, about 1.5%.

5. The singletons are harder but doable in a pinch (adjust for open spaces then number of possible singletons):

2-1 is 78%
3-1 is 11/23 * 4/3 of that, about 50%
4-1 is 10/22 * 5/4 of that, about 28%
5-1 is 9/21 * 6/5 of that, about 14%
6-1 is 8/20 * 7/6 of that, about 7%

So...

If you can figure out short suits and maybe some voids on the fly and remember these:

3-2 68%
4-2 48%
3-3 35.5%
4-1 28%
4-0 10%

You can probably work out the rest. 4-3? Well, 2-1 is 78 and 3-2 68 so subtract about half that difference from 68 to get 63 (actually 62). 5-3? All the off by 2s are right around 48%, should be a bit less (in fact 47). 5-2? 3-0 is 22, 4-1 is 28, so add half the difference to 28 and get 31 (in fact 30.5). 4-4? 2-2 is 41, 3-3 is 35.5, subtract half the difference and get almost 33 (in fact 32.7).

6-2 is maybe a bit harder. We memorized 4-0 as 10%. 5-1 is about half of 4-1 (9/21 * 6/5 to be precise), call it 14% (we can check this also by noting that 3-3 and 4-2 add to 84, so it should be a touch less than 16%). 6-2 is probably around 16% (in fact, 17.1. 4-0 is a bit less than 10% and 5-1 is 14.5, so my extrapolation suffered from some rounding).

You could also get there by noting that 5-3 and 4-4 add to 80%, so 6-2 ought to be most of the rest. Delving a bit further, you could consider there are 28 6-2 layouts vs 8 7-1. The latter are about half as likely, also (the last card has 12 open spaces vs 7), so call it 7:1, so the 7-1s are about 1/8 of 20% and the 6-2s are the rest (8-0 never happens, right?): 17.5%

The harder of these are not that practical, but trying to estimate these numbers and occasionally checking your results will result in better memorization. Read more!

More squeezing, follow-up

Following up on this post from last month.

		♠	A 6 5
		♥	7 6 4
		♦	A Q J 9 5 2
		♣	K
♠	Q J 8 7			♠	10 4 3
♥	K J 10 9			♥	8 3 2
♦	8 7 3			♦	10 4
♣	7 6			♣	Q J 10 3 2
		♠	K 9 2
		♥	A Q 5
		♦	K 6
		♣	A 9 8 5 4

Chris showed me this deal. South opens a 14-16 1NT and winds up declaring 6D on a trump lead. What is supposed to happen?

At the table, declarer won in dummy, unblocked clubs, crossed in trumps to ruff a club and drew trumps. East had a problem and discarded a heart. At which point, declarer lost a heart finesse but eventually got home on a double squeeze. Could the defense have done better?

Let's wait on East's pitch, and assume that declarer pitches a spade on the 3rd trump, then crosses in spades to cash and ruff a club (finding out what's happening in that suit) and plays his last trump in this position:

		♠	A 6
		♥	7 4
		♦	2
		♣
		♠	9
		♥	A Q 5
		♦
		♣	9

Note that the H6 has been unblocked.

East must keep a club, so Declarer will pitch his last on the D2. In the 4 card ending, the opponents have 7 major suit cards. Declarer would like to take a marked endplay if possible, or a heart finesse followed by an attempted squeeze (which may have already developed). Say there are only 3 hearts outstanding -- declarer can take the finesse and either win it or establish a long heart (ignoring, for now, the possibility that West kept 3 hearts and East none). If there are 5 hearts (and thus only 2 spades) then declarer might as well play SA, maybe establishing a trick, maybe establishing an endplay, and otherwise playing for the HK (now blank) to be onside. [Note that the defense would prevail if East kept all his spades and declarer played this way -- this requires an immediate heart pitch, though, which did happen but declarer played along different lines.]

If the defense keeps 4 hearts, it's kind of interesting. If they're 2-2, then in practice declarer can't go wrong -- SA and a spade will work, or a losing heart finesse followed by spades splitting will work. So what if East keeps 3 hearts and West stiffs his K? Then the HJT9 will all have been pitched and declarer can play the 6 to the Q. When this loses, a spade will come back, East will show out, and hooking the 5 will be marked. If West keeps 3 hearts, again East had to pitch hearts immediately (to keep a spade guard). Now declarer (if he plays in this counterfactual way) has to guess, but could go right: cash SA, then play a low heart and duck it.

In practice, the key is how likely declarer thinks East is to pitch a heart on the 3rd trump from an original 2=4=2=5.


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New squeeze article

The start of an article on compound squeezes with 2 "helper" menaces (such as a clash menace and a guard menace, both of which are necessary) now here. As always, an index of all articles in progress is at the top of the right column.

It still needs work, but a number of positions are identified.

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More squeeze defense

Jonathan made a good point in comments about defending this end position:

♠	4
♥	K 10
♦	K 7 6
♣
♠
♥	A 9 3
♦	A 9
♣	10

West is known to have the spade guard and, if he started with 3 clubs, must have pitched 1 card from an original 6 red cards (the defense started with 7 of each red suit). His goal is to present declarer with a straight 50-50 guess as to whether the suit he pitched from is still guarded or not. When he's 3-3 in the reds, he has no control over that, whichever suit he pitches is unguarded. This happens 40.8% of the time (7c3^2 / 14c6, see below for a faster approximation). So, when he has a long suit, he'll want to pitch from the long suit (still having a guard, 50/59.2 of the time (84.5%)) and from the short suit the rest of the time.

Given that the red lengths are symmetrical, it's easy to work out that with 3-3 in the reds you should discard each suit 50% of the time. With unbalanced red suits, you'd ideally like to do the above arithmetic to figure out the optimum discard frequencies. The problem is, this might take some time, potentially revealing that you aren't easily able to identify the optimum.

Is it therefore ethical with 3-3 to do the same calculation you would want handy if you had been 4-2?

Maybe it's not that hard. Throw out voids and having 1-5 cards in a suit is 1:3:5:5:3, so 3-3 is 25:(15+15+3+3), so with 61 holdings you want to pitch from a long suit 30.5 times and you have a long suit 36 times, or a touch more than 5/6. As evidence that this approximation is effective: 50/59.2 is 84.5%, 30.5/36 is 84.7%.

In case that last paragraph was too fast: having 1 diamond is 7c1 = 7 combos. 2, 3, 4, & 5 diamonds are 7c2, 7c3 etc, which are 21, 35, 35, and 21. There's a factor of 7 in all those numbers, so the odds simplify to 1:3:5:5:3. The ways to hold 1-5 hearts have the same combinations, but 1 diamond implies 5 hearts, 2 diamonds implies 4 hearts, etc, so flip those odds to get 3:5:5:3:1 and pairwise multiply to get the total number of ways to have both 1 diamond and 5 hearts (1x3), 2 diamonds and 4 hearts (3x5), 3d3h 25, 4d2h 15, 5d1h 3. Add them up to get 61 equally likely possibilities, of which 25 are 3-3.

In this weighting, the voids are 1/7 each and the 6 card suits are 1. (30.5 + 1/7) / (36 2/7) would be the precise calculation.


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Alternate threat compound with variations

This is from Problem 6 from the August (2002, I think) Pav problem set. I think it was played in the European Championships sometime before that:

Axx
AKx
AKx
Axxx
 
QJx
QTxxxx
xxx
x
 

LHO opened 1C and you land in 6H. CK led. How do you play?

Duck (creating that Ax/void basic menace that's often useful), ruff the 2nd, play SJ forcing LHO to cover (or you'll have a black suit squeeze), then run trumps coming down to:

 
x
-
AKx
Ax
 
Qx
x
xxx
-
 

Clubs is the basic menace (vs West), spades is the alone ambiguous menace, and diamonds is the ambiguous menace with the basic menace, except that South has an alternate threat. If West has unguarded spades, the extra entry in diamonds is needed to get the CA out of the way before coming back to hand and cashing the last heart for a simultaneous type R.

If West unguards diamonds, the diamond threat in dummy is not useful because of entry problems, but this can be overcome by using the alternate diamond threat in hand. Note that the recessed club menace is key to make room for that alternate threat. In fact, that's a general feature of alternate threat compounds: the basic menace needs a winner that is not useful as an entry such as shown, or AKx/x, or Axx/K, etc.

This deal has an alternate solution – cash all the red winners coming down to:

    Axx
    -
    x
    Ax
Kxx      T98
-        -
Q        Ji
QJ       x
    QJx
    xx
    x
    -
 

This was an alternate threat squeeze where clubs was the basic threat, diamonds alternate, and spades the alone ambiguous threat. Get rid of the diamond entries, though, and it still works because West can’t keep pitching spades (the alternate threat is still important, though – in fact, the original threat is idle). Play 2 hearts pitching a diamond and then (unless it’s good) a club. West can’t bare the SK or the spades will run, so he must pitch a diamond and a spade. Since he can’t duck the SQ, it’s basically a B1 with the R (diamond) winners already out of the way. This spade menace is fairly strange, neither guard nor clash. I think it's a "shortstop" menace.

Switch the SQ and SK and it’s just a simple black suit squeeze. Do that but also switch the SJ and ST and it’s a compound guard squeeze (Type-R Guard-O in my classification -- R since the basic threat is alone (the diamond and 3rd spade with North are both idle), O since the guard menace is opposite the basic threat).


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Veering Squeeze Card Variant

[UPDATE: lots of posts the past couple of weeks; trying to settle in to a regular weekly schedule again starting now, though. I have several things lined up, so you should be able to rely on that for a while.]

Here's an 8 card double-dummy problem demonstrating a secondary compound squeeze with a veering squeeze card in the ending:

		♠	A Q 9 2
		♥	A K 5 4
		♦
		♣
♠	J 10 8			♠	K 4 3
♥	Q J 10			♥	9 8 7
♦	K J			♦	A Q
♣				♣
		♠
		♥	3 2
		♦	4 3 2
		♣	A K Q

Clubs trump. South to lead and take 7 of the last 8 tricks.

Solution below the fold.



Cash a trump. West must pitch a diamond (or set up spades or heart-spade strip vs East), then East is triple-squeezed. If a spade is pitched, use the 2 heart entries to ruff out the king and then enjoy the queen. If a diamond is pitched, duck a diamond to set up that suit. So, East must part with a heart.

On the next trump, West is triple squeezed. On a spade pitch, you can again cross to ruff out the king while pinning West's honors. A heart pitch sets up that suit. So West must pitch another diamond.



Now, cash the hearts and lead a 3rd one in this position:

		♠	A Q 9
		♥	4
		♦
		♣
♠	J 10 8			♠	K 4
♥	Q			♥
♦				♦	A Q
♣				♣
		♠
		♥
		♦	4 3 2
		♣	Q

This is the "familiar" veering squeeze card ending. If East pitches down to one diamond, ruff and throw him in to lead into dummy's spade tenace. If East blanks the ♠K, pitch a diamond. West wins and leads a spade so you can drop the king and get home.

Verified with Deep Finesse.
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Which squeeze? My solution

I posed this problem yesterday:

♠	A K Q 4 3
♥	K 10 4
♦	K 7 6
♣	6 4
♠	6 5
♥	A 9 3
♦	A 9 3
♣	A K Q J 10

You're in 7N facing the ♠J lead. How do you play?

This might not be right, but let's say that you start with 3 rounds of spades and RHO shows out on the 3rd round. Take over from there (don't forget to pitch something on this trick!).

Yesterday I suggested pitching a diamond, then running 4 clubs (pitching a spade and a heart) for a compound squeeze. The problem is that this is a restricted squeeze and you have to make a key guess before cashing the last club. There's a way to make it unrestricted, though, which gives you much better odds of reading the position. Answer below.



Pitch a diamond on the 3rd spade, run 4 clubs pitching a spade and the HT dummy, then cash DK, DA, and play the last club in this position (planning to pitch a spade unless it's good):

♠	4
♥	K 4
♦	7
♣
♠
♥	A 9 3
♦
♣	10

This is a compound guard squeeze that can work if LHO has either missing heart honor. You still have to read the position, but you'll almost always be able to. Your next play is the HK, and, unless the diamond is good, a low heart towards your hand. When RHO follows low, only then, halfway through trick 12, do you face your guess (and even then, only if you've seen a heart honor from LHO. Either RHO's last card is the other heart quack and you finesse (this is why you unblocked HT), or LHO has it along with a spade and you drop it.

For starters, if heart honors are split and you play for it, you'll always make: a bit over 52% of the time. You'll also pick up a bunch of scattered things, such as when RHO starts with the sole diamond guard (or LHO unguards diamonds unwisely) and both heart honors.

On the other hand, once you play this way, they can always beat you if LHO guards diamonds and RHO has both hearts.

Overall, not that big an advantage, but it's there and the play is cooler.

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Which squeeze?

I'm interested in problems where there are multiple squeezes you might play for and selecting the best one. There are some of these in recent posts. Here's one that I just constructed:

♠	A K Q 4 3
♥	K 10 4
♦	K 7 6
♣	6 4
♠	6 5
♥	A 9 3
♦	A 9 3
♣	A K Q J 10

You're in 7N facing the ♠J lead. How do you play?

This might not be right, but let's say that you start with 3 rounds of spades and RHO shows out on the 3rd round. Take over from there (don't forget to pitch something on this trick!).

Some thoughts below, my full answer tomorrow.



If you've been reading the blog at all recently, you've probably noticed some compound squeeze talk. One line is to pitch from one red suit, run 4 clubs pitching a spade and the other red suit from dummy, coming down to something like this with 6 tricks to go:

♠	4
♥	K 10
♦	K 7 6
♣
♠
♥	A 9 3
♦	A 9
♣	10

LHO is known to hold a spade guard, so can't guard both red suits. Play off the king and ace in the red suit they've unguareded, then the ♣10 effects a double squeeze.

So, you can always make it on this line if you read LHOs shape properly. Say he starts with 2 clubs, though. He'll always be able to pitch 1 from each red suit and you'll have to guess which suit he started with a majority of -- a straight 50-50 guess.

I think there's a different line with much slightly better odds.

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Another NY Times compound

This deal is from a recent NY Times column:

(When I checked, the full deal appeared wrong, but the end position was right. Some spots in the full deal may be misplaced in my diagrams):

		♠	A 6 4 2
		♥	Q 10 5 4
		♦	K Q 10 8 4
		♣
		♠	K 9
		♥	A J 8
		♦	A 6 2
		♣	A K Q J 4

Trying for a BAM win, you land in 7N. At the table, declarer ran some diamonds and some clubs, discovered RHO had a club guard, unblocked the HQ and came down to:

		♠	A 6
		♥	10
		♦	8
		♣
		♠	9
		♥	A J
		♦
		♣	4

Declarer played a spade to the Ace and when RHO showed out he was able to play it as a double squeeze: cash the last diamond forcing East down to 1 heart, pitch the last club, and now West is also down to 1 heart.

This is pretty enough, but is not really any better than the heart finesse or stiff K with West. If West had had the HK, East would not unguard spades and expose West to the major suit squeeze.

Could declarer have done better? ...


In practice, I don't think so. But in theory, if he knew early enough that East had the club guard (for example if West shows out on the 3rd round), then I think a different line of play would be better. Details below the fold.




I think declarer wants to reach this position with the lead in the North hand:

		♠	A 6 4
		♥	10 5
		♦	8
		♣
		♠	K 9
		♥	A J
		♦
		♣	J 4

By not cashing the 4th club winner (impractical single dummy if both follow to the first 3) there's room for an extra heart with North. This will also require a spade entry to South in some variations. Presuming RHO still has a club guard, that only leaves room for 4 major suit cards, thus he can no longer guard both majors. If you judge that hearts have been unguarded, cash the last diamond pitching a heart, HA, CJ for a double squeeze around spades. If spades are unguarded, SK, CJ (pitching a heart), SA, diamond for a double squeeze around hearts.

This is an alternate threat compound. Cashing the CJ too early wrecks it by squeezing North.

What about the odds? Say RHO shows up with 6 clubs and 2 diamonds. He's going to pitch 1 club and 1 major before you make your decision and you should play for the major he pitches to be unguarded. The layout where you rate to go down is when he's 4=1 or 5=0 in the majors and pitches a spade, which happens about 19% of the time by my math (less a couple percent for stiff HK). Or, if he's 2=3 in the majors and pitches a heart, another 32% or so. So, in fact, this is a virtual toss up compared to the finesse.

On the other hand, there's some scope for misdefending on the compound line. I think, though, that restricted compounds rate to be hard to read in general and not much better than finesses. Of course, if you don't have those nice middle heart honors, the compound is still about 50% and there's no other line.

How could this be unrestricted, allowing you to cash an extra diamond before committing to deciding which major East has unguarded? A good start would be to move the SK to North (and a small spot to South). Now you don't need that 2nd heart in dummy, can cash all the clubs and then finish diamonds coming down to:

		♠	A K 4
		♥	10
		♦
		♣
		♠	9
		♥	A J
		♦
		♣	4

Now you'll have seen 2 major suit pitches from East. If he pitches 2 from the same major, you only lose to 5=0 or 1=4, both very unlikely. If he pitches 1 from each, you have to guess whether he was 4=1 to begin with or 2=3. You'll guess the latter, and wind up making something like 80% of the time.

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Squeeze Articles

I've occasionally thought I might write a squeeze book someday. I've got drafts of some chapters and I'm starting to put them up here. There's also a link on the right tool bar.

Please use this as a spot for leaving comments on these articles.

UPDATE: The Compound Squeeze article and the Compound Guard/Clash squeeze article are both in good shape. The latter also delves into Saturated squeezes (very briefly) and what for now I've dubbed "Cover" squeezes (similar to guard squeezes).

UPDATE July 2010:  I've filled in some more Compound squeezes where a ruff is used for an entry.  I've also added "Ruffing Communicator Squeezes" discussing positions where the ruffing menace also provides compensation for flaws in other menaces (sort of similar to a clash squeeze).  

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Maastricht Challenge

I'm a big fan of Tim Bourke's _Maastricht Challenge_. The introduction states "Many of the quizzes reflect my interest in developing better technique in trump, criss-cross and multi-loser squeezes." If this sounds appealing, you should definitely check it out. Many of the problems also rely on estimating the chances of various distributions, so I've been re-reading it to practice some techniques from the latest Rubens book.

This is problem 9:

♠	5 2
♥	A K 10 7
♦	K 8 6
♣	A K 4 2
♠	K 6
♥	Q J 5 3
♦	Q 7 5
♣	Q J 9 3

West opens 1♠, North doubles, East passes, and you wind up in 4♥. Opening lead is the ♣8 with runs to the ten and your jack. Everyone follows to the first round of trumps. Now what? [You may want to stop here and think about it.]

As the solution points out, if trumps split you can duck a spade from both hands and later exit the ♠K to force West to lead away from the ♦A. (Presuming that West has both Aces for his opening bid.)

What if trumps are 1=4, though? [Again, consider stopping to consider.]

Now you run trumps and clubs coming down to:

♠	5 2
♥
♦	K 8 6
♣
♠	K 6
♥
♦	Q 7 5
♣

You have 2 options here: if West has 2 spades, duck a spade and again he'll have to lead away from ♦A. If he has 3, then you can lead a diamond to the K and duck one on the way back. Bourke says if you're unsure of West's distribution, you should play East to have the most even possible distribution in spades and diamonds, or exactly one more spade. This is good general advice, but ignores an advantage to the 2nd line: if West started with 2 or more of the jack, ten or 9 of diamonds then a diamond to the K and covering East's jack or ten on the way back will work even if you misguess his shape.

If West started with 10 spades & diamonds, this advice is good enough. If he pitches 2 diamonds, then playing diamonds is guaranteed to work (assuming he didn't open 1S on 4=1=6=2). If he only pitches 1 diamond, then the key cases (for RHO's initial holdings in spades=diamonds) are 2=4 and 3=3. By my math (similar to below but not shown) this is 1:4. Playing diamonds will work in the first case or half the 2nd case (again see below), for 60%, so play spades and make it 80% of the time.

But, say West started with 3 clubs and so 9 spades and diamonds. Again, if he pitches 2 diamonds you can't go wrong. But if he pitches 1, the relevant cases (again for East, though you could also think of these as diamond layouts) are 3=4 and 4=3. This time, the odds (ignoring the auction) are 1:2 (I'm placing West with 2 Aces and the SQ but allowing all the other spades & diamonds to be distributed randomly). Bourke's advice is to go with 4=3 and so play on spades. But, playing on diamonds will work in the 3=4 case and half the 4=3 cases and so it's essentially a toss-up. (I get "half" since each defender has 3 non-Ace-diamonds and West needs a minority of 3 middle diamonds to defeat you with perfect defense).

So, this isn't really an error. However, I do think that going into more depth suggests that the alternative line (when West starts with 3 clubs) is slightly better. When you consider other possible inferences, everything points to the alternative: Perhaps East would have acted over 1♠-X with 4=4=3=2? Perhaps with AJxx or ATxx in diamonds, West will fail to unblock the low honor?

With no Jacks, West might not have opened (e.g. if he follows the "rule of 20"), or he might be more likely to open a 6133 hand than a 5143 hand, and/or a hand with good diamond spots (the 10-9).

What if we assume a religious rule of 20 West and place him with 1 or both key Jacks? Since I've come this far I'll try to work it out:

1. (40% of the time) West has SJ, East has DJ. Diamonds started 4=3 vs 3=4 is 2:1 (2=4 spade spots half as likely as 3=3 while diamonds-below-J are 3-2 in either case). Ducking a spade works 2/3, playing on diamonds works 1.6/3 (1/3 + original AT9x) + as much as another .6 vig if West might fail to unblock from ATxx.

2. (60% of the time) West has DJ, SJ in either hand. 4=3 vs 3=4 is again 2:1 (7 spades 3=4 or 4=3 equally likely while 5 diamonds twice as likely to be 2=3 as 1=4). Here, the recommended line is a 2/3 shot, while the alternative is 2.4/3. The possible vig of an unblock failure gets it to 100%.

Ignoring the vig, this makes the recommended line 2/3 and the alternative 2.08/3, for a small advantage. More intuitively, the lines started as a tossup, but West should be a bit more likely to have the DJ than open spaces suggests and that helps the alternative line by making it more likely that West can't (or won't) be able to get off lead even when he shows up with 4 diamonds.

Finally, if West has both Jacks but no SQ another diamond spot could be important to whether he opens. This again points to the alternative line.


Read more!

More squeezing

		♠	A 6 5
		♥	7 6 4
		♦	A Q J 9 5 2
		♣	K
♠	Q J 8 7			♠	10 4 3
♥	K J 10 9			♥	8 3 2
♦	8 7 3			♦	10 4
♣	7 6			♣	Q J 10 3 2
		♠	K 9 2
		♥	A Q 5
		♦	K 6
		♣	A 9 8 5 4

Chris showed me this deal. South opens a 14-16 1NT and winds up declaring 6D on a trump lead. What is supposed to happen?

More below, more to follow in a future post.


At the table, declarer won in dummy, unblocked clubs, crossed in trumps to ruff a club and drew trumps. East had a problem and discarded a heart. At which point, declarer lost a heart finesse but eventually got home on a double squeeze. Could the defense have done better? Read more!

Compound squeeze defense

Jonathan already beat me to the correction to todays NYT column.

		♠	K Q 4 3 2
		♥	J
		♦	A Q J 9 3
		♣	A 8
♠	J 10 9 8			♠	5
♥	Q 7 4			♥	10 8 6 5
♦	10 6			♦	7 5 2
♣	Q 5 3 2			♣	J 6 4
		♠	A 7 6
		♥	A K 9
		♦	K 8 4
		♣	K 10 9 7

After a long relay auction, South placed the contract in 7♦ and got the ♦10 lead. According to the report, declarer drew trumps (West pitching a club), tested spades, then played 2 more trumps effecting a compound squeeze: West shook hearts, then ♥A, ♥K squeezed him in the blacks, and ♣A, ♠Q squeezed East in the rounds.

Of course, once a club was pitched and the spade break revealed, declarer could ruff a club, either establishing a trick or uncovering who held the sole guard and arranging either a black suit squeeze vs West or a double squeeze organized around hearts.

But, I'm more interested in figuring out whether as a pure compound squeeze how the defense should have gone. Let's imagine that the extremely revealing relay auction happened to make North declarer so that the defense knew what they were facing. Let's further imagine that the hand is in NT so we can ignore the club threat possibility and the order of discards. Picking up after testing spades and diamonds, declarer should run diamonds and come down to this ending:

		♠	Q 4 3
		♥	J
		♦
		♣	A 8
		♠
		♥	A K 9
		♦
		♣	K 10 9

West is known to have a spade guard and to have started with 7 round cards to East's 9. West must be down to only 4 round cards and so can't guard both clubs and hearts. Declarer's strategy is to cash dummy's winner(s) in the unguarded suit (perhaps pitching a spade on the 2nd heart if that suit is still guarded), then CA, SK will squeeze East. In fact, West must unguard a round suit on the 4th diamond, but the position allows cashing a 5th before attempting to read which suit he unguarded (this is not always the case in compound squeezes).

The defense's strategy is to present declarer a guess as to which suit West unguarded. To solve this fully, you need to consider all club-heart breaks, what West should do in each (possibly mixed), and the resulting guess (if any) this presents to declarer. For now I'm not going to tackle that, but I think we can get pretty close to the right answer:

West in fact pitched 2 hearts and 1 club. Unless this was hopelessly unguarding both suits (e.g. from 4=3), this is most likely from an original 3=4 in hearts=clubs (as it was in practice) or 5=2.

I think in practice declarer should assume that it is: from extreme holdings like 1=6 or 6=1, I think pitching 3 from the long suit is likely to succeed, so we can probably rule those out. From 2=5, pitching 1 heart and 2 clubs is probably best: likely to look like an original (and more likely 4=3) and lead declarer astray.

So, for starters, declarer should work out that the odds of West holding 3=4 vs 5=2 is 10:9 (if you don't know how to verify that, check out Jeff Rubens's latest book -- it's 9c3 * 7c4 : 9c5 * 7c2). You can ponder the psychology of the order of discards, but a proper expert should identify the 3 discards needed and make them in a random order. I suppose in practice most experts would try to unguard early (so pitch 2 hearts first) rather than late. Perhaps West was playing a deep game by discarding in the "easy" order (of course, in practice West had to consider many possible hands for declarer).

So, if West was playing a perfect game-theoretic game, his best bet was to discard (as he did) 2 hearts and 1 club and hope that declarer miscalculated. East could have helped this illusion by pitching clubs (as if he started with 5) instead of hearts, though theoretically his discards should be ignored (so long as he guards the suit that West unguards).

This also means that West can use some 3=4 "losers" to "protect" his 6=1 winners -- occasionally pitch 3 hearts (or clubs) from that holding so that declarer can't conclude that 3 pitches is always from an original 6. This will reduce the 10:9 odds, but not enough to change declarer's best strategy. (Of course, the HJ makes that a bad idea with this particular holding.)

So, basically I think the defense is slated to lose when West starts with 3=4 or 4=3, but succeed otherwise. By my math, that's about 64%.

In practice, I think if East had pitched a club and a heart or 2 clubs, declarer had a realistic chance to go wrong: 5=2 (West hearts=clubs) is almost as likely as the actual 3=4, but in practice there must be a 10% higher chance that East pitched clubs from an original 5 instead of an original 3, which could be enough to tip declarer to the wrong decision.

Read more!

Pyrrhic victory

This was not a success, but still kind of a cute
hand
.

The key diamond suit was remarkably similar to this deal.



Read more!

The Monthly Trout?

Sorry for the long absence.

I've been reading Jeff Rubens new book, _Expert Bridge Simplified_. I quite liked it. A lot of it I was already familiar with (but anyone that isn't would likely benefit a lot from that material), but the stuff that was new to me (e.g. estimating the chances that 2 suits will break such that the same opponent is short in both) was really cool. Even for the stuff I was familiar with, it really cemented some important stuff in my mind. How often this material will actually help me, I'm not sure, but I'll try to pay attention.

The subtitle is "arithmetic shortcuts for declarer" and it focuses a lot on choosing approximately the best line. Many problems go to a lot of trouble for an ultimate answer of "who knows" or "you could work a lot longer on this to get a precise answer, but I [JR] am not interested". Also, often it's about convincing yourself you have the best line without necessarily knowing how good it is overall or how much of an improvement it is over the alternative.

So, there were a couple of deals where I thought there was a bit more of interest than JR brought up, but it was within the spirit of the book not to bring it up. Here's one example:

♠	A K Q 10 3
♥	Q
♦	10 9 8
♣	10 9 8 7
♠	5
♥	A J 3 2
♦	A K Q J
♣	A K Q J

After starting 2♣ you wind up in 7N and get a diamond lead. How do you play?

The solution from the book, and my own are both below.



The books solution was to point out that you should play for spades to come in and if they don't you have to choose between a finesse and a squeeze. The squeeze requires the 2 card psuedo-suit of outstanding-major-suit-honors to split 2-0, a bit less than 50%, while the finesse is a straight 50-50 shot and so better. He explicitly says he's not bothering to consider possible info learned from the minor suit distributions because it's too complicated.

In a variant on this problem, that was true, but I think here it's not that hard. You can learn about both minors and most of the spade info before making your final decision: run diamonds (shake a spade) and 3 clubs, then 2 spades (shake a heart) and play a 3rd spade. After seeing East's play, you have to decide whether to unblock clubs and play for the squeeze, or pitch another heart and play for the finesse.

Case 1: RHO shows out, LHO has 5 spades. If the 11 outstanding minor suit cards break 4=7 it's a pure guess based on open spaces. If they break worse, play for the squeeze, better play for the hook.

Case 2: RHO follows. Assume LHO is about to also follow small -- if he shows out then the finesse and squeeze have the same odds (both require RHO to hold HK). Now we know 17 cards (all the minors and the spade spots). If LHO has 6 open spaces (minors break 4=7), then the squeeze is 6/9 * 5/8 + 3/9 * 2/8 = 1/2, while the finesse is only 1/3: play for the squeeze. If LHO has 5 open spaces, then 5/9 * 4/8 + 4/9 * 3/8 = 4/9, the same as the finesse.

This seems to be worth only 1 or 2%, but is not that hard to work out at the table.

Read more!

This week's deal

♠	Q 5 3
♥	10 8
♦	A J 8 6 5 2
♣	K 2
♠	K J 7 6 4
♥	J 3 2
♦	K 7
♣	A 10 4

West	North	East	South
			1♠
Pass	1N	3♥	Pass
Pass	3♠	All Pass

Is North worth an upgrade to 4♠?

♣Q led, what's your plan? More below...

Say you win in hand and play ♠K and it holds while RHO throws a heart. Now what?
Read more!

Update

I can't keep up the "daily" any more, so I've renamed the blog.


Read more!

A common bidding problem

Sorry for the light posting this week.

♠	8
♥	K 7 5
♦	A K Q 5
♣	K 9 6 4 3

Your call. What's your plan after a 1♠ response? What about 1♥? Anyone have a sense for the chances of each?

A followup below the fold...


Opponents passing, say the auction goes:

1♣ - 1♠; 1NT - 3♠ (good suit, slammish). Now what?

Read more!

Advancing problem -- result

From last Thursday:

IMP Pairs
Both Vul

You, South, hold:

♠	K 10 9 6 5
♥	K J 6 3
♦	Q 10
♣	K J

West	North	East	South
1♦	1♠	Pass	2♦
3♣	Pass	Pass	?

Would you bid something else the first time? What do you do now?



The consensus of the comments, and the person who held the South hand, and me, is that this hand should not drive to game. I could live with another try, but would settle for 3♠ myself. Partner held 5=3=3=2 with AQ/A and happened to make.

I play it as a "mixed raise", but think there's a lot of merit to THG's suggestion of using a jump-Q as a 4 card raise with more ambiguous strength (making the jump raise a bit wider-ranging too to take off some of the pressure). I'd have been happier to do that then bid 2♦ the first time around. Or, if it's available, 2NT as a 4+ trump limit raise.

Read more!

Team trials assign the blame -- my assignment

From last Tuesday:

Had this auction in a KO match. How would you assign the blame, if any?

Unfavorable

♠	8 4 3
♥
♦	K 10 8 5 2
♣	A Q 10 6 4
♠	K J 5
♥	A 3
♦	A Q 7
♣	K J 7 5 2

West	North	East	South
		1♥	Dbl
3♥	4N	5♥	6♣
Pass	Pass	6♥	Pass
Pass	7♣	Dbl	All Pass

In practice I think the hands were a bit different than what's shown here. North definitely had a heart void, and we were definitely missing ♠A, but the rest is fairly roughly reconstructed. But, I think the analysis below applies equally to the hands shown above as to the actual hands we held.

I held the South hand. In retrospect, it's simply not possible for North to have the ♠A on this auction (in addition to the necessary minor suit honors). That would leave East with about a 9 count for his opener, and West with a 0 count. Not to mention North would have quite a lot for 4N.

While we hadn't discussed it, North made the excellent point that this sort of auction should be asking for a heart void. That's the only really plausible undiscovered feature that could make grand biddable. Also, the odds of making grand do not have to be that high for it to be a worthwhile bid since the downside isn't a small slam but rather a moderate penalty against 6♥X. Conceivably we could be off an Ace and still make it. Not to mention they might bid 7 themselves.

So, while I think North could have fielded it, mostly I think this was my fault.

East, a former world champion, said he doubled not really knowing if he was beating it, but didn't want his partner to sacrifice since he held ♠A. At the other table, our teamates did bid 7 over 7 so we would up with a big loss.

Read more!

Another team trials bidding problem -- result

This is mostly a week of sharing results on recently posted problems. This hand is from last Monday:

I held this hand in a knockout match (spots approximate):

♠	Q 5 4 3
♥	K
♦	A K Q 10 7 5 2
♣	A

West	North	East	South
	1♣	Pass	1♦
Pass	1♥	Pass	1♠
Pass	2♠	Pass	?

What is your plan? Imagine that partner makes a weak spade bid over your next call.

Also, we often bypass to rebid 1NT.



At the table, I bid 4♦, then blackwood over the expected 4♠. Partner showed 2 without and I offered 6♦. He held 4=4=1=4 with no ♠J, so we were able to stop in 6♦ rather than the inferior 6♠.

Read more!

Defensive problem -- solution

[UPDATE: THG makes an excellent double-dummy point in the comments. Elaboration in the "solution" section.]

This was the full deal from Wednesday's defensive problem:

IMP Pairs
Dlr West
Vul North-South

		♠	K Q 5 3 2
		♥	A J 4
		♦	9 8 7
		♣	J 9
♠	J 9 8 4			♠	10 6
♥	K 10 9 7 6			♥	8 5
♦	A 10 3			♦	Q 4 2
♣	7			♣	A K 8 6 5 3
		♠	A 7
		♥	Q 3 2
		♦	K J 6 5
		♣	Q 10 4 2

West	North	East	South
Pass	Pass	3♣	Pass
Pass	3♠	Pass	3NT
All Pass

What would you lead?

Say you lead the ♥10 which runs to declarer's queen. Declarer plays a club to the jack, holding (partner shows even count), and another club to partner's king. Partner plays a heart back to dummy's jack. What is your plan?

At this point, declarer played ♠A and a spade, ducking it to East's ten. Now declarer had 4 spades, 3 hearts, 1 club, and 1 trick in whatever minor gets played next.

What went wrong? Answer below...


Declarer avoided losing a spade to West who could have cleared hearts while retaining a diamond entry. East could have played the ♠10 on the first round, or West could have hopped ♠J on the 2nd round.

3NT was cold (from this side of the table), though. How did declarer go wrong? (I don't know the answer, but deep finesse claims this is true.)

UPDATE: As THG points out in the comments, you had to pitch something on the 2nd club. A spade is clearly a disaster. If you pitch a heart, declarer can set up spades and wind up only losing a trick in each suit. If you pitch a diamond, declarer can (perhaps after 2 spade winners) play a diamond to the jack and set up 2 diamonds (while only letting you in once and stranding your long hearts) to go with 3 spades, 3 hearts and a club; losing 2 diamonds and 2 clubs.

This answers my question about how 3N was cold. Yet another triple-squeeze hand, entirely by accident. Reminds me also of the back-and-forth entry attacking seen on this deal.

In practice, pitching a diamond and hopping ♠J is still a good single-dummy effort.
Read more!

Advancing problem

IMP Pairs
Both Vul

You, South, hold:

♠	K 10 9 6 5
♥	K J 6 3
♦	Q 10
♣	K J

West	North	East	South
1♦	1♠	Pass	2♦
3♣	Pass	Pass	?

Would you bid something else the first time? What do you do now?


Read more!

Defensive problem

A friend of mine entered the Allendale sectional IMP pairs recently. He shared 3 interesting hands with me that will appear this week and next, starting with this defensive problem.

IMP Pairs
Dlr West
Vul North-South

		♠	K Q 5 3 2
		♥	A J 4
		♦	9 8 7
		♣	J 9
♠	J 9 8 4
♥	K 10 9 7 6
♦	A 10 3
♣	7

West	North	East	South
Pass	Pass	3♣	Pass
Pass	3♠	Pass	3N
All Pass

What would you lead?

Say you lead the ♥10 which runs to declarer's queen. Declarer plays a club to the jack, holding as partner shows even count, and another club to partner's king. Partner plays a heart back to dummy's jack. What is your plan?


Read more!

Team trials assign the blame

Had this auction in a KO match. How would you assign the blame, if any?


Unfavorable

♠	8 4 3
♥
♦	K 10 8 5 2
♣	A Q 10 6 4
♠	K J 5
♥	A 3
♦	A Q 7
♣	K J 7 5 2

West	North	East	South
		1♥	Dbl
3♥	4N	5♥	6♣
Pass	Pass	6♥	Pass
Pass	7♣	Dbl	All Pass

Read more!

Another team trials bidding problem

I held this hand in a knockout match (spots approximate):

♠	Q 5 4 3
♥	K
♦	A K Q 10 7 5 2
♣	A

West	North	East	South
	1♣	Pass	1♦
Pass	1♥	Pass	1♠
Pass	2♠	Pass	?

What is your plan? Imagine that partner makes a weak spade bid over your next call.


Read more!

Kelsey error? -- Solution

From Wednesday:

Game All.

♠	10 7 6
♥	K J 9 8 7 5 3
♦	6
♣	K 4
♠	K J
♥	A 10 2
♦	A K 10
♣	A 9 7 5 2

West	North	East	South
1♦	3♥	Pass	6N
All Pass

Lead: ♦Q. You win and both follow to the ♥A. Plan the play.

Kelsey says (in APAB) that playing for the ♠Q to be onside is unlikely to succeed and recommends playing West for ♠A, ♠Q, ♦J, and at least 2 club honors. After running 6 hearts you reach this position:

♠	10 7 6
♥	3
♦
♣	K 4
♠	K
♥
♦	K 10
♣	A 9 7

On the last heart, pitch the ♠K and West has to give up his next to last club (he's holding onto ♠AQ and ♦Jx, thus only one club; remember you started with ♠J). Now cash the ♣K and finesse the 9.

A nice enough guard squeeze without the count, but it seems to me it's possible to do better...



In the same end-position, just cash ♣K, the last heart pitching a club, and ♣A. If you still haven't seen a spade honor pitched, then the ♦J should be dropping. If you have, exit a spade to endplay West into conceding 2 diamonds.

Conceivably West might pitch ♠Q and keep a low one, but this doesn't help: when you exit a spade and he wins ♠A and plays another, the 10-7 in dummy will win the last 2 tricks. If it's still possible for East to have 3 spades to the 9 or 8, that means there are 5 spades outstanding in the 3 card end position and your diamonds are good (so you don't exit). So East is squeezed also: he can't pitch all his diamonds or you will have no guess, so has to pitch down to 2 spades. You won't know what your last 2 tricks are when you exit ♠K, but you'll know you have 2 coming.

Both lines assume the spade and diamond honors are with West, but the guard squeeze line requires guessing who has the last club honor. More importantly, this line doesn't require any particular club holding with West and so must be superior.


Read more!

Defending preempts, part II

In a recent MSC (July 2009 Problem G) the panel had to interpret (2♥)-X-(4♥)-P-4♠ by partner. I think the consensus is that it cannot be a solid one-suiter. Rodwell's summary of the possible hands for that auction seems the most accurate -- it is either a 3-suiter, or maybe a 6-card suit where the hand is too good for 3♠ but the suit is not good enough for 4♠.

So, this hand (posted Monday) facing a 2♥ preempt:

♠	A K Q J 8 3 2
♥	A
♦	5
♣	K 9 6 4

...must, I believe, choose between 4♠ and 3♥. Between those, I have no idea what's right but would probably choose the former. One commenter suggested using 4♥ to show this hand type, seems like a plausible idea to me.

At the table I doubled and bid 4♠ over more hearts and partner came close to pulling to 5♦, which would not have been good. One of my first posts shows I've been getting these auctions wrong for a while (I bid 3♥ over 2♦ with something like Ax/AQT9xxx/Kxx/A, which seems like a clear underbid).

Over a 2♦ preempt, you might be able to get away with doubling and bidding spades over their diamond preempt or partner's heart bid. This might sound more like 6 moderate spades and 4 clubs, but if partner does pull to clubs you're probably fine. And you might have a fighting chance of reaching a difficult slam.

Read more!

Kelsey error?

[I posted this deal to rec.games.bridge in 1995]

In the Pressure Play section of Kelsey's _Advanced Play at Bridge_, he gives the following problem:

Game All.

♠	10 7 6
♥	K J 9 8 7 5 3
♦	6
♣	K 4
♠	K J
♥	A 10 2
♦	A K 10
♣	A 9 7 5 2

West	North	East	South
1♦	3♥	Pass	6N
All Pass

(I guess preempts were a bit more reliable then.)

Lead: ♦Q. You win and both follow low to the ♥A. Plan the play.

Kelsey's solution below, my solution later this week.



Kelsey says that playing for the ♠Q to be onside is unlikely to succeed and recommends playing West for ♠A, ♠Q, ♦J, and at least 2 club honors. After running 6 trumps hearts you reach this position:

♠	10 7 6
♥	3
♦
♣	K 4
♠	K
♥
♦	K 10
♣	A 9 7

On the last trump heart, pitch the ♠K and West has to give up his next to last club (he's holding onto ♠AQ and ♦Jx, thus only one club; remember you started with ♠J). Now cash the ♣K and finesse the 9.

A nice enough (triple) guard squeeze without the count, but it seems to me it's possible to do better.
Read more!

Spingold bidding problem -- outcome

I posted this last week:

Both Red at IMPs, you, East, hold:

♠	Q 8 3
♥	A
♦	7 5 2
♣	K J 10 6 5 4

South	West	North	East
1NT	Pass	2♥	?
2♠	Pass	Pass	?

Do you act at either opportunity?

In the comments, basically everyone passed (with one exception bidding 3♣ after 2♠ was passed around). This is also what happened at my table.

Partner had something like: xx/Jxxxx/AQJ/Qxx. So we had 10 tricks available in clubs (not surprisingly the ♦K was onside) and instead went -110. In practice this was a push, though we don't know the result at the other table (we think it was 5♣ down 1, in fact).

My instinct (and takeaway for this deal) is that people generally fear losing 14 IMPs too much in competitive auctions and should be more willing to take that risk in order to win 5 or even a game swing: bidding directly over the transfer might be required to get the game-beating lead, for example.

Bidding early also may put opener in a bind. Probably will be unwilling to pass or double with 3+ spades, and how firm are everyone's agreements here anyway?

Of course, partner has to be on the same wavelength and not drive too high with a fitting hand.


Read more!

Defending preempts

At summer nationals (forget which event) I held (approximately) this hand:

♠	A K Q J 8 3 2
♥	A
♦	5
♣	K 9 6 4

What is your plan if the opponents open 2♥?

Does it matter if they open 2♦ instead? For me, a cuebid is michaels in this auction (if you don't play that way I think it's right by a lot) but not over 2M. Read more!

Trivia question answer

Last week in this post I posed a trivia question. If you haven't seen it yet, go check it now. There's a hint below the fold of the original post, and further hints in the comments.

Now for some final hints, with the answer below the fold.

1. As suggested by the lead and some strange features of the play (most notably North signaling with the ♣7), this deal was played at Whist.

2. The character's initials were H.H.



Answer: Horatio Hornblower, in _Beat to Quarters_. For what it's worth, I'm a huge fan of the whole series.

http://www.amazon.com/Hornblower-Beat-Quarters-C-S-Forester/dp/0316289329

[I get nothing if you buy the book, just posting for convenience]
Read more!

Team trials bidding problems outcome

These 2 hands were previously presented as separate bidding problems (North post, South post):

♠	Q J 6
♥	Q 8
♦	J 8 7 4 2
♣	A 10 4

♠
♥	J 5 4
♦	A K 6 5
♣	K Q J 9 5 2

South	West	North	East
			1♠
2♣	4♠	Pass	Pass
Dbl	Pass	5♣

I think acting with the South cards is right, but now prefer 4N to double. I also think bidding over double is right with the North cards, though that was not a popular choice in comments. In fact, the opponents can make 4♠ if they double hook in trumps, which is probably marked if you pass. 5♣ is down one (you must lose a diamond).

In practice, the double took 20-30 seconds behind screens and that was enough to get the result rolled back to -790. For what it's worth, the committee concurred that 5♣ was the right call, but concluded it was also suggested by the hesitation.





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Spingold bidding problem

Both Red at IMPs, you, East, hold:

♠	Q 8 3
♥	A
♦	7 5 2
♣	K J 10 6 5 4

South	West	North	East
1NT	Pass	2♥	?
2♠	Pass	Pass	?

Do you act at either opportunity?



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Unusual right-siding problem -- Solution

This deal was solved in comments fairly quickly. West to lead and defeat 5N. 5N with East on lead cannot be defeated:

		♠	Q 3
		♥	K Q J 6 4 2
		♦	A 7 6
		♣	A 8
♠	K 9 5			♠	J 10 8 7 2
♥	8 7 5			♥	A 9 3
♦	K 10 3 2			♦	9 8 4
♣	J 6 3			♣	Q 9
		♠	A 6 4
		♥	10
		♦	Q J 5
		♣	K 10 7 5 4 2

The only positional possibility is in the club suit, so West must need to lead a club. The interesting variants are, after declarer wins ♣A:

1. Declarer attacks hearts. East wins and plays a spade. If declarer ducks, he has 11 tricks set up, but West can tangle his entries by leading a 2nd club -- this would not be possible if East had opening led the ♣Q as South would have a tenace. If declarer wins and plays ♦Q, West had better cover or declarer wins, takes ♦A and all the hearts and has a (non-repeating) triple squeeze for his 11th trick -- in the 3 card ending West must hold ♠K, ♦K, and the guarded ♣J. If West does cover, then in the 4 card ending he can only hold 1 diamond which can be stripped with ♦J, then a spade exit would force a club lead away from the J. Again, it is critical that the opening lead have been from West so that East's ♣Q guard against an endplay.

2. Declarer wins and plays 3 rounds of clubs. Now West must play the ♦K to kill the heart suit. A bit unusually, South could prevent the hearts from being killed by ducking, except that then ♣J, ♦K, and ♥A are 3 tricks for the defense.

A nice collection of communication disrupting plays.

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Unusual right-siding problem

Played in my annual club game recently and noticed something funny in the deep-finesse analysis of the hand records. On the deal below, North can make 5NT, but South cannot. So the question is, what's the killing opening lead for West? Given the siding analysis, that actually shouldn't be that hard (but still took me a while to believe). Once you've got that, then how does that hold it to 10 tricks?

		♠	Q 3
		♥	K Q J 6 4 2
		♦	A 7 6
		♣	A 8
♠	K 9 5			♠	J 10 8 7 2
♥	8 7 5			♥	A 9 3
♦	K 10 3 2			♦	9 8 4
♣	J 6 3			♣	Q 9
		♠	A 6 4
		♥	10
		♦	Q J 5
		♣	K 10 7 5 4 2

Might not publish the answer to this until I see it in comments.

Have a great Labor Day weekend. No new posts until Tuesday.




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Trivia question

I read this deal in a book novel. The exact spade-diamond shape in the North hand is not certain:

♠	x x x
♥	Q x x
♦	x x x
♣	K J 7 x
♠	x
♥	A K x x x
♦	A K Q x x
♣	A x

Here's how the play went:
♥K led to the first trick, then ♦K, ♥A (everyone following), heart to the ♥Q, diamond to the ♦Q, running diamonds, North pitched ♣7 at his first opportunity, then (after all the diamonds), ♣A, club to the ♣J (winning), ♣K at which point South pitched a spade and claimed the last 2.

What book novel is this from? A hint is below the fold.

The book's protagonist, North, shares initials with a well-known fictional bridge player.

UPDATE: There is an additional hint in the comments.

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Suicide squeeze

There isn't much to this story, but I don't see a suicide squeeze every day so here it is:

		♠	J 9 6 5
		♥	Q 5 4
		♦	J 9 5 2
		♣	10 5
♠	Q 8 7			♠	K 10 3
♥	K 9 7 6			♥	10 3 2
♦	A 7			♦	Q 8 4 3
♣	Q 7 6 4			♣	A J 2
		♠	A 4 2
		♥	A J 8
		♦	K 10 6
		♣	K 9 8 3

I opened 1N and bought it. The defense started with a low club to the ace and jack. I won and continued the suit; LHO won that and played a 4th round, North and East both pitching hearts. I tried a heart and LHO won the king and continued the suit. I won in dummy, and ran ♦9 to LHO's ♦A. Another heart came back and RHO pitched a diamond without trouble. This is the end position:

		♠	J 9 6
		♥
		♦	J 5
		♣
♠	Q 8 7			♠	K 10 3
♥	9			♥
♦	7			♦	Q 8
♣				♣
		♠	A 4 2
		♥
		♦	K 10
		♣

With 4 in the bank for each side, I tried a low spade, and when LHO played the ♠Q the defense was finished. In practice, he cashed the long heart and squeezed his partner, but a spade or diamond would not have been any better. At this stage, the only winning defense is to let RHO win the ♠10 and continue with ♠K.



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