Unusual vs Unusual

ANNOUNCEMENT: I'm off to summer nationals and probably won't be posting tomorrow or next week. Regular posting should resume on August 3rd.

Enough play hands for the moment.

I've come up with many pretty dumb bidding ideas, but also a couple that I think are sound. One is a generalized defense to overcalls showing 2 known suits. Usually people use the available cue bids to show a LR+ or the 4th suit (usually forcing). To me, this has 2 problems:

a) it doesn't fully exploit useful space
b) it might not generalize to, e.g. 1H-(2N) showing minors, and really doesn't generalize well to 2 suited jump overcalls such as 1S-(3C) showing clubs and hearts.

So, I propose:

0. NT bids, natural raises, and jumps mean whatever they normally mean. (I like to use cheapest JS into a minor as a GF raise establishing a force.)

1. The first priority is to have an LR+ bid below 3 of opener's suit. But, this bid does not require any room, and should otherwise be as rich as possible. For example, 1S-(2N)-3H is a limit raise, regardless of which 2 suits 2N might show.

2. If room is available, we should have a negative free bid in the 4th suit available. But, this is a fairly precise hand-type and so should use the next most expensive bid, except not above 3 of the 4th suit (which would be illogical). If this turns out to be an artificial bid, then it could be planning to bid again. So if 1S-(2S) shows the reds, 3C is the natural nfb, but if it shows the minors, 3D is an nfb in hearts. (So I use 1H-(2N)-3S as a nfb and only make the bid on hands with a strong pref for spades over hearts, some might prefer to also require the nfb bid to be below opener's suit.)

3. The next available bid is the forcing in the 4th suit bid. This will often be pretty cheap, allowing the most room to work out the best strain.

I'm not sure I've ever had a "success" attributed to this system, but I do feel confident that we're prepared for any crazy 2-suited auction that might show up.

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Why was I sent this hand?

Arch sent me this deal from P. 152 of "Bridge for Money" by David Bird and Martin Hoffman (Review: I found the humor a touch mean-spirited, but I do like this deal):

     743
     764
     K75
     AQ74
86         KQJT2
9852       3
J93        AQT8
JT82       653
     A95
     AKQJT
     642
     K9

After E opens 1S, S plays 4H. W leads a spade -- you may want to give it a try (perhaps even single-dummy).



Win the second round. Then 4 rounds of hearts followed by 3 rounds of clubs.

The 4th round of clubs comes in this position:

   -
   -
   K75
   4
-      QJ
-      -
J93    AQ
J      -
   9
   T
   64
   -

Clearly East can't pitch a spade, or you ruff and throw him in. But if he pitches a diamond, you pitch a spade and duck West's forced diamond play. The DA is played on air and you can ruff the spade return and cash your DK.

Why did someone send me this particular hand? My first (and probably last -- it took me many years to write) Bridge World article described several positions like this (March 2009, "Ruff or Sluff"). I coined the term "veering squeeze card" to describe the technique.

Basically what's going on is that you have a strip squeeze but are missing one of the requirements -- you don't have control of either suit. If you had a major tenace in diamonds, or if they switched to a trump or club at trick 2, you would have an ordinary strip squeeze (by running three clubs then all trumps). Playing the actual holding along strip lines, RHO can defeat you by keeping two spades and baring the DA on your last trump -- you can duck a diamond to set up your king, but it does no good as RHO cashes two spade winners. With the veering squeeze card, though, you make a loser-on-loser play and retain your trump for control when RHO inevitably leads a spade. You also enlist LHO in leading diamonds for you.

There are a number of variations; for example, in the same ending say you did have a major tenace in diamonds--but none in your hand--then you don't need the trump to control spades, but you do need LHO's help in getting to diamonds if RHO pitches his guard. In the article I covered all of the "basic" varieties I could derive in the article, as well as a couple more esoteric examples. (There's also at least one very complicated hand in _Adventures in Card Play_ that has a similar theme.)

I found working through these very useful for learning more about strip squeezes. I don't expect to ever see a veering squeeze card, but I do expect to find more strip squeezes and defeat more pseudo strip squeezes as a result of the work.

If anyone ever does see one, or constructs a novel arrangement, I'd love to hear about it.


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Double-dummy solution

This hand is from yesterday's post, this time with the solution below the fold:

      AK32
      AK
      32
      A8532
T98765      -
J           T9876
QJ          T87654
T976        QJ
      QJ4
      Q5432
      AK9
      K4

South to make 6N on DQ lead.


What attracted me to the hand was the feature that each
opponent is triple squeezed, but not in the same 3 suits
(The D6 hand in _Right Through The Pack_ has that same
feature, though it is a much different hand. Also "saturated"
discussed by Don Kersey in the Bridge World and appearing
in a subsequent post here.). I also haven't seen the menace
(vs. East) in the club suit before, though it is very similar to
a guard menace.

Win DA, cash HA, HK, SQ, HQ. West will be stripped of 2
spades. Now 3 more spades (plus the one already played)
puts pressure on East. 3 diamonds may be pitched, but
then a club must be let go. Now DK completes the strip
against West and CK, club forces West to split -- duck
in dummy and claim the last 2.
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Double-dummy problem

This hand appeared in the May, 1994 Bridge World as a "bits and pieces" bit (or maybe piece) called "Mystery Feature".

      AK32
      AK
      32
      A8532
T98765      -
J           T9876
QJ          T87654
T976        QJ
      QJ4
      Q5432
      AK9
      K4

South to make 6N on DQ lead.



[UPDATE: Solution deleted; will post separately in a couple of days]

I have a couple of follow-ups to this post I hope to get to soon.

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More game theory

If you've been following the recent posts, there's some fascinating followup at Jonathan's blog. He's actually a game theorist, so pay attention. And don't neglect the comments.
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Game theory addendum

The last post started investigating a game theoretic mixed-strategy situation where I speculated that the best strategies for maximizing tricks might not be the best strategy for maximizing boards (at BAM scoring).

      A7
      -
      T
      -
?3             ?8
-              -
J              -
-              6
      QT
      -
      7
      -

Initially spades were 2=4, and we're presuming there's no additional information about the a priori location of the SK. You throw LHO in with a diamond and he leads a spade. How often is RHO supposed to bare the K if he has it? How often is declarer supposed to let the spade return ride to the Q?

Basically, if LHO has the SK, playing SA wins 1 trick, and low wins 2. If RHO has the SK and pitches a club, you always make 1 trick. If RHO has SK and bares it, going up wins 2 tricks and low wins 0.

Jonathan and I suggested that for trick maximization, RHO should bare the SK 1/4 of the time that he holds it, so that when declarer sees a spade discard he expects the SK to be on his right 1/3 of the time -- then going up expects to win 1 trick 2/3 of the time and 2 tricks 1/3 of the time for 4/3 tricks; while playing low wins 2 tricks 2/3 of the time and 0 the rest, also 4/3 tricks. (When declarer sees a club pitch--which happens half the time--declarer always makes 1 trick, so the total expectation is 7/6. If RHO never bares the K declarer can score 4/3 tricks by always playing low.)



But, BAM scoring complicates the analysis. Intuitively, the 1-trick error (flying SA when the endplay was on) always costs a half a board, while the 2-trick error (losing to stiff K instead of dropping it) usually costs you (proportionately) a full board (when the other table just pitches a club holding SK), but only costs you half a board when the other declarer also faces the same problem, which he will some of the time. So the BAM cost of the 2-trick error is not twice the BAM cost of the 1-trick error. Therefore, declarer should be more willing to risk the 2-trick error, and the defense needs to bare the SK more often to be optimal.

Suppose I know my opponents believe that baring 1/4 is optimal (if it really is optimal, I won't be able to exploit this). I will always play a low spade. Meanwhile, at the other table, I plan to bare 30% of the time and to tell them. Believing that this is suboptimally high, their response should be to always play SA (which will in fact win more tricks). If this happens, then:

SK on left (1/3): My team wins the board.
SK on right and my opponent bares (1/6): My team always loses the board.
SK on right and my opponent discards a club (1/2): I always take 1 trick. Meanwhile, at the other table, they take 2 tricks 30% of the time (when my 'mates bare SK) and 1 trick 70% of the time (when my 'mates also discard a club), so we push the board 70% of the time.

In total we score 1/3 + .7/4 for a touch under .51 boards.

What if the other declarer also always plays low? Then:

SK on left (1/3): both take 2 tricks, push, 0.5
SK on right and my opponent bares (1/6): 30% push, 70% lose, 0.15
SK on right, opp discards a club (1/2): 30% win, 70% push, 0.65

Total expectation: .517

So, clearly 1/4 baring does not maximize boards won. By my math, the right frequency of baring the K in this situation is 1-sqrt(0.5), or about 29.3%. I wasn't previously aware that a rational bridge strategy could ever be an irrational frequency.

Finally, note that if spades had initially been 3=3 (or more with LHO) things are much simpler: RHO should always bare the SK and declarer should always play low. Theoretically declarer can adopt any strategy and have the same expectation, but always playing low gains against non-barers without losing expectation to barers (presuming, of course, you have no read on your opponents).

To me, it's a bit interesting that in the 2=4 case RHO wanted P(SK on right | RHO kept club) to be over 0.5, but exploiting that option in the 3=3 case (by not always baring) is wrong.



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Names withheld to protect the innocent, part II

This is a followup to yesterday's post here.

Jonathan has the ending analysis correct in the comments. In this position, there's no harm in playing a diamond and then deciding what to do when West plays a low spade.

       A7
       -
       T
       -
?3             ?8
-              -
J              -
-              6
       QT
       -
       7
       -

In practice, RHO discarded the S8 and I played for the endplay, losing the last 2 tricks and going down.

I also concur with Jonathan's statement that East should bare the SK 1/4 of the time when he has it. He wants declarer to be indifferent between SA and S7. Since SA gains 2 tricks when right and S7 gains only 1, the odds declarer should face should be 2:1 against bare SK. A priori West has it 1/3 of the time, so the odds will be 2:1 if East only bares it 1/4 of the 2/3 of the time he's dealt it (recall that spades were 2=4).

Similarly, declarer should aim to make East indifferent between baring and not baring when he has the K. Baring risks a trick to gain a trick, so indifference is achieved if declarer goes up 50% of the time.

Of course, this analysis is for each side maximizing their expected trick taking. I think maximizing boards (or matchpoints) might lead to a slightly different optimal strategy. Perhaps I'll revisit. UPDATE: In fact it does. See next post

Also, if East knew he was working on a book, he may have had an extra incentive to bare the K. As Jonathan said (suggesting experts might prefer flashiness), this should make declarer go up more often.


In fact, this deal was written up in "The Master Reveals His Secrets, Helgemo's World of Bridge" (Review: never actually read the book, but Tim said it was good.) I was simply referred to as "declarer". A copy is below the fold...

        A742
        AQ75
        T82
        QT
J3               K865
9842             63
KQJ653           9
8                A65432
        QT9
        KJT
        A74
        KJ97

"On the next deal, where Three No-Trumps was the contract around the room, we shall see Tony and Geir cooperating well to push declarer over the edge. Both needed to be on the ball to succeed.

"Since the club ace was not with the diamond length, the contract was safe. Like every other West, Tony Forrester led the king of diamonds which declarer allowed to hold the trick. The next diamond was taken by declarer's ace as East pitched a club. South now played on clubs and Geir
let him make the first two tricks, but took the third one and cleared the suit. He had thus established a trick for himself in the suit, but apparently in vain because declarer had nine top tricks.

"It is hard to see how the defenders could give declarer a problem here. However, Forrester's creativity turned a dull board into a nightmare for declarer. West had to make three discards on the clubs and he let go his three little diamonds. Four hearts tricks followed and Geir discarded two spades. This was the position:

       A7
       -
       T
       -
J3             K8
-              -
J              -
-              6
       QT
       -
       7
       -

"Declarer call for the ten of diamonds from dummy. He had endplayed Forrester, who was known to have only one diamond left, to lead a spade. This could not have happened had Forrester not discarded so many diamonds. If the jack and king of spades were interchanged, South would have been his team's hero on this deal. But he was soon disappointed.

"Geir had not fallen asleep, and he understood what Tony was up to. On the ten of diamonds Geir discarded the eight of spades. Forrester now had to play a spade, and declarer called for dummy's seven. So East took the last two tricks with his now bare king of spades and a club. Dummy's ace of spades never took a trick, and this magic one down gave the Shugart team
the point for the board." Read more!

Names withheld to protect the innocent

From the 2nd day of the '98 Reisinger in Orlando (i.e. scoring = BAM vs strong opponents).

Sadly, I forget the auction (maybe Tim knows it), but you're declaring 3N with these hands:

 A742
 AQ75
 T82
 QT
 
 QT9
 KJT
 A74
 KJ97

To start off, you duck the DK lead and win the 2nd as RHO pitches a club. RHO wins the 3rd round of clubs and plays a 4th (LHO follows once and then pitches 3 diamonds).

I'll turn it over here. If forced to make pitches, each opponent will cling to one minor suit winner.



Say you cash your hearts and come down to this 3 card ending with the lead in dummy:

 A7
 -
 T
 -
 
 QT9
 -
 -
 -

LHO has a diamond, RHO a club, and they each have 2 spades (if you care, LHO had 4 small hearts). Now what?

More later.


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My other bridge column deal

This is my one other hand that made the bridge column. I'll try this as a low-tech bridge movie. If you want to play along, cover up the screen and reveal it until you see a line with "Now what?" and consider what you would play.

[UPDATE: my partner insists that I switched the HT and HJ both here and in the hand reported to the NY times. The analysis is basically unaffected, but the bidding is even less impressive and the play a bit cooler.]

    A83
    K64
    K852
    T94
 
    QJT964
    AJ95
    73
    3

East  South  West  North
1C    1S     Dbl   2S
3C    3H     Pass  4S
Pass  Pass   Pass

How about that 3H bid?

A low club is led and RHO wins the K and plays the Ace. Presumably you ruff.

Now what?



I think that starting with a diamond towards the K is best (for reasons to be revealed). At least that's what I did. LHO wins the DA and taps you again with the CQ.

Now what?



I think RHO must have the SK on this auction, so I reject the spade finesse and play SA -- this is why I wanted to test diamonds first. Both follow low.

Now what?



Now try a partial elimination to see if you can avoid a heart guess: DK, diamond ruff, exit a spade. There are no discards and RHO wins SK and leads a club in this position:

    8
    K64
    8
    -

    9
    AJ95
    -
    -

Now what?


Ruff in hand, LHO pitches a heart, and...

Now what?



LHO must have started 2=4=4=3, so there's no need to guess the hearts: pitch a heart from dummy, HK, S8 squeezes another heart from LHO and now HA drops the Q and HJ is your 10th trick.

There was a kind of non-material aspect to the endplay after RHO won SK -- I had 9 tricks already if I just ruffed a diamond in my hand, but the ruff-sluff got me to 9 while preserving that diamond as a menace.

Full deal and link below.



This was the whole hand.

    A83
    K64
    K852
    T94

72          K5
Q872        T3
AJT6        Q94
Q85         AKJ762

    QJT964
    AJ95
    73
    3

NY Times column here.


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What are the odds?

UPDATE: In the comments, Jonathan demonstrates some errors in my below-the-fold analysis. I'll try to summarize in a subsequent post, but briefly the chance that a suit splits evenly just because both opponents follow once or twice to a suit where they have several cards goes up much less than an empty-spaces approach would suggest. --Franco

I used to participate regularly on rec.games.bridge. Apparently I posted this hand back in 1995:

AJxx
KQ7x
9x
AK9

T8x
Axx
AKJT8x
x

Declare 6D on the SK lead (North opened 1N, the opponents did not bid).

You win SA, RHO follows. Do you:

a) Run the D9,
b) Play DA, CA, then hook DJ,
c) Play DA, CA, then run D9, or
d) Play DA, DK, then set about trying to pitch your spades?

There are a couple of potentially useful odds-related links in the links section to the upper right should you care to try for a very precise analysis.

Some further discussion is below the fold...



For some reason, when I first read _Winning Declarer Play_ many years ago, a hand around this trump suit tripped me up: I thought it was right to cash an honor then hook, but of course (as I'm sure all my readers know) that only picks up stiff Q offside and an immediate finesse gains against any other singleton (since you can repeat the finesse).

That's true in isolation, but here you have decent chances at an endplay: DA, CA, D9 as LHO shows out. Then ruff a club, HA, HK, CK (pitching a heart) HQ. If the CK or HQ is ruffed: overruff, draw trumps, and set up a spade. If they all survive, pitch a spade, ruff a heart, and exit a spade to score the last 2 in trumps. It's very close, but by my math it comes out slightly ahead (note that the immediate finesse might pick up 5-0 onside with a similar endplay which makes it even closer). Perhaps I'll work it out precisely in a subsequent post.

So, line B is easily dominated by C, and C appears to be very slightly better than A (which, in turn, is very slightly worse than 50% -- it picks up all onside Qs except Qxxxx with <2 hearts which happens about .5% of the time).

How about trying to drop the Q or get fast spade pitches? Roughly 1/3 chance of dropping the Q. The rest of the time, your only hope is 3-2 trumps (about 42% given the Q hasn't dropped) and 3-3 hearts (about 40% given all the known cards, so the parlay is 16.8%). This rough estimate comes in about 50%, so seems better than the immediate finesse. Whether it's better than C requires a more careful calculation.

In the small-world dept, Jonathan happened to comment on this thread back in '95. His analysis of the playing for the drop concluded it was inferior, but that analysis had a small but important error (I implicitly made a similar error at the time): as cards become known, the chance of even splits go up (where I said in the last paragraph 1/3 + 42% x 40%, he said 32% + 41% x 36%). These difference appear to be enough to swing in favor of the drop over the finesse.

Finally, to get this right note that you have to make some assumptions, such as whether 8-1 clubs is no longer possible. To me, the interesting one is what are the "known cards" after the SK lead and RHO following? Naively LHO is known to have started with at least 2 spades, while RHO only 1. But LHO had a chance to make a revealing lead that RHO didn't.

My head hurts.

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Coolest hand follow-up

[Diagram repeated from yesterday's post]

JT8
KJ
AT95
J642


A
AQT8732
K63
A8

RHO opens 2D and you wind up declaring 6H on a trump lead (trumps are 2-2). How do you play?

See here for the technical answer.

See below for a different approach.



At the table I allowed the HK and HJ to hold (both following) and called for a diamond. RHO played the 4, so I let the 5 ride.

If he had covered, the technical line was still available.

[This deal was published in Truscott's column, here, though the website apparently omits the diagram -- non-critical spots and the exact black shapes may have been different.  UPDATE: Found a hardcopy and updated the non-critical spots and black suits.]

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Perhaps my coolest hand

[Update:  Found a copy of the column and updated the deal.  

  Analysis unaffected.]

JT8
KJ
AT95

J642


A
AQT8732
K63
A8

RHO opens 2D and you wind up declaring 6H on a trump lead (trumps are 2-2). How do you play?

See below for an answer...

Correct technique is to run all your trumps. In the 6 card ending, RHO must keep 4 diamonds (or you can duck a diamond) and so only 2 black cards. Guess which black suit RHO has abandoned (if he has one of each it doesn't matter) and cash that Ace -- he still must hold 4 diamonds, so he must pitch another black card. Now you can draw his last black card, play DK and a diamond to the T for an endplay.

But, this could still go wrong if, say, you guess wrong and cash the SA and RHO follows, then you cash the CA and RHO pitches a diamond -- the endplay doesn't work if RHO can retain a black exit.

Can you find any extra vig? My solution tomorrow.
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Introduction

I've been enjoying JLW's bridge blog so I thought I'd give it a try. This will also serve as an archive for some old bits and pieces I keep forgetting and reconstructing, and perhaps a diary of errors in the hope that I repeat them less often. Read more!