Dumb and dumber

I've heard of "dumbing down", and the ACBL is certainly quite "masterful" at it (get it?).  But this has to be some sort of world record:  looking at the results of a recent NAP game, I note that a C pair "qualified" with a 32.3% game!  They didn't beat anyone, either in their own section or the other section.  What is going on?  Could this be because there was a simultaneous novice pairs going on at the same location?

Meanwhile, in the third round* of this evening's club Swiss, playing the eventual winners, my team benefited considerably from the non-linear IMP and VP scales.  In six boards, between our two pairs, we managed to lose a total of 59 imps on "errors" with respect to double-dummy bidding and play.  That's 5 imps per pair per board!  Fortunately, the opponents made 18 imps of errors and the net was only 34 (instead of the 41 that would accrue on a linear scale) [our net loss in total points was 2030!]  Of course, this all adds up to being blitzed.  But again, it's better to have all your errors in one set because of the non-linearity of the VP scale.  Thanks to the non-linearity, and despite being 1 IMP (and 90 points) in the hole overall, we still ended up 2 VPs above average and in the money!

As they say, in bridge it's better to be lucky than good!

But enough of this silly philosophizing.  What you want to see is a hand!  Here's one from the second match that both pairs did well on (although this time the non-linearity worked against us of course).

Dealer North. E/W Vulnerable.
	♠ K Q J 10 5 ♥ A 10 5 ♦ 9 7 6 ♣ 6 5
♠ 8 ♥ K J 8 7 3 2 ♦ K 8 ♣ K J 9 3		♠ A 7 6 4 2 ♥ Q 6 4 ♦ A 5 ♣ 8 7 2
	♠ 9 3 ♥ 9 ♦ Q J 10 4 3 2 ♣ A Q 10 4

At the other table, Kim opened the South hand with an excellent third-seat "pressure bid": 3♦.  This effectively silenced the West player.  Tony raised the preempt to 4♦ and there it rested.  [BTW: it's usually not necessary to raise a pressure bid unless you have really excellent shape – see my blog Pressure Bids].  Result: -50.

At our table, the South player started with 2♦ and my partner, Len, deemed his hand just good enough to bid 2♥ (and I agree).  If I recall correctly, North passed and I was left to consider my hand.  In the context, my hand was about as good as it could be for a passed hand in support of partner's 2♥: three golden cards.  The only improvement might be if the ♦A was seconded to the clubs instead.  Thinking about the 5:3 reward/risk ratio for a vulnerable game, I jumped to 4♥ and we played it there.  Result: +650.  As you can see, game is cold.  Indeed it takes a slightly unlikely club lead to hold it to 10 tricks.

This was good for 12 imps but, like a 75 yard kickoff return, it was Kim's 3♦ call which got us into a winning position.  Imagine that our North and East players both decided to pass.  We'd still be gaining 7 imps on the board.  As it happens, that would have translated into only one fewer VP for the match.

* Incidentally, on this set, the North hand averaged 14.67 hcp per board (including one 2 point board).  That's quite a marked deviation from the norm.

A tale of two books

At a recent tournament, I was pleased to find two books that I hadn't seen before which interested me a lot.  One was Deceptive Defense: The Art of Bamboozling at Bridge by Barry Rigal.  The other was Bridge, Probability & Information by Robert F. MacKinnon.

The first of these is an excellent book, a must-read for anyone who wants to improve their game.  Whereas it's fun to pull off an advanced play such as a squeeze or endplay, it's even more fun to perpetrate a successful deception.  The look on the opponent's face is always worth it.

As a long-time student and enthusiast of probability theory as it applies to bridge, I've generally bought any book that I could find on the subject.  These range in quality from completely pointless (Frederick Frost's book) to totally brilliant (Kelsey and Glauert's Bridge Odds for Practical Players).  So, it was with great anticipation that I began reading MacKinnon's new book.  Especially given the allusion to information theory.  By the time I started to read the book a day or two later, I had seen a rave review in the ACBL Bridge Bulletin.

But I immediately found the style of the book somewhat annoying.  The book reads like a series of short essays on bridge probability.  They do not follow each other in logical order and each section is prefaced by a pithy, but typically totally irrelevant, quotation.  There are several really important concepts that MacKinnon puts forward.  But he seems to do so in such an off-hand manner, that the impact is very much lessened.  And he goes so far out of his way to ensure that the book does not read like a textbook that, where a little logical derivation of a result would be extremely helpful, it is usually missing entirely.  The author generally states these important results as facts or axioms without making it entirely clear how he derives the result.  The layout is not always as helpful as it might be, for example, the table he uses to demonstrate that the ratio of the number of combinations (and, therefore, probability) comes from the small number on the right divided by the large number on the left.  In this instance, the splits (large:small) are not aligned between the columns as suggested in the text.  Even the examples which he shows from actual play do not always seem to be entirely relevant to the ongoing argument.  I think that what this book craves most is a good editor.  The author definitely knows his stuff but, in my opinion, needs help in presentation.

This is definitely not a book for beginners, or even advanced players unless they have an abiding love of probability topics.  While it does "correct" some misconceptions suggested by other books, I do not think it will supplant Kelsey's book as the premier book on the topic.

Meanwhile, Rigal's book is, as always with this author, excellent.  It reads so well, and is sufficiently interspersed with relevant examples, that it is a hard to put down.  It concludes with a spectacular example of deceptive defense by the late great Maurice Harrison-Grey.  Grey's hand was ♠83 ♥9643 ♦AQ3 ♣KJ54.  His LHO opened 1D, partner bid 3S and RHO closed the auction with 3NT.  Grey led ♠8 and dummy tabled the following hand: ♠9 ♥AQT ♦KJ9852 ♣982.  Declarer held up his A until the third round (as the spade bidder could easily have held only six spades).  Put yourself in Grey's seat.  What do you discard on the third spade?  The hand went down one, by the way.

If you want to know the answer, you'll have to buy the book!  Or you could just ask me.

Show and Tell – More on Defensive Strategy

The bridge defender's dilemma: when you make a discard (or other signal) do you:

• show partner where you have something; or
• direct the defense by telling him what to do?

Often these come to the same thing in which case there's no problem.  But not always.  Note that I'm not talking about deceptive carding here, that's a separate subject.  The assumption is that we want to give partner good information and we're not too concerned about declarer seeing it too.

At first glance, it seems like we might be able to make an agreement with our partner: I'll always show you where I have high cards; or I'll always help you find the right defense.  But that idea of course would be nonsense.  You want to do different things at different times.  The trick is knowing what partner is telling you on any given hand.  How can you figure it out?

First, I think we have to assume that partner is an intelligent, sentient bridge player who was also listening to the auction and can clearly see the dummy!  He already knows which tricks might be going away and where declarer's weakness might be.  In particular, he can see if dummy has a dangerous suit or whether declarer is going to have to make his tricks the hard way.

So, my suggestion for the key to which defensive strategy should be (or is being) employed is this: urgency.  It stands to reason that the degree of urgency is greatest when the opponents are in a distributional suit slam and least when they're in a balanced 1NT contract.

Thus the following seems like a reasonable rule:

• if the situation is urgent, direct the defense by telling partner what to do;
• otherwise, show partner where you have a useful card or two.

Let's take a couple of examples, all assuming standard bidding and carding.  You are dealt the following hand at teams: ♠976 ♥K953 ♦7 ♣A9876.  Partner deals and opens 1♥, RHO bids 1♠ and you contribute 2♥.  LHO bids 3♥, partner passes and RHO closes the auction with 3♠.  You decide to lead your singleton ♦7 and the following dummy comes down: ♠AT4 ♥J74 ♦AT8 ♣QT53.  The first trick is made up of the 8, 9 and declarer's J after which the ♠Q is passed around to partner's K (not declarer's best play).  Partner leads the ♣4 which you win, returning the ♣6 for partner to ruff.  At this point, we have three tricks, but partner isn't sure what you want returned (declarer followed to the two club tricks with the K and J so that the location of the ♣2 is still unknown).  In order to figure out whether you want a diamond ruff or whether we can cash two heart tricks, partner plays the ♥A.  You know that a second ♥ trick won't stand up (partner can't be sure) and your trumps will be drawn if you don't get a diamond ruff immediately.  Urgency suggests direction (telling) over information.  Therefore, even though you actually have the ♥K, you play a discouraging 3.  You get your diamond ruff for a set, instead of letting them make.

Here's another hand: all are vulnerable at matchpoints and you deal yourself ♠A54 ♥62 ♦KQ82 ♣J863.  Your LHO opens 1♥ and RHO bids 1NT which is passed out.  You choose the ♠4 as your lead, eschewing the good diamond suit (this actually works out rather well).  Dummy is ♠982 ♥KQ874 ♦AJ ♣Q95 and partner's J is won by declarer's K.  Declarer now sets about enjoying the hearts, having started with A9 in his own hand.  On dummy's Q, you have to discard and you know that partner will be winning the next trick.  What should you discard?  You'd like partner to continue with spades of course, but he'll likely be doing that anyway.  Is there anything that you think partner needs to know about your assets (he knows you have between 10 and 14 hcp but he doesn't know where they are exactly).  He's also expecting you to have 4234 shape (he can only see four clubs so if you don't have four, declarer has six).  I think he needs to know that you have a stopper in diamonds (if he happens to have the ♦T, we may even be able to get 3S, 1H, 3D and 1C).  I believe that you should show your diamond values by discarding the ♦8.  There's no great urgency here, so our signal should be seen as informative (showing) rather than directing.

When I played this board recently, my partner holding the hand given, discarded the ♦2 (because he wanted spades continued, i.e. he was telling, rather than showing).  But I assumed he was showing.  Figuring then that partner must have the ♣K and only one of the ♦ honors, I wanted us to be able to cash out our clubs when the spades were finished.  Since I held the singleton ♣A, I felt that it was essential to cash it before running the spades (I held QJ63 originally).  Declarer now took 1S, 4H, 1D and 2C for an overtrick.  Although Deep Finesse says that declarer should always make the overtrick, our declarer wasn't going to without our help.

So, if potential tricks could go away quickly unless you metaphorically kick partner in the pants, tell him/her what to do.  If an active defense is likely to give away tricks, use your signals to show partner where you have useful values.

When attitude is known

It's customary when signaling to show attitude when we lead a suit.  If they lead a suit, our attitude is assumed to be bad and we skip to showing count.  If both attitude and count are known, or if bridge logic says that neither of these is important (e.g. a singleton in dummy), we skip to suit preference.

So much is reasonably standard.  Some people like to show count even on the opening lead, others on the opening lead if dummy presents a certain number of cards in the suit, etc.

In this blog entry, I would like to propose a variation: when attitude is already known from the auction, we give count on the first trick.  It's a method I've been playing for a while with one of my partners.

How does it operate?  When is attitude already known?  The premise is that when we get to show a good suit during the auction, our attitude is considered known (and good).  What constitutes showing a good suit?

• an overcall;
• a rebid of a suit;
• a "free" bid in a suit (when pass would be a valid alternative) [according to my principle of "stuff"];
• a lead-directing double of an opponent's artificial bid;

Thus, if we are not obliged to try to win the trick, for instance when partner leads a high card, or we cannot beat the dummy, our carding shows count, not attitude (when attitude is known from the auction).

Here's why it works: in all of the cases given, we have suggested length and strength in the suit.  Because of the length, the suit will not be standing up for very many tricks.  But how many tricks?  That's why count is so important.  Fie, I hear you say, sometimes I make bad overcalls.  Well, that may be true, but assuming partner is going to lead your suit anyway, the damage, if any, will already be done.  Much of the time the play to the first trick will clarify the position.  Yes, it's possible that a tempo or even a trick may be lost when partner gets in and, assuming good attitude (because you weren't able to discourage at trick one because of the obligation to show count), leads the suit a second time.  But for that to cost, four conditions must be met:

1. you have to have made a questionable bid during the auction;
2. you must have been in a position to signal at trick one (i.e. you were not trying to win the trick);
3. declarer/dummy must have sufficient cards in the suit for it to make a difference;
4. it must not be obvious from dummy's holding what's going on in the suit.

The chance of all these happening at the same time is actually quite small.

The same idea applies when the bidder is the one leading the suit.  On opening lead, it is normal to show count in any case so there's really no difference there.  But during the hand, it's common to make attitude leads of new suits.  Again, it's better to show count when we are leading our own "good" suit.

Note that this scheme may also apply (according to partnership agreement) when partner is leading his own known-to-be-good suit: our carding should show count if we can't win the trick.

As always, comments welcome.

Light third-hand openers

I've never found a really good written formula for when and how to open a sub-standard hand in third seat.  I've presented some ideas myself earlier in this blog: Third and Fourth Seat Openers.

A hand came up yesterday evening at the club which suggests a new rule for light third-hand openers: once partner has raised your "suit", never bid a new suit (unless partner forces you to).  This should never be necessary if you start with your best suit.  My partner picked up the following hand: ♠– ♥AJT8 ♦KQ432 ♣T843.  Only the opponents were vulnerable.  After two passes, partner bid 1♥.  My hand was ♠A976 ♥Q53 ♦J6 ♣K975.  My RHO passed and I contributed 2♥.  This went around to my RHO who backed in with 2♠.  Considering that I had a flat maximum, and somewhat forgetting that I had passed originally, I doubled.  Partner now felt that 2♠ was a likely make (it was) and decided to retreat to 3♦, giving me a choice of red suits.  I took this as a good distributional but solid opener, and jumped to the heart game.  My LHO was happy to double this and we went four off for a round zero (even two down would have given us the same matchpoint result).  Double-dummy, we can make 1♥, 2♦ or 4♣ (the par result).

So, what lessons if any are to be learned?  I've always believed that a passed hand should not take any questionable actions.  Doubling 2♠ was not automatic so I should not have done it.  But I think partner should have opened the hand, if at all, with 1♦ (his best suit).  If I bid 1♠ (as I surely would, assuming no intervention), he can then retreat to 2♣.  I would assume a "full" opener of course but the hand really is a full opener (27 Zar points which is an automatic opener in any seat) and, as noted, we can actually make 4♣.

So let me restate my guidelines for light third seat openers (with the new addition):

• Open only in a good suit of four or more cards, one which you'd like led [no "prepared" bids];
• Be ready to pass partner's one-level new suit bid [you can't rebid 1NT because you have too few points, by definition];
• Unless there's a suit you really want led, tend not to open with a very balanced hand, especially vulnerable;
• Don't bid a new suit of your own unless partner makes a forcing bid (he shouldn't, as a passed hand, unless he has a very good hand and fit for you).

Here are a few hands that I think should open 1♥ in third seat:

• ♠A86 ♥KQ93 ♦J6 ♣T975 (probably should pass this if vulnerable);
• ♠K862 ♥AQT5 ♦6 ♣T975, assuming you can't open this with an artificial 2♦ (if partner bids a natural 2♦, you'll just have to suck it up);
• ♠A86 ♥KQ963 ♦86 ♣T95.

 Here are a few hands that I think should probably be passed in third seat, especially if vulnerable:

• ♠A86 ♥KQ93 ♦J65 ♣T97;
• ♠A86 ♥KJ93 ♦Q5 ♣T975;
• ♠A6 ♥K83 ♦Q65 ♣QT975.

Comments welcome.

Protecting Equity

The concept of protecting your equity applies to any form of bridge scoring and at any bidding level but it is especially pertinent for part-scores at matchpoints.  The idea is that if you think you were going to make your contract and the opponents bid on, you have to double them in order to protect your equity.

In the double-or-pass decision, only their vulnerability is relevant.  In most situations, where our part score would score more than 100, doubling has much more to gain if they are vulnerable. Otherwise, doubling only makes good sense if we expect to set them two or if we were planning to get 90 (in 1NT or 2-of-a-minor).  Doubling to protect our equity in the latter case would be extremely rare.

Let's give an example.  Only they are vulnerable and both sides have found a fit.  We have bid 3H, expecting to make (+140) and the opponents counter with 3S.  We basically have two choices: bid on, hoping that we can actually make 4H (or be down only 1 while they can make 3S) or double them, hoping that they can't make 3S.  There is of course the option of passing, which is appropriate if we are vulnerable and/or we think that they have the balance of power.  If we pass and they are down 1 only, our +100 will not score well against those making +140, which is why we would want to double to protect our equity.

Let's say we encounter this board in the last round of a 13 round duplicate.  So far, the board has been passed out once and 3S their way has made twice and gone down one undoubled twice.  3H our way has made four times and gone down once.  One pair our way went down in 3NT doubled and another pair actually made 4H.  Assuming that our defense is going to be accurate, we expect to score +100 as is, earning a 6 (on a 12 top) for an average score.  In other words, if we do nothing, we will get an average board.

We might make 4H (for 11.5) but at the risk of going down (only 2.5 if they double) [gain:5.5 or lose 3.5], but let's say our hand is fairly balanced in light of the auction so we are not seriously considering 4H.  If partner still has a bid, he might bid 4H regardless of what we do, but let's suppose that whatever we do will be final.  Let's say that we decide to double to protect our equity.  If we're right, we will earn an 11 (gain 5).  If we're wrong, we will get an absolute bottom (lose 6).  On the other hand, if we had allowed them to make 3S undoubled, that would have scored only 1 matchpoint so, in fact, our double actually has a rather good reward/risk ratio: 5 to 1. 

Note how important it is that they are vulnerable.  I was reminded of this by my partner Steve yesterday in the morning STAC game.  On board 16, I elected to double 3S.  On paper, this wasn't a terrible decision, because I rated to gain 4.5 mps on a 15 top (there were 9 pairs in 3S the other way) and, assuming that we weren't setting it, we probably were only getting something like 6 mps anyway.  But now the reward/risk ratio is actually only 3/4 (nothing like the 5/1 we had above).  This is primarily because they weren't vulnerable!  So, our hypothetical gain was only from beating the 9 defenders of 3S (who we would otherwise have tied).  Because of the opponents' lack of vulnerability, the hoped for +100 wouldn't have restored our equity which in this case was +110 for 3C.  Assuming that there were a few pairs our way making 110 or 130, we'd have gained a whole point against each of these if the opponents were vulnerable, meaning that our R/R ratio would at least be greater than 1.

As it happens, of course, we couldn't defeat 3S (actually we let them score an overtrick) and 4C would have been down 2 vulnerable, possibly doubled.  Despite our 21 hcp, they can take 9 tricks in spade while we can take 8 tricks in clubs.  The commonest number of total tricks (17) but on this occasion biased in favor of the other direction.  Allowing them to make 10 tricks would only have earned us 3 matchpoints so in a way we only lost those 3.  But maybe our defense would have been more passive if we weren't trying to set the contract, in which case we'd have scored 7.

Jacoby Two-Notrump Rebids

Not much to write about these days from the bridge trail.  I haven't seen any really interesting hands.

However, one topic has been on my mind for a while and an example came up just the other day in the STAC tournament (Friday morning, board 4).  As dealer, with both sides vulnerable, you pick up the following hand: ♠QJ953 ♥3 ♦KQ ♣AK542.  You have a decent 15 point hand although you couldn't say that it was a great 15 points.  Anyway, with silent opponents throughout, you open 1♠ and partner responds 2NT (game-forcing with four or more spades and either a good 13 or more hcp or a balanced hand, or both).  What should your rebid be?  What is the most useful thing for partner to know?  The singleton ♥3 or the good club suit?  Of course, that depends on partner's hand.  But one thing is for sure, partner will know you have a singleton (or void) regardless of which bid you choose.  A computer simulation is probably the best way to determine the best call. With ♠QJ953 ♥3 ♦K5 ♣AKQ42, I think that 4♣ stands out a mile.  Even with the actual hand, I think that 4♣ is best, even though it uses up more bidding space.  On this particular hand, responder held ♠AT72 ♥AK865 ♦92 ♣Q6.  Given that we're off an ace and the trump K, no good pair is going to bid the slam (which makes by the way).  Nevertheless, the responding hand will have cause to get very excited and bid 4♥ over 4♣ because whether opener's shortness is in hearts or diamonds, it really doesn't matter much as there's no wastage either way.  Over the actual 3♥ rebid, responder bid 3♠ leaving the door open but we ended up subsiding in 4♠.  However, if opener's hand had been ever so slightly different, ♠KJ953 ♥3 ♦KJ ♣AK542, we probably would have missed an easy and biddable slam.

So, what sort of suit quality does a 4-level rebid promise.  I'd say the usual "two of the top three" honors is about the minimum (similar to a positive response to a 2♣ bid).  Missing the ace or king, we'd probably want the J too, or at least the ten.  So AKxxx, AQJxx would all qualify but nothing less.  KQTxx would be OK when every other aspect of the hand is perfect.

Comments?