Thursday, August 8, 2019

Thinking ahead

In a recent Daylong IMP tournament on BBO, I picked up the following hand: AKT742 AQJ62 void KT. We were vulnerable vs. not vulnerable and my robot partner dealt and opened 1. RHO bid D. What's your bid going to be?

You've got both majors, so how about a negative double? Predictably, LHO now bids 4 and when it comes back to you, you can offer a choice of majors by bidding 4. Did you land on your feet? Hardly! You can surely make slam and possibly a grand slam. How are you getting there when partner passes 4? So, you're kind of obliged to bid 6 now.

In other words, just thinking one move ahead in the auction tells you right away that double is a bad idea. Actually, it could be even worse. Suppose partner's hand is xx xxx AQx AKxxx? He might even pass 3X and you might score only 500: not even compensation for game.

I've seen some abuses of negative doubles in my time, but I think this one takes the cake. The primary purpose of a negative double is a bit like Stayman: opposite a relatively balanced opener, let's see if we can find a 4-4 fit. Opener is reluctant to bid a three-card suit opposite a negative double. How many cards in the majors do you really expect partner to have here?

At my table, I bid 3 over 3 and, after my LHO predictably raised to 4, my partner was able to raise me to 4 with his Q96 holding. Roman keycard Blackwood did the rest: I found out that we had all six key cards (including the A in case I wanted to bid 7NT) and I didn't really have to think too long and hard to bid the grand. But which grand? If it had been MPs, I would have probably bid 7NT. But at IMPs, you should maximize the chances of making by using your nine (hopefully) trumps.

Here's the whole hand:


The contract was lay-down. I scored six spades, five hearts, two clubs, a diamond ruff, and the A. I'm kidding as that adds up to 15 so I never scored a diamond or the fifth heart.

There were five others in 7 (we won 12.5 IMPs on this hand), ten in 6, ten in a spade game, and one unfortunate fellow in 7 down six. To say that he (or she) was hoist by their own petard would be an understatement: South never bid either of his majors: he began with a negative double then, after his partner doubled 4, he chose 5 (which the robots interpret as showing club support).

Monday, July 8, 2019

How to lose 50 IMPs in a 12-board Individual

Yes, you read that correctly. Sometimes when I'm feeling particularly masochistic, I enter one of the ACBL individual tournaments. The denizens of this particular enclave are all regulars. I have notes on many of the players. Of course one's result is almost entirely the luck of the draw. It's seldom that I make an error so egregious that it significantly affects my score as the standard of play is so bad that you really have to go out of your way to lose a board all on your own. So, basically my score is always a combination of my so-called partners' efforts and those of my opponents.

Today's was exceptional. Board one was uneventful. The opponents bid and made a game. Lose one IMP.  The second board was where the (un) fun started. My CHO (partner) was in 3NT:


As you can see (by pressing Next), declarer won the opening lead in dummy and proceeded to cash the CA just in case it "went away." Then they figured that since they were there for the last time, it might be a good idea to take a finesse. There was only one suit with a finessing position and that was hearts. So, despite the fact that they could ill-afford to lose the lead before setting up the diamonds, they finessed the HT. This had approximately a 25% chance of success. Partner was unlucky. From there on, there simply wasn't time to get the diamonds going. The result? Down 2 instead of making 6. But it was IMPs, so the three overtricks we didn't make were just gravy (or lack thereof).

The next, however, surpassed even this.


The funny thing is that, after the hand, CHO messaged me to say "look at the other tables to see how you should bid this hand." Some had opened the West hand (not terrible), some Norths didn't open 2D. Of the Wests where the first round of bidding was the same, some bid only 2H (but their partners still got them to game). One player bid 4H (obviously, if I'd known anything about CHO I would have done the same). But most, like me, bid 3H. No other partnership got the magic +230, nor yet 1430. That was another 10 IMPs.

The next hand was interesting. Neither I nor my CHO did anything terrible:


RHO got a bit lucky that North didn't have four clubs to the J as he might have done. If he doesn't cash his clubs out, we can easily come to 10 tricks. You can blame me for not bidding 3NT instead of 1S. But, seriously, although this rated to be a not uncommon result, it was in fact unique. Lose another 8.

I managed to staunch the flow a bit over the next three boards, for only another 7 IMPs. The third one of these offered 12 tricks to the opponents, but nobody bid the slam.


Most Wests opened the bidding with 4D, some 3D and at least one opened 1D. In every one of these cases, East bid his hearts and 4H was made. There is an argument for 1D but I think it's better to get the hand off one's chest right away. 8 IMPs.

The next board was an unmitigated disaster and I was significantly responsible for it.


Believing my partner to have no defense against 5D (he passed in a forcing pass situation), I decided to try for 5H. I took a while to decide whether to run the HT and cost us an additional 4.5 IMPs (over the 7 we were destined for) when I changed my mind and went up with the ace. Of course, most of the players in these events have no concept of a forcing pass, so it was silly to take such an inference.

Here is the final exhibit:


Watching the play as dummy, I was praying for my partner to claim before anything bad happened. My prayers went unanswered and he decided to take a practice finesse at trick 8. Lose another 9.

At this point, I was an incredible 62.5 IMPs under water on only ten boards! I did manage to get some back on the last board, but surely this is a record. I'm hoping that someone will nominate me for the Guiness Book of Records.

Sunday, June 30, 2019

A very ordinary hand

It has been said that the way to win at bridge is to make sure you get the ordinary hands right. In other words, squeezes, endplays, deceptions, coups of various sorts, etc. don't come up sufficiently often to give an advantage to the better player. But ordinary hands come up all the time.

Here's a hand from yesterday's STAC game:

I was sitting West and essentially took no part in the proceedings. Our opponents, two experts who are married (to each other) and sometimes--but not usually--play together, had the auction all to themselves. I might have opened 1C in third seat and perhaps I should have but I suspect that would have pushed them into a making 4H).

At my club, every N/S pair was in a heart part-score, mostly 2H by North but sometimes, as at our table, 3H by North and, once, 3H by South. My partner led the C4, clubs being the only safe-looking lead, although either red deuce would also be safe on this layout. Declarer ruffed out the spades, took two diamond finesses and emerged with 10 tricks pointing his way. A flat board, right?

Wrong. This was by no means a flat board. Here were the scores: 1 @ 200 (11), 6 @ 170 (7.5), 3 @ 140 (3) and 2 @110 (.5). I'll dispense with the anomalous scores of 200 and 110 and concentrate on the 170s and 140s.

At first, I couldn't see why our score was below average (3.5). We didn't put a foot wrong. How could declarer not take 10 tricks. And then I saw it: some declarers must have taken the spade finesse.

This hand of course is a perfect illustration of the (general) superiority of a 4-4 trump fit over, say, a 5-3 or 5-2 trump fit. You can usually use long cards in the long suit to discard losers from the other hand while using small trumps to ruff with, possibly ruffing out losers to establish the long suit.

But the main point here is that considering a suit, the spades in this case, in isolation may yield a different plan than considering the suit as part of a whole hand. If you were in a spade (or notrump) contract here, you would consider your play in the spade suit and opt for the 43% likelihood of the bringing in the suit with a finesse against the queen, versus the 18% chance of dropping a doubleton or singleton queen. Not even a close decision.

But here, you are in a suit contract and you have the luxury of being able to ruff a spade (we'll assume that trumps are 3-2, as here, for the sake of simplicity). The probability of dropping the queen after a ruff is: 36% for a 3-3 split, plus the same 18% chance that the queen would have dropped anyway. That's a total probability of 54%. The failure zone (46%) is made up of 32.3% for Qxxx, 12% for Qxxxx, and 1.5% for Qxxxxx.

So, again, it's not really a close decision if you know your probabilities (54% vs. 43%). Incidentally, it's a very common error to regard the finesse as a 50/50 shot. But when we can only finesse twice, as here, there will be holdings on our right that we can't pick up: half of the Qxxxx and Qxxxxx layouts we noted above, that's to say 6.75% of cases.

The conclusion is that the situation where you are missing six cards is a tricky one--and also a common one. It's worth spending some time to learn the probabilities.

Monday, June 24, 2019

Discipline vs. guessing

One thing I've noticed about experts is that they try not to guess. That doesn't mean they never guess. But they do try never to take the last guess. Is this the same thing as "discipline?"

One type of undisciplined bid is when you deliberately fudge your hand to fit a bid that you'd like to make. For example, you pick up a balanced 14 count with no special features and, just because you feel like it, or want to be declarer, you decided to open 1NT showing 15-17. Sometimes, this will work well when partner has 9 hcp and a long minor and 3NT is cold on 23 hcp. But other times, partner will invite game and the limit of the hand will be 1NT. This kind of thing is a partnership issue, and your partner will eventually become unhappy, unless your declarer play is first rate.

But there's a different kind of discipline where you are likely making the last bid for your side. Partner is probably not going to bid again, so can't really be deceived. A lot will depend on the form of scoring and the state of play, so to speak. Matchpoints vs. IMPs? Competitive situation vs. non-competitive? High-level or low-level decision? High entropy or low entropy (entropy is complementary to information)?

Here's a high-level, IMP pairs, competitive, high-entropy situation, i.e. a lot is resting on this decision:

AKJ3 KJT983 T8 9. All vulnerable.

Partner opens 1S in second seat and RHO bids 5C. That's annoying! We have no idea whether partner has a minimum or maybe is just below a 2C opener.  Well, we do have a pretty good idea that RHO has most of the high cards in clubs and we have 12 high card points. Partner can't have much more than 18 then.

Let's do some arithmetic.  What might happen if we pass? Partner will probably be passing too and we might go anywhere from +200 to +400. What about double? Assuming that partner doesn't take it out then we could score 500 to 1100. If he takes it out to 5D, we can always go back to 5S.

Can we make 5S? Assuming that we have no trump losers, we've got three losers. Surely, with his opening bid, partner can cover one of those. So, it looks like 650 is likely available to us. There might be a few pairs defending 5C, possibly doubled. Bidding 5S is probably worth about 4 to 6 IMPs over defending.

What about slam? This is where, the lack of information is really troubling. We can no longer ask for keycards so it's going to be decision time immediately.

If partner has two aces (particularly if one of them is the diamond ace--not an unreasonable expectation), we can very likely make 1430 for 13 IMPs over and above the 650 and about 14 IMPs over and above defending. In other words, just by bidding 5S we are almost locking in 5 (approx) IMPs. Bidding 6S will gain an additional 9 IMPs if it makes.

But, what if it doesn't make? We will be -100. We lose not only the 5 for grabbing the declaration but an additional 7 or 8 for going down.

To put it mathematically, we risk 13 to gain 13. An even money bet. We'd take the same bet at matchpoints.

This is how many bridge players would evaluate this choice: mentally flip a coin, likely favoring the slam decision simply because it's just more fun that way.

But the true expert will say this: "I can't find out if 6S is on, so I'll assume that it isn't and just bid 5S." A popular expression that covers this situation is "when you're fixed, stay fixed."

Wednesday, June 12, 2019

The Vienna Coup

Looking at the MITDL Bridge Club's web site recently, I was a little embarrassed to note that there's a link there to my blog claiming that it's updated every week. Those were the days! This is my first post for nine months!

Today I had the pleasure of playing with Harrison Luba a.k.a. The Twerp. He's currently a freshman in High School and is an incredible player already. Like most Juniors, he believes that all doubles are for takeout unless it's blindingly obvious that they're for penalties. Those of you who follow (or attempt to follow) my blog know that I have a set of very specific (although quite simple) rules on this. So, we had a couple of bad scores today (-730 and -670) due to differences of opinion about doubles. Well, I will admit that perfect--I would claim double-dummy--defense by me would have turned the second one into +200 (and 8/11 matchpoints).

We mostly make up for these setbacks with many tops of our own. Here are a couple which are entirely due to Harrison's good play.

First board. The unopposed auction is short and sweet: 2C--2D--2NT--7NT.  The lead is a small club, if I recall.

83 Q432 AQT6 AQ2

AKQJ4 AK6 J7 K95

Maybe there was some slight overbidding going on but don't worry. The play's the thing. There are an easy twelve tricks on top. The diamond finesse is a 50% shot. But, and Harrison figured this out in a couple of milliseconds: the spades will furnish three discards from dummy. That makes a Vienna Coup possible (cash DA and then pitch all of dummy's small diamonds).

But you need the same player to have the DK and the heart length. Doesn't that bring the probability down to 25%? No, that's the beauty of an automatic squeeze like the Vienna Coup, i.e. where dummy has an idle card and so doesn't have to commit a threat card before RHO plays. We can victimize either opponent this way, which means that the probability of success is back up to 50%. Indeed, the diamond King was off-side. But that player also had five hearts. Scoring up 1520 for all the matchpoints.

One other pair got to a making 7S but most were in 6NT making 6.

Two boards later. Partner's arithmetic seems to have gone off the rails a little and we end up in 4NT when everyone else will be in 6NT.

AK32 A862 J3 AQ2

QJ4 KQ7 AK85 963

The helpful lead is a small diamond which allows dummy's jack to score a trick. Now, we're up to 11 tricks. This time, the chances of making 12 tricks are basically 36% for a 3-3 heart split plus a few more percentage points for the same player having four hearts and KJT of clubs (or a very small chance of one player having a singleton club honor). Because that would allow for another Vienna Coup, either opponent will do as victim. The probability of success here is going to be something like 36% (hearts split) plus 64% x 12.5% (three specific cards in same hand as the heart length). That gives a total of 44%, not too bad actually. 

And so it proved. Harrison rectified the count at trick 2 by ducking a club to RHO's ten. He could always take the club finesse later if he wanted to. As it turned out, RHO had five hearts and the club ten. Maybe she'd have the K and J too.

This is where the beauty of a squeeze comes in. A finesse risks losing the lead, even to a stiff honor. But squeezes (mostly) don't give up the lead--you just keep playing and either the last trick comes out right or it doesn't. 

Harrison worked out one other thing. Almost everyone will be in 6NT and if the finesse of the king is on (and they receive a helpful diamond lead) they'll have 12 tricks in the bag. We basically cannot outscore those declarers. But, if the CK is indeed offside (knowing that RHO has the heart length), then we will likely outscore any pair that's not in slam and certainly all of the pairs that did bid the slam.

It's always fun and educational when I play with Harrison. I enjoy it to the max while I can!

Monday, September 17, 2018

Non-linearity in Bridge

I apologize in advance for the length of this article. I could perhaps make it shorter, if only I had the time. But if you don't want to wade through a lot of preamble, then skip to the last few paragraphs.

We live in a world where the observed relationships of quantities, at least at the macroscopic level that we normally experience, are either linear, quasi-linear (or, more formally, monotonic), non-linear, or unrelated.  We take linearity (or at least quasi-linearity) for granted – for example, we press a little harder on the gas pedal and the car goes a little faster.  Of course we learn from experience that this is not a purely linear system – pushing the pedal twice as far down doesn't make the car go twice as fast.  But there are other times when non-linearity rules, for instance when a microphone is placed in front of the speakers at a wedding reception or similar gathering and we experience the dreaded squealing of the audio system.  Non-linearity is one of the key factors in chaos theory.

Because of the integral nature of the various scoring tables at bridge, scoring shares some similarities with quantum theory – there is a finite set of states that any particular deal can take on.

Indeed, there are several different scoring tables at bridge, depending on which phase and/or form of the game we are playing at the time.  None of them is purely linear.  And that is perhaps the essence of bridge – why we all find it such a fascinating game and part of why it takes so long to learn to play well.

Let's take as our first example a contract which makes eight tricks in spades, nine in notrump or clubs.  For simplicity, we will leave out the red-suit contracts.  We are not vulnerable and we'll assume that our opponents will double when we are more than one trick short of our contract.  Starting then with 1♣ and going up to the five level, here are the scores we will receive:

Potential scores for black-suit or NT contracts:
level NT
1110 110150
2110 110150
3110 -50400
4-50 -300-50
5-300 -500-300
This is so non-linear, it's almost chaotic.

The next way of looking at things, is to compare, for a given contract, the score for each trick we take. For example, the contract of 1NT, doubled but not vulnerable.  When we compare our score with tricks, we find that it is quasi-linear.  Score monotonically increases with tricks, but the increment varies (it's either 300, 280, 200 or 100).  Here are the scores for taking 0-13 tricks:

-1700, -1400, -1100, -800, -500, -300, -100, 180, 280, 380, 480, 580, 680, 780. In practical terms, though, it isn't enough to know how the scoring table behaves. Duplicate Bridge isn't normally played at total points. In some ways the most complex situation is matchpoints because there are typically many other tables in play and the complexity of estimating your matchpoints based on your actual score is way beyond the scope of this blog.  The best you can do at matchpoints is to guess whether the call you are contemplating will have a better than even chance of improving the number of matchpoints you will receive. The scoring at teams however is more tractable and, as usual, quasi-linear.

The reason that it's easier to predict outcomes at teams is that there is only one other table and the IMP table is fixed and monotonic (order-preserving).  Normally, at any stage of the game you will be choosing between one of two options, each of which has a predictable outcome.  Let's take as an example a decision as to whether or not to bid a vulnerable game.  If you bid it and it makes (for now, we assume perfect play at your table), you will score 0 or 10 imps, assuming that the opponents at the other table are making a similar choice.  If you stop in a making part-score (no game available), you will score 0 or 6 according to the decision at the other table.  To simplify the decision, we temporarily ignore the other table and think as follows: bidding game risks losing 6 to gain 10.  These are reasonable odds and account for the fact that players like to bid vulnerable games at teams.  Or another way to look at it is this: if the game contract depends only on one finesse, then our expectation of gain for bidding the game is 5 – 3 = 2 imps.  Of course, this calculation ignores the fact that trumps may be stacked against you and that if you bid the game, an opponent might double.  Thus, if you make such (normal) games three times out of every eight (37.5%), you will break even.

Now, let's assume that we've bid the vulnerable game and there are two lines of play from which to choose.  One is successful, the other is not.  Assuming for now that the other declarer is in the same contract (our outcomes will be different if that is not the case), we will score either 13, 0 or -13 IMPs, depending on the other declarer's actions.  Again, we will ignore the other table and consider that our play will either win or lose 13 imps.  As an extreme example, let's say that we have a sure line to make and an alternative line that will make an overtrick.  Again, we assume that our counterpart is facing the same decision.  Taking the alternative line risks 13 to gain 1.  Such a gamble would be crazy -- unless of course you're playing the last board of a KO and you strongly suspect that the current net score is zero or plus/minus one. Knockouts are the most non-linear scoring system of all (they involve a mathematical function called the Heaviside Step Function).

There's one more important non-linearity to consider with IMPs, which arises when the two tables are not in the same contract. If there's nothing to the play, the IMPs changing hands will be simply based on the differences in the contract. But suppose that there is a difference in the play: now, the total IMPs available on the board is greater than in either of the other two cases (contract the same, play the same). You're in game, you have three inevitable losers outside of trumps and you take a finesse for the trump queen (missing five). It loses and you are -100. At the other table, declarer is in a part score: he can afford to lose to the trump queen but cannot risk a ruff so plays trumps from the top picking up the doubleton queen. At that table, you are -170. You lose 7. But if you too had dropped the queen, you'd have won 10 instead. So there were 17 IMPs available on that board and you lost them all!

So much for the non-linearity of IMPs in general and knockout matches in particular.  How about a Swiss (or Round-Robin) where we are playing for victory points?  The VP scale is a mix of quasi-linearity (in the middle) and non-linearity (at the extremes).  This is where the ability to estimate is so important.  You must forget all about those odds of 37.5% for a vulnerable game as you get closer to the end of a match.  Let's say that things have been going well for you in this set.  You bid an iffy vulnerable game earlier and made it.  The opponents had a misunderstanding with a slam auction and went down non-vulnerable.  You've made a couple of good part-score decisions and the other boards were flat.  You estimate five for the game you bid (there's a 50% chance the opponents got there too) and 11 for the slam (your teammates never make that sort of error).  The part-score decisions have you up by approximately another four IMPs.  So, you estimate that you are up by 20.  If the last board is flat, you will win the match by 18-2 victory points (assuming the 20 point scale*).  Bidding a game will gain 10 imps (but only 2 VPs) if you're right, but could lose 6 imps (2 VPs) if you're wrong.  It's therefore a toss-up.  If the game is likely to go down on a wrong finesse or a bad break, then you shouldn't bid it.  What you've been taught as odds of 5:3 are now no better than evens.  That's because the VP scale isn't linear.

20 point VP Scale:
IMPsVPs
010-10
1-211-9
3-412-8
5-713-7
8-1014-6
11-1315-5
14-1616-4
17-1917-3
20-2318-2
24-2719-1
28-20-0

In general, if you're already well ahead (or behind) in a Swiss match, the decisions that you make will be less significant than otherwise because the slope of the VP scale is lower than it is at the start of the game or if there have been no big swings.  However, when you're up, the upside of a good decision is always less than "normal". Conversely, when you're down, the downside of a bad decision is less than normal. Let's look at another example: to bid or not to bid a non-vulnerable slam.  At the start of the match, you need at least a 50% chance of making the slam for bidding it to be right: you risk 11 to gain 11 (non-vulnerable).  But suppose that the slam arises later in the set and you estimate that you are down by 10 imps because you missed bidding an easy vulnerable game.  What odds do you need for the slam now?  If you make the right decision and win 11 imps that is worth 5 VPs.  If you make the wrong decision and lose 11 imps that's 4 VPs away. In other words, you should be bidding any slam that has at least a 44% chance of making.

Odds summary: expressed as reward:risk
EstimatePsychVul Game Non-vul Slam
-303:02:03:0
-204:24:24:2
-105:44:25:4
05:64:35:5
104:74:24:5
202:52:22:4
300:40:10:3

In the table above, we assume that the pysch (or other swingy action) stands to gain 12 IMPs if it succeeds but will lose 15 IMPs if it crashes and burns.

As an aside, in a recent flight A Swiss, we were perhaps slightly ahead after five boards and bid 6, going down. On the last board, I decided it was therefore right to push to an iffy 6♣. It went down too. Chances of winning that match were close to nil. But, we had done better on the first five than I thought, the other team also bid the first slam going down, and we still came out comfortably ahead!

Now, here (finally) is the important point.  Notice that it's not so much a question of bidding the slam to make 5 versus losing 4 when you're down by 10.  It's more that you should be contrary (also known as "swingy") when you are losing and, conversely, follow the herd when winning.  If you're behind and you think that your opponents will be in this slam, then you might consider not bidding it.  If there are twelve easy tricks, you will be another 4 VPs in the red. But suppose that it goes down at the other table while you make a conservative 450, then you will gain 5 VPs.  If you think they won't be in it, then bid it.  Now, of course, we need to have an idea of who our opponents are.

But, if we estimate that we are ahead in a Swiss (or KO), then we should play down the middle. We should bid all normal games, normal slams, etc. The other team will (or should be) swinging a bit. Let them. I was once in a KO (many years ago now) where my team was up by 24 at the half. I took my foot of the gas pedal a little and didn't bid a game that was a reasonable vulnerable game, thinking that I should be conservative. We ended up losing the match when the opponents won 10 on that board and some others. Being conservative doesn't mean not bidding games. It means bidding all games that you expect to have a decent play, but not stretching to thin games.

I will conclude with a horror-story which happened just yesterday (we are now in 2018). A certain team had had some considerable successes in a Swiss and was in fact 16 IMPs ahead at that point. Building on that success, with the same feeling gamblers get: "I can do no wrong," our hero psyched a preempt. You guessed it: lose 16 for a tie. That cost 6 VPs! Was there much of an upside? Hard to say. The best it could likely achieve would be that opponents talked out of game, or stampeded into bidding too much. Perhaps a 10 Imp gain? Or they might brush it off and the result would be a push. Even in the best case, the pysch would gain only 3 VPs. So, when you're ahead, stay ahead by bidding and playing according to the book!

* I wrote this article back in 2014 before the new Victory Point Scale which uses fractions instead of integers.

Friday, August 24, 2018

Anna Karenina

Ordinary bridge hands are all alike. Every extraordinary bridge hand is extraordinary in its own way. The Anna Karenina principle--with apologies to Tolstoy.

That's not to say that you can relax on the ordinary hands. Far from it, especially at matchpoints. A defensive slip in a routine 4H contract, for example can easily give you an absolute bottom. Yet, the extraordinary hands are, typically, where most of the IMPs and matchpoints flow. Sometimes, we have to be on our guard right from the moment we pick the hand up. But how do we recognize such hands?

Here are the clues you might notice when you pick up the hand:
  • extreme distribution ("Goulash" hands, for instance);
  • non-purity (short suits with honors, long suits without);
And here are further red flags that pop up as the auction progresses:
  • high-level preempts (or interference);
  • partner bids your short (singleton or void) suit;
  • somebody puts down the red card or, especially, the blue card;
  • dummy has a long suit.
Of course, there are many other danger signs that arise as we declare or defend a hand, but by that time, everyone at the table already knows a lot about the hand. This article is about early indications of trouble.

When we recognize such a hand, we need to sit up straight, and gather our concentration. The two early indicators are suggestions that the hand we are about to play will not conform to the "law of total tricks". There are likely to be more total tricks (in the first type) and fewer (in the second type). We must therefore be on our guard.

Here's a hand that came up recently in a BBO Speedball, that's to say matchpoints, where you are the dealer and at favorable vulnerability:  A2 ♥ K A765 J87652.

The "non-purity" bell should be ringing loudly in your head! Are you going to open this hand? Hard to pass a hand with two aces along with two other face cards. But what are you going to do when partner responds one of a major? Rebid that moth-eaten club suit? You certainly can't reverse into diamonds. What about opening one diamond? Now, you will not be embarrassed by having to make a 2C rebid. But it does distort the hand. So, you recognize immediately that this hand looks like trouble. Nevertheless, you forge ahead into the unknown with one club.

It gets worse. LHO overcalls 1NT and partner doubles. This is always a tense situation when partner doubles 1NT after we have opened a minimum hand. Do we actually have sufficient firepower to defeat the contract? What if RHO passes? Would we dare rebid 2C when LHO probably has much better clubs?

We breathe a sigh of relief when RHO bids 2H. This is not alerted but after our pass, LHO bids 2S and partner now bids 3H and RHO passes so, pretty clearly, RHO has a weak hand with spades.

Are your alarm bells still ringing? They should be. Could anything worse have happened? Yes, partner might have doubled again. So, what does partner have? He has good hearts and they were probably his main reason for doubling last round. What about strength? Well, 3H isn't forcing and isn't game so he probably doesn't have opening count. He has a good chance to make this contract. Let's leave well alone and pass.

But, is that really the right call? We know (and presumably partner doesn't) that our clubs are absolute trash. And we can be pretty sure partner won't want to lead hearts if LHO decides to bid 3S. What will partner lead? A trump? Yes, maybe. A diamond? That would be nice but will he find that lead? How about bidding 4H?

Insane, you say? I don't think so. Clearly, there must be some play for 4H. We have the King of partner's good suit. We've got two aces on the side. And, if partner is short in clubs, there will be no wastage there. 4H could actually be a good advance save against 3S, especially if it's not doubled. This is matchpoints, after all and -50 or -100 beats -140.

So, you pass and, as expected, LHO bids 3S. Partner doubles and your worst nightmare has been realized. If you bid 4H now, you are definitely getting doubled and this could be -300 on a bad day (it is a bad day!). But, if you pass, partner will probably lead a club since your bidding--1C followed by three passes--strongly suggests a weak hand with long clubs. Away will go dummy's losing hearts and -730 will be the result.

Are we happy with our original opening bid now? Are we happy that we passed over 3H? No, we are not but there are no undos in bridge.

The result? -930 (0%). Even worse than we feared. Partner (I was that partner) could have saved the day by cashing the HA. Or leading spades or diamonds and overtaking our HK return. But he woodenly led a club and that was that.

-300 would have been worth 6%, -100 was worth 26%. +500 (somehow, steering partner away from a club lead) would have been worth 100%.