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%.

Sunday, June 24, 2018

Breaking BADD

What's "BADD," I hear you ask. It stands for Bridge-related Attention Deficit Disorder. However hard I try, I just can't break it. I try to concentrate, I stay hydrated, I skip lunch. I get the occasional coffee. It all helps, but somehow I just can't stay 100% focussed.

This last week I played four days of bridge (and evening side games) at the Granite State Getaway tournament in Nashua, NH. During that time, I revoked, exposed three penalty cards forgot my notrump range, and various other lapses of concentration too numerous to mention.

But today's was such a classic, and involved such an unlikely parlay that I just have to tell you about it. It's like one of those terrible plays that a goalkeeper makes when he doesn't properly clear the ball. A perfect example of that occurred just this week in the World Cup matchup of Argentina vs. Croatia. Caballero, the Argentine goalie, failed to properly clear the ball and Rebić scored a brilliant goal to help Croatia to a 3-0 win.

So back to my play. Here was the board:


As you can see, our bidding was reasonably sophisticated. 2S was the "impossible spade," showing a good club fit and a game invitation. 3H suggested that spades may not be a problem, but was checking on the heart situation. 3NT is a good contract, making 9 tricks on a spade lead and 10 on any other lead. I got a heart lead and soon set about making overtricks.

The H3 was led, I played low from dummy and took the queen with the ace. I ducked a diamond to the ten and East's jack. A heart came back to West's king and after cashing the spade ace, he returned a heart to my jack. On this trick, I had to find a discard. At this point, I had nice rock-solid tricks and was interested in making the rest. In fact, I have the rest of the tricks just by cashing one spade, two diamonds and five clubs in addition to the two hearts already in the bag. At this point, they had three tricks so that's all there is.

But somehow, my counting was off and I thought I should at least try to generate an extra trick. In order that I wouldn't have to decide now whether to pitch the small diamond or the small spade, I pitched the totally unnecessary ace of clubs. Now, I set about cashing the top spade and then the clubs. I cashed the king and queen, then overtook the ten with the jack. At this point I realized (duh!) that there were no more losers so I faced the C8 and claimed the rest. "Not so fast," says West and produced the nine. Since I had no longer a stopper in spades, the defense took the next two tricks for down 2.

Pretty embarrassing! This "coup" should really have a name. Here's what was necessary to pull it off:

  1. miscount the tricks so that I was in effect looking for a tenth trick with a squeeze that was extremely unlikely to succeed and, so, "unblock" one of the high honors in my club suit;
  2. unblock the high spade (for the phantom squeeze, I could equally have chosen to keep the SK and unblock the DA);
  3. not notice that East showed out of clubs at the first trick and then overtake the ten with the jack (when I could just as easily have used the DK as the reentry to my hand);
  4. not notice even then that I had a total of seven tricks facing my way and didn't need a club for my contract: all I had to do was to cash the top two diamonds.
Four separate errors in one hand. Of course, errors 2 thru 4 all arose as a consequence of error #1. But, at any point, I could have quite easily recovered.

The his perhaps the most egregious, hilarious, and simply bizarre display of incompetence I've ever encountered, let alone, perpetrated!

So, how does an otherwise reasonably intelligent brain come up with this sort of thing? I don't know. I just call it BADD and do what I can to avoid it.

My teammates were remarkably understanding. This 10-IMP error (the contract at the other table was 5C down 1) cost us 3.45 victory points which normally would have meant a drop of several places in the standings. But, remarkably, it made no difference at all! We were sixth overall and second in X for a little over 11 masterpoints.

And, to add icing to the cake, England beat Panama 6-1 this morning in the World Cup!

Monday, May 28, 2018

Sometimes a bad split can be your friend

We all know, when we are declaring a contract, that bad splits are the enemy. It's nearly always harder to make our contract when suits don't split well. Nearly always!

Let's take the following contract as an example:


Clearly, this is going to be no problem if diamonds split 2-2. So, we draw two rounds of trumps and duck a diamond. Another heart comes back and you ruff. What do you pitch from dummy, by the way?

Now you play to the DA but unfortunately, RHO pitches a heart. Down one.

Not so fast! You aren't down yet. Cross back to your hand with the SK (RHO plays the Q) and, using vacant places and restricted choice you confidently run the nine. It wins and you are able to pitch your losing diamond on the fourth round of spades. You didn't pitch that little spade earlier, did you?

I wish I could tell you that I played like this. I could have. I should have! But I didn't. I just lamely conceded a diamond for down one and got on with the next board. As Eddie Kantar writes in his wonderful book Take All Your Chances, you should never just give up when there's even a glimmer of a hope. Notice that if spades had split a more normal 3-3 or 4-2, there would have been no hope at all. Well, it would make sense to run all your trumps and hope for a bad discard. But against good defenders there'd be no hope.

But the moral of the story is: sometimes a "bad" split is better than an even split. And, when there's a massive preempt at the table, this becomes even more likely.

The full layout:


If you're interested in the odds of the S9 winning the trick at T8 (as described above), then we know that East started with at least 8 hearts (based on the bidding and the opening lead), a diamond, two clubs and the spade Q. He has one vacant place for either the SJ or a ninth heart. West has shown 3H, 2C, 3D and so has five vacant places for the SJ. Taking restricted choice into account, the odds are 10 to 1 that running the nine will be successful.

Sunday, October 29, 2017

How many errors can GIB make on one hand?

The other day, I was playing one of those 25 cent all-day tournaments on BBO (IMPs). On the last hand (none vulnerable), my GIB partner picked up the following hand: J875 96 AK8763. RHO dealt and passed, as did GIB. LHO opened 1 and partner overcalled 2. RHO now raised the stakes with 2. You have some useful looking values. What do you call?

Double (technically a "responsive" double here, but I'm treating it as just another competitive double) would suggest sufficient points for it to be our hand, four hearts and four clubs (maybe five if the suit is not headed by good honors). The other four or five cards should be one or two diamonds (else why not raise?), and two--possibly three--spades. In other words, a relatively balanced hand with both the round suits, and about 10 or more points.

Why do I say at least two spades? Because experience has taught me that when you are short in the opponents trump suit, if partner leaves it in, those little trumps that you do not have will be in declarer's (or dummy's) hand. And it's slightly more more likely that partner will have four and leave it in with the hope that the opponents are on a seven- (or at most eight-) card fit.

And why should you have the balance of power? Because whether you choose to play in a possibly poor trump fit, or to defend a doubled contract of the opponents', you need to have some reasonable expectation of making or setting them, as the case may be. This is especially true at IMPs where an injudicious contract our way can get doubled and go for quite a number, or where doubling their part-score into game could be very expensive. You should aim to have at least 22 hcp between your two hands if you're forcing partner to bid at the three level (or defend). In this case, we can assume partner has 12 hcp (he did make a 2/1 overcall) so we should have 10.

Here, we have too few hcp (eight) and too few spades (singleton). Not a hand to double, therefore.

What about 3? Well, if you do bid here, you should have a good honor sequence so that partner's lead of your suit (if we end up defending) isn't an instant own goal. And, you should have at least a decent five-card suit with some tolerance for partner's suit in case he has to go back to his suit. 3 would be the perfect bid here! You have the very best possible lead-directional suit, headed by AK. And a doubleton diamond on the side.

Eschewing the obvious 3 bid (you don't want to miss a 4-4 heart fit!) you double and partner, trusting your judgment, passes. It's unfortunate because 5 our way is cold (partner has Qxx and they split 2-2). Partner leads a trump, not his diamonds. What do you deduce from that? Possibly a broken suit, so the hand has scattered honors. After drawing trumps, declarer starts to eliminate clubs. You win and lead your 9 covered by ten, jack, ace. A second club comes which you win and now there's one obvious card in your hand that will set the contract--your other diamond. But being the GIB, you don't worry about partner getting endplayed and you lead a heart. Game over.





Saturday, September 16, 2017

You can squeeze, too

One of the first things we learn about the playing of the cards in Bridge is how to take a finesse. If you lead towards your AQ combination and the person on the left has the K, you will win two tricks. Otherwise, one. Of course, there's a little more to finessing. There are also ruffing finesses, two-way finesses, intra-finesses, “obligatory” finesses, and so on.

The situation is similar with squeezes. What was that you said? Surely, squeezes are much harder than finesses? Well, they are a little bit harder but it really isn’t rocket science. The first bit of added complexity is that, whereas in the case of the finesse, where your LHO must follow suit if able, a squeeze operates on two, or sometimes three, suits at a time. In fact, when you lead the "squeeze card” to the squeeze trick, your victim will be out of that suit and have to discard. But that’s where the fun (for you) begins. If the squeeze is working, your victim will have to discard either a winner, a guard to a winner, or a card that he could have led to his partner’s winner. Either way, he loses out.

Note that I didn’t say “LHO” but victim. That’s because sometimes your victim is on your right, although that’s a bit harder to pull off because he will be discarding last, after everyone else. But that’s when you play your “ace in the hole,” so to speak. More on this later.

For now, let’s stick to squeezing LHO, because that’s the easiest situation—hence its name: “simple squeeze”. In the following situation, either the enemy trumps are all drawn or it’s a no-trump contract and you are in your hand. RHO doesn’t have any cards in the three critical suits (he can be playing with Happy Families cards for all you care). Here’s the layout at trick 11 when you play the 2, the squeeze card:

         A3
         2
 
         
54              
A               
—               
—               543
         2
         
         2
         2

According to the rules of bridge, LHO will have to play one of his cards before you play from dummy. His A is a winner, of course, and if he discards it, your lowly deuce will be promoted to master rank. What if instead he decides to pitch the 4? Now—and here’s the fun part—you pitch that little deuce of hearts because it’s no longer useful. When you cross to the A, with your deuce, your trey will now win the last trick. So, we just swindled LHO out of his useful cards simply by virtue of playing after he does. These cards which can be potentially promoted into tricks are called “threats” or, “menaces”—the word the Brits use to describe them. Note that LHO didn’t make a mistake—he had no legitimate choice because all his plays were going to give something away. That’s the essence of a squeeze! Sometimes you can gain a trick by a defender pitching the wrong card just because they don’t remember what’s out. That’s called a "pseudo-squeeze" and it's better than nothing (although don’t run a pseudo-squeeze against an expert—it’s a little bit insulting).

So, let’s look at this situation and see what really happened. There’s a reason that there are only three cards each in this layout. If there were any more, LHO would have a spare card to throw and you wouldn’t know which card to pitch from dummy. Basically, you have to be in the situation where you’ve lost all the tricks you are willing to lose but you don't want to claim yet because there’s a chance the squeeze will operate for an extra trick. You also had to have a (single-card) entry to dummy's two card holding. Your threats have to be positioned in the upper hand (the one that plays after your victim). And, finally, your victim has to be the one guarding the two suits where you have threats—he said to be busy in both suits.

From these conditions described in the previous paragraph, we get the famous BLUE law for squeezes: Busy-Lost-Upper-Entry. In this short article it’s impossible to go into all the details of why you need these four conditions. But deal out some cards yourself and try it. You’ll soon see what happens.

I will just add some observations on situations that are a little more complicated than what we just had (you knew it wasn’t really that simple, didn’t you?). You might have noticed the presence of the 2 in your hand in the situation above. It didn’t seem to play a part, certainly not a starring role. It’s a spare card. In this case, it could equally have been a small heart. And RHO’s cards didn’t all have to be clubs: they could have been any small cards as long as there weren’t two spades (the suit of your two-card threat). If the spare card happens to be in the upper hand, and you have a threat in your own hand, you have what’s called an “automatic” squeeze. The title doesn’t mean that it will play itself (although actually, if you’re paying attention, it will). What it means is that it operates against either defender. So, in the diagram above switch your 2  (the spare card) for dummy’s 2. Now, when you play the squeeze card from your hand, you know ahead of time that you’re going to pitch from dummy—the spare card. But you do have to look out in case someone (either player) discards the A because if that happens, and you've been paying close attention to the hearts, you now cash the 2 in your hand, and then cross to dummy’s A for your last trick. In other words, in this situation, you could swap all of LHO's cards for RHO's cards—in an automatic squeeze you don’t care who your victim is—lefty or righty.

What you can do with two suits, you can sometimes do with three. These situations are a bit more complicated, but not much. For one thing, their end positions (i.e. at the squeeze trick) will have more cards in each hand. Just as with the two-suit squeeze above, there are two major forms: the triple squeeze where only one player is busy in all three suits and the double squeeze where both players are busy (each of them in just two suits). The triple squeeze itself has at least two forms: in one, you can actually gain two tricks! Triple squeezes aren’t common but they are even more fun than a two-suit squeeze. Some double squeezes are easier to pull off than others. There are even ruffing squeezes. But, for these you need to do some reading. There are lots of good books on squeezes. The classic (and not too long) is Clyde E. Love's Bridge Squeezes Complete or, if you can find it, its predecessor: Squeeze Play in Bridge. Perhaps the ultimate is Hugh Kelsey's four volume set (now published in one very thick volume as Kelsey on Squeeze Play). But my favorite, with the inimical style of David Bird—and with lots and lots of examples—is Squeezes for Everyone.

But whether you want to read about squeezes in books or not, here is a pretty simple way to try for one of the simpler squeezes on your next hand. Don’t worry too much about preparing the ground (yes there are some techniques you can use but they are a bit more advanced). Just follow this checklist:

  1. Do you have exactly one loser? If you have more, try to lose the tricks you must lose early on, for example ducking from a suit where you have Axx opposite Kxxx. If you no losers, claim: don't torture your opponents.
  2. Are there any trumps out? If there are draw them. If you can't, or if you need the trumps yourself for a cross-ruff perhaps, then this is not a squeeze hand.
  3. Run all your winners—Yes, even your last trump—I know you'll feel naked without it, but it's essential.
  4. If your single threat (2 in the example above) has come good, cash it and claim. If not, use your entry to the other hand and hope that its companion will be good. If it isn't, then there was no squeeze but you've done your best. Note that in the example where we had Axx opposite Kxxx, and we ducked a trick early, if that suit splits 3-3, you will end up making the same number of tricks as everyone else. But if that suit was 4-2 and the one with the four had to guard another suit, Bingo! you just made an extra trick. Believe me that this will score a lot of matchpoints in your average club game.

I'm sure I'm going to regret publishing this article when you are making extra tricks against me! But you deserve to have more fun at bridge. Happy squeezing!

Monday, September 11, 2017

A leading question

The problem of which card to lead from a sequence or near-sequence of honors has been with us since the early days of whist. "Standard" leads are the top of any sequence, except that from AK, the K is led. At first glance, this may seem inconsistent but of course there was a good reason, historically speaking. In whist, there was always a trump suit so, typically, only one or two rounds of a suit would be cashing (it's unusual in a suit contract that you happen on the lead of a suit where all follow to three rounds). So, therefore, it was important--if you held the lead--that you don't give up a trick on the second round in case there was a useful third round. That's why the "come on" signal was developed to help you know whether to continue or to switch.

Originally, this was called a "peter" after "Blue Peter," the flag that told sailors in port that their ship was about to set sail. Failure to heed the Blue Peter would result in a charge of desertion. Not good. At bridge (or whist) the consequences might be expensive but you wouldn't (normally) lose your life over it. These days, in North America, we call it an echo or, less poetically, an attitude signal.

A minor diversion on a subject I think I've addressed here before: sequences. Bridge (the play) and whist are, to a large extent, a game of sequences and position. If you are the last to play to a trick, you have the luxury of being able to cover whatever is the highest card (assuming you have such a card). You don't have to worry too much about it. But if you are one of the early position players, especially leader and third-hand, you want to try and make the best use of your sequences if you have any. You don't normally lead unsupported honors, at least not unless you have good reason to think your partner might have a touching honor (thus giving our side a sequence).

This is why defense is so much harder than declarer play. Defenders cannot directly see where they might, between them, have a sequence. A suit might be distributed KJ53 opposite AQ42. If declarer has that suit, he knows for sure that there are four tricks to be had, however he plays it. But if the defenders have that suit, each partner may be reluctant to lead the suit for fear of giving away a trick. Just last week I gained two overtricks in a suit contract because my LHO was twice reluctant to lead from KJTx (his partner having AQxxx).

Returning to opening leads: if the K is led, partner knows, holding the A, that he always wants to encourage a continuation because the K promises the Q (or perhaps Kx). This guards against the so-called Bath coup (a whist term) where fourth hand has AJx of the suit and holds off the first trick. But what if opening leader's partner holds the J but not the A? If partner led K from KQ, then the card will form a sequence with leader's remaining card and, therefore, another lead in the suit is safe. But what if partner holds the AK and declarer has the Q. A continuation would now be unfortunate because the declarer has the Q for the third round. But as mentioned already, the rules were set up to keep us relatively safe for just two rounds of any suit. Recall that in whist, there is no declarer. The hand playing last to the opening lead may not have sufficient high cards ever to draw trumps and cash that queen.

The problem with this cozy little scheme is that, in bridge, we do have a declarer. That player, fourth to play on the opening lead, likely does have sufficient high cards and/or trumps to eventually make use of that queen on the third round of a suit.

So, various schemes over the years have tried to clarify opening lead sequences. One rather complex scheme was developed by Norwegian Helge Vinje and was later reported by the Bridge Journal in 1964. Such leads became known as "Journalist" leads. They tend to be more popular as leads against notrump contracts, although Vinje actually described two somewhat different schemes for trump and notrump contracts. There is much to be said for these lead conventions, but they are too complex for most casual partnerships.

A very common revision of "standard" leads is always to lead the highest of any sequence, even ace from AK. One problem of course is that when you want to lead an ace, you don't always have the king and partner may well go wrong (this is more typically true of higher-level contracts). It's common, especially in Europe, to agree that against suit contracts at the five-level or above, ace still asks for attitude (but now it's only the king that is good) and the king asks for count. There's also a perhaps minor problem that has to do with UI (unauthorized information) when you agree to play ace from AK. How long does it take you to select a lead from a hand with an AK combination in a side suit? About half a second. So, when you quickly lead an ace, your partner knows that you have the king to back it up. But when you think for thirty seconds and then lead an ace, partner knows that you don't have the king. He's not authorized to know this and so must go out of his way to avoid taking advantage of such information. Is this really a big problem in reality? I don't know. But experts like to avoid giving their partners any kind of problem so that brings us to one more opening lead convention: Rusinow Leads.

Originally banned by the ACBL, they were adopted by Blue Team greats Belladonna and Avarelli and sometimes therefore called "Roman Leads." The principle is simple: you lead the second of touching honors. Typically, it is agreed to play this only against suit contracts and not in partner's suit. When asked about honor leads, the defenders will say "shows the honor above or shortness." Usually, the ten is considered the lowest "honor" for this purpose so that the 9 could be from T9(x) or it could simply be the 9 from 9(x). There will always be a little ambiguity with any such convention but isn't it much better to have the ambiguity over the 9 than over the ace?

It's easy to forget that you're playing Rusinow. We have all done it. Even though I've played Rusinow (or Vinje) leads perhaps more than any other lead convention, I've still forgotten it occasionally, sometimes with disastrous consequences. But, if you are part of a regular partnership that wants to improve, Rusinow leads are a very sensible and simple lead convention.

Incidentally, whether or not you play Rusinow yourself, you should be aware that some people play it. If you are declarer and you need to know the location of a particular high card (that's to say most contracts), you may need to know what their lead conventions are. You can simply ask "leads and carding?" or you can pick up their convention card and look for yourself. You probably shouldn't ask "is that lead standard or Rusinow?" as that tends to give away the fact that you don't have one of the adjacent honors.