Spider bridge

Of course, you've heard the story about Robert the Bruce and the spider. Twice the spider failed to connect its web, but succeeded on the third try. That spider and, thus inspired, Robert the Bruce, refused to give up and were successful in the end. Here are two consecutive deals which looked hopeless at first. But I refused to give up...

Rixi Markus was fond of saying "most contracts can be made, and most contracts can be defeated." That's what makes bridge so much fun (and occasionally frustrating). Both of the the contracts shown here could (and maybe should) have been set. But they weren't!

Sometimes, I take the descriptions of the robot's hand a little too optimistically. As David Bird would say in the title of his excellent book: "Somehow, we ended up in 6NT." 

Assuming RHO doesn't have DT7653, we have 11 tricks after knocking out the spade ace.  So, all I had to do was to win the opening lead of CQ, and play a spade up to the queen. If it loses, I've "rectified the count" for a squeeze, and it it wins... then I've still got my 11 tricks, but without having rectified the count.

At this point, the double dummy play is to duck a spade to RHO's now singleton ace. But, in any case, I should have cashed the CK before crossing back to dummy, in order to tighten my grip on the defenders. I suspect that, had I done so, they would have defended correctly and I would go down.

Instead, RHO felt squeezed in three suits (he wasn't squeezed in clubs and should have known that from the opening lead). Nevertheless, we pitched three hearts in quick succession. Up to this point, I had no trouble pitching losers from my hand: the three small black cards. On the last diamond, the "squeeze card," RHO played yet another heart and I discarded the C4. It was unlikely to be useful since LHO who was certainly guarding clubs would be playing after me.

At this point, there were only four hearts out and if they all fell under the AK, the contract would be mine. And so it proved.

If there is a moral to this story, it is this: even if you don't have a true squeeze, and even if you don't play it perfectly, your opponents may not quite know what's going on and give you the contract anyway.

The next hand was an example of that uncommon situation: the "impossible spade." Kudos to the robot for knowing this convention but shame on him for not understanding the follow-up bids. My 3D was "to play!" If I'd wanted to be in game, I could have made any other bid. Notwithstanding his minimum invitation and poor trump support, my CHO put me in 4H.

The D8 looked ominously like a singleton (although it wasn't). I had two spade losers, at least one club loser and, since I was missing KJ9743 of trumps, it looked like at least one, if not three trumps losers. Was there any hope at all? I opted to win the opening lead in the dummy and play a low trump to my queen. For better or worse, I decided to return a trump, using the ten to force at least one of the top honors out. LHO, somewhat obligingly, played the nine while RHO followed the principle of playing the card he was known to hold, the king.

At this point, RHO made a play (CQ) that wasn't exactly wrong, but certainly made my life a little easier, since I was the one with the jack. After caching the spade ace at trick five, he can easily get himself a trump promotion by continuing with a low spade to his parter's king. But this is where the play of the CQ led to their failure: believing that RHO had the CJ for the setting trick, he gave up on the trump promotion and played a club. After winning the trick and drawing the outstanding trumps, I could claim another impossible contract.

Papa the Greek outdoes himself--or Greed can be a very bad thing

A robot tournament hand that came up the other day on BBO reminded me of several similar situations from Victor Mollo's wonderful Bridge in the Menagerie series. In these stories, Papa the Greek plays the role of S. J. Simon's "Unlucky Expert" while his frequent partner, Karapet Djoulikyan, we are told, is the unluckiest player in both hemispheres. 

So, please forgive me if I put names to the robot characters in my story. Since no great masterstroke was required to make this hand (just normal careful play), I assigned myself the role of Colin the Corgi, the facetious young man from Oxbridge. My partner was that inveterate point-counter, Walter the Walrus. 

As Karapet would surely have said after the hand, "If you're going to double based on your two aces, at least have the decency to cash them!"

+1680 was worth 96.5%, tying with two others and losing to one brave soul who "sent it back."

The push double

A situation often arises in competitive bidding where one side pushes the other side into (usually) a game contract and then the pusher doubles.

Like many aspects of bridge logic, this one can be interpreted by looking at the scoring table. Let's take a look at an example:

South suspected that he could not defeat 3♠️ so decided to push the opponent into a game that he hoped he could defeat. If the push was successful, then plus 50 would be a much better matchpoint score than -140.  There would be absolutely no good reason to risk the double here. If the push was unsuccessful, then, without a double, -420 would probably have company. But -590 would clearly be a lot worse than the -170 that the opponents were probably going to make without the push.

So, it seems to me that the double cannot be to increase the penalty. Often going from 50 to 100 doesn't even change your matchpoints! It must be lead-directing. But to what?

Without the double, you were going to lead a club, right? If partner was happy with you leading a club, why would he double? 

So, what's the best lead here? Not a trump--that cannot be right. How about a diamond? It could be right but it doesn't look right with this holding. So, you lead your singleton heart, partner wins the ace and gives you a ruff. We will come to a spade, a heart, a heart ruff and we must score the ♦️K. +100.  Dummy is void in clubs so your trumps will be drawn before you can score a heart ruff (if you led a club).

Actually, I told a little white lie here. Partner didn't have the Ace. But declarer failed to go up with dummy's ace and partner won his King and you still got your ruff.

Sound unlikely? Well, yes. Declarer went up with dummy's ace, drew trumps and bye-bye heart ruff. Scoring -590 for 0%.  Pushing them without doubling would have scored 16%. Failing to push? Hard to know. Dummy had six spades, a club void, the ♥️A and the ♦️Q. Would they have raised to 4? Quite possibly not. So, the push strategy was misguided this time.

But the principle of the "push double" being lead-directing is eminently sound.

Boxing and the Horizon Principle

 A hand came up recently which I thought was a good example of when (and how) to use the ideas of boxing and the horizon principle. Let's define them.

Whenever you make a limited bid, you have "boxed" your hand. In other words, you have to a greater or lesser degree reduced the number of possible hands that you can hold. No subsequent bid can get you out of the box. So, if an ace was hiding behind one of the other cards when you made your earlier bid, no amount of persuasion can convince your partner that you have that ace. You will have to make a unilateral bid if you feel that it is necessary. [I covered this topic in one of my first blogs: The No-undo principle]

Similarly, if both partners have boxed their hands, then certain contracts are no longer "on the horizon."

For example, you open 1♠️ and partner responds 2♠️.  If you are playing a strong club system, you have "boxed" your own hand to somewhere between 11 and 16 points. Partner's hand has between 5 and 10 points. The most you can have between you is 26 points, but this would only occur when both partners are balanced. Slam is not on the horizon. Both partners know this, so any bid that you make now is a game try and cannot be a slam try.

If you are playing a standard bidding system where you are limited to, say, 20 points, it's conceivable though unlikely that you still might have slam. So, a bid of a new suit (a game try of some sort) might turn out to be an advance control-showing bid in search of slam if partner accepts what he sees as a game try (following the related principle of "game before slam"). 

When partner is unlimited, certain contracts, such as a small slam, maybe on your horizon but, from partner's point of view--when you have boxed your hand--those same contracts may not be on his horizon.

Enough discussion. Let's look at the hand (matchpoints):

♠️K74 ♥️AK984 ♦️AQ82 ♣️8

A nice hand for sure. You deal and open 1♥️ (nobody is vulnerable). LHO gets in there with 1♠️. Partner, predictably, makes a negative double. RHO passes and it's up to you.

Partner is unlimited (he should have at least 7-8 points) and you have boxed your hand somewhat by your failure to open 2♣️ and the fact that you opened in first seat. So, 11 to 20 points or thereabouts and at least five hearts. You could easily have a slam here, although presumably not in hearts. What about diamonds? 

You are about to re-box your hand. If you bid 2♦️, you will have effectively boxed your hand to something like 11 to 16 points, with at least nine cards in the red suits. You may still have visions of slam, but what about partner? He will need substantially more than a minimum to entertain slam now. From his point of view, 2♦️ will likely take slam off the horizon.

What about 3♦️? You will be refining your box to something like 16 to 20 points with the same red suit cards. If partner has a fit for diamonds (as the double suggests he might) and something like 12 or more points of his own, slam may still be on the horizon for both partners.

You decide to rebid 2♦️ and partner cue-bids 2♠️. Partner's hand now has a new box: at least 11 points and, probably (but not definitely), fewer than three hearts, as he would likely have bid 2♠️ immediately with three hearts and 10-plus points.

It looks like we have a diamond fit (with four or five spades, partner may have opted to trap-pass so partner likely has eight minor suit cards). Possible contracts are 2NT, 3♦️, 3NT, 5♦️, 6♦️, 6NT. Partner's sequence is consistent with all of those contracts. At matchpoints, we would tend to favor 2NT over 3♦️ and 3NT over 5♦️.

Is partner's bid forcing? Obviously. But forcing to what? There are several opinions on this, but let's look at the hand from partner's point of view. With our hand boxed into 11-16 points, partner will need something like 16 points for slam to be on the horizon. What about game vs. part-score? If partner only has 11-12 points, he will want to know if we are at the low end or the high end of our box.

The two bids then that could legitimately be passed by partner are 2NT and 3♦️. We decide to bid 2NT and partner passes. We make twelve tricks in notrump for a somewhat embarrassing +240.

Here is the actual hand:

Sacrificing for Dummies

It's ten years since I last wrote something here on the Law of Total Tricks. My goal this time is to come up with something really simple to remember when considering a save.

My thoughts on this were prompted by a recent hand:

My overcall of 1♦️opposite a passed hand was not a thing of beauty, I'll admit. But, I'm loath to make a sub-standard takeout double when our side is probably out-gunned. South's 3♣️ was described as "weak." What should West do here? I think a responsive double might work out best. If partner has four spades, we'll find it. If not, we'll likely be playing 3♦️ which can't be all bad. At the table(s), many pairs played 3♠️ either by East or West which mostly made given that N/S didn't find the double-dummy lead of ♦️K or ♦️T.

Over partner's 3♦️, North made a crazy leap to 5♣️. I could have been the hero by doubling (+300) but "knowing" that partner cannot bid higher (see Passed Hands may make only one Free Bid), I thought I'd allow him to pass or double, as appropriate. 5♦️ was completely unexpected and, as I'll show below, very unlikely to be the winning action. It's almost never right to take the last guess! And, it's OK to save with the ace of the enemy suit because it's likely to be of value at defense and offense. But kings, queens and jacks in their suit should be a red flag as they may be useful only on defense.

In fact, along double-dummy lines, N/S can make 3♣️, 2♥️, or 2NT. E/W can make 2♠️ or 3♦️.  21 total trumps. 18 total tricks. I would suggest that the shortfall in total tricks is due to the lack of useful shortness: each side has the (short) top honors in the other side's trump suit.

For the remainder of this article, we will consider entirely hypothetical situations. The following table shows the number of total tricks to make a sacrifice profitable at matchpoints, according to the levels of bidding involved:

Levels	Favorable	Equal Red	Equal White	Unfavorable
4/4	17	18	18	19
5/4	18	19	19	20
5/5	19	20	20	21
6/5	20	21	21	22
6♠️/6♥️	18	19	20	21
6/6m	19	20	20	21
7/6M	19	20	21	22
7♣️/6♦️	20	21	21	22
7/7	18	19	20	21

Note that it is assumed in all cases that the opposing contract is actually making. The requisite number of total tricks may be available but if they are distributed too evenly, the save will be a phantom.

Let's remind ourselves that the most common number of total tricks is 17. If the opponents bid 4♥️, and we have a good spade fit and are at favorable vulnerability, we can consider saving in 4♠️. How do we know if there will be 17 (or more) total tricks? The bidding will give clues as to the fits around the table. But, the simple number of tricks in each direction isn't really sufficient information (see "I Fought the Law"). A trick total of 17 will likely involve some shortness (singleton) somewhere at least. Do you have it? Did partner show shortness? Did one of the opponents? If so, you may try it. Otherwise, you might want to hold back until you think there are 18 total trumps.

There are several likely outcomes in 4♠️. Any time 4♥️ was not making, we will get a poor score, unless 4♠️ makes. Even if they didn't double, -100 instead of +100 (or 200 if we had doubled) will not usually score well.

But let's assume that 4♥️ was indeed making. If they didn't double 4♠️, we are guaranteed a good result. If they do double, as long as our estimate of 17 total tricks was accurate, we should be fine. Except when they could have made 650 and we are down four for -800. That's an all-too-common disaster. That's why, even in this situation, you really would like to have 18 total tricks.

And this is, according to the chart above, the most advantageous situation for taking a sacrifice (shown in green in the table).

There are three other situations where we might seriously consider a sacrifice (yellow rows in the table):

• at the 5-level over their 4-level game;
• 6♠️ over 6♥️;
• 7 over 7.

In each of these cases, we require 18 total tricks (not an uncommon situation) and of course favorable vulnerability. Each worsening of the vulnerability situation (see table) requires one additional total trick. Except in goulash-type hands, deals with 20 or more total tricks are rare. Also note that in the second and third of these situations, the all-white and unfavorable situations are particularly dangerous because they require 21 and 22 total tricks respectively (in each case, one more than the 5/4 sacrifices).

From the red rows in the table, we can also see that we should never (well, hardly ever) even contemplate a sacrifice at the 6-level over a game contract, or 7♣️ over 6♦️, as these require at least 20 total tricks. Don't even think about these when not at favorable.

The other situations (amber in the table -- 5 over 5, 6 over 6 minor, 7 over 6 major) should generally be avoided too. To consider any of these at equal vulnerability--especially the last one when all white--is, well, just madness.

Bust hand?

When playing a "standard," i.e. non-big-club, system, the 2♣ opening usually is an artificial bid showing a strong hand of 22+ hcp (if balanced) or an unbalanced hand that only needs one "card" to make game. Traditionally, responder bids 2♦ and then, after opener has described their hand (balanced or with a good suit), responder gets to show that they have a "bust" (the second negative) or not.

But there's a popular response that shows a bust immediately by bidding 2♥. There are lots of reasons not to like this convention but the one I'm going to concentrate on here is that responder must make their decision before knowing anything about opener's hand. A common understanding is that 2♦ shows an ace, a king or two queens. I've never been comfortable playing that agreement because "two queens" might be just what partner needs for slam, or tram tickets. Let's take this example: ♠x ♥xx ♦Qxxxx ♣Qxxxx. If partner has a balanced 22, either (or both) of these queens might be useful. But suppose partner's hand is ♠AKQTxx ♥KQxx ♦Ax ♣K. How useful do you think your two queens are now?

For a real life example of the perils of this method, I present a hand from a friendly team match:

If partner shows a balanced hand, this could be quite a useful hand. We'd like to play game or slam in hearts by partner. But, what if partner has an unbalanced hand with spades? Our hand might not be so useful. Here's what happened (the auction ends in 6♠ if you can't see all of it):

On any lead but a club or diamond, the contract is down 2. On a club lead, there's a chance only if the opponents mis-defend. On a diamond lead, the contract is always down 1.