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:

Asleep at the switch

To my faithful readers: for some reason, Blogger/Blogspot has "fixed" something that wasn't broken and needless to say they haven't provided any explanation for it. The upshot is that I can no longer post hand diagrams (I can only link to BBO for rendering in a separate window). I've tried BridgeBlogging but apparently they unimpressed by my material (and were insufficiently polite to mention that fact to me). Anyone got any ideas whither I could transfer my bridge blog?

Meanwhile I still suffer the craziness of sitting at random tables when I have a few minutes to spare but no more. The errors that players make simply astound me. Was I ever that bad, I wonder? No, I don't think so. At least, I hope not!

Here's the latest misdemeanor: random hand at random table. Notice how disciplined I was not doubling 5D, although it certainly looked like it was going down. One ill-advised player did double 5D (see below). When dummy came down, I was surprised how good it was, but this kind of leap to game is not at all uncommon for beginners. Especially after a weak-two opener, they just don't know if, say, 2S would be forcing. Other declarers might be in 6D going down, so it was important to ensure that this contract didn't succeed.

Notice what happens at trick 7. West (declarer) takes a no-win "finesse" of the CQ (is there a name for this type of finesse? Chinese finesse?). I'm flabbergasted at how common such finesses are at these tables. My guess is that there's one every second or third board, especially when my partner is declaring.

But wait, apparently such a finesse can win! All you need is for the one with the K not to cover. Of course, this could never happen if that person was fourth-in-hand. Especially if he/she was looking at the J also. But nevertheless, my partner was asleep at the switch. After that, we have no defense. I get my two trump tricks and that's it. Perhaps I should have ruffed the club continuation which would require declarer to think about the play. But I can only ever come to two trump tricks if declarer plays correctly.

Take two. Things could have been worse. Really, you ask? Look what happened at this table. I have taken the liberty of assigning names from S. J. Simon's Why You Lose at Bridge. It's hard to count the total number of errors ("chucks" in Simon's terminology) committed here. I could post an ATB on BridgeWinners, I suppose but there's really just too much sin all round. First, do we agree with The Unlucky Expert's opening bid 1D? It's a tough call. 2D, the bid at my table, is flawed for various reasons, notably the void, the bad suit and too many stray queens. But is this hand good enough for 1D? Zar says it is (28 before any negative texture adjustment which meets the threshold of 26). KR puts it at 11.8 which is not quite an opening bid for most of us, I think.

In any case, 1D seems reasonable. Mrs. Guggenheim responds 2C which is just plain bizarre when she has more spades than clubs. Maybe she just wanted to announce the strength of her hand immediately, and a two-bid sounds so much stronger than a mere one-bid. Mr. Smug now says 3S, an appalling bid--but quite normal for Mr. Smug. Perhaps not the worst bid in the history of bridge, but certainly a doozy! The Unlucky Expert, who by rights has nothing to say, naturally bids 4D (to show his six-card suit)--Mrs. Guggenheim must have been just itching to double. Futile Willy, under the mistaken impression that his partner has something, decides to double this (cold) contract. Does he really think that he's getting this freely bid contract down more than one? Particularly, when he has such good support for his partner's "suit." Wouldn't you think that Mrs. Guggenheim would be ecstatic for her partner to be in 4DX? No, the scoring table was never her strong point and she decides to "take it out" into the diamond game.

The rest of the auction is inevitable and hardly worth mentioning. Futile Willy, his manhood so dreadfully impugned by Mrs. Guggenheim's 5D, must double again. And, when this comes around to the Unlucky Expert, he just knows that the contract is cold as Mrs. Guggenheim always has her bid if she bids a game. The fact that his own bidding has hitherto shown a decent hand with good diamonds is immaterial. He redoubles.

Now for the play. It would never occur to Futile Willy to lead low from Qxx of his partner's suit so he leads the SQ. No matter, it makes no difference this time. Declarer takes dummy's ace and crosses to his own HA. Based on the auction, he can be pretty confident that a finesse of the nine will succeed and indeed it does. Of course, he still should be down at this point but he knows the caliber of his opponents and is not worried. He decides to sneak a club through Mr. Smug who surely has the CK for his ridiculous spade bid. The latter, confident that his king cannot "go away" (does he imagine that declarer started with five clubs and never raised his partner?) plays low smoothly. At this point, The Unlucky Expert could claim but naturally he drags it out to the bitter end to extract the maximum degree of squirming from his two gentleman opponents.

This hand would have been a pretty good "Goulash" hand. 16 tables played it and the range of scores was +1600 (4SXXE-4) to -800 (the latter being our heroes' result). That's a spread of 29.8 IMPs! The par result is actually 400 E/W for 3NT which cannot be touched. This was reached by the perfectly appropriate auction (N/S silent): P--1S--2D--3D--3NT.

How to be a lucky player

This is the title of the new book by Matthew Thomson, Australian professional bridge player. As mentioned previously here, Matthew is the best player I've partnered – totally by lucky chance (for me, that is, not for him).

The book is basically an extreme version of the hand evaluation techniques I've always tried to follow (I learned a lot that day). Here it is in a nutshell:

• aces are good;
• more aces are better (any hand with two aces is a good hand);
• intermediates in your long suit are important;
• honors in partner's suit are golden;
• the 5431 shape is magic, especially when you have a 4-4 fit with partner;
• when all your cards are working, bid more, and you will likely get lucky [no, not that kind of lucky].

OK, that was a pretty trashy summary. You'll have to buy the book. On the other hand, I can't recommend the book. Not at all. If all my opponents were armed with the wisdom that he dispenses for lucky players, I'd never win anything.

Here's an example of me trying to bid the lucky way with the robots (dealer, not-vul vs. vul): ♠KQ53 ♥AK9432 ♦982 ♣–. I opened 1♥ and partner responded 1♠. The moment of truth. On the plus side, although I didn't have 5431 with four spades, I did have 6430 with four spades. Surely that was even better. On the minus side, my intermediates in hearts weren't terrific. Nothing daunted, I splintered into 4♣. Partner cue'd in diamonds as I did in hearts. Partner had heard enough to launch Blackwood. I answered 5NT showing two key cards with a void somewhere (guess!). Partner bid 6♠.

With confidence, I put down the dummy. Partner struggled mightily (this was a Classic robo tourney) but went down one. How could that be? Apparently, the robots have also read Matthew's book, especially the bit about any hand with two aces is a "good hand".  He had exactly that, the aces of spades and diamonds, but no kickers. But surely that's not enough to drive to slam over a game-forcing rebid? He also had the QJxx of clubs, but those were valueless opposite shortness – the robots know that, don't they?

The club ace or the diamond king would have been the twelfth trick. Even the diamond queen would have given us a 50% chance. My lack of intermediates in hearts were not the problem. BTW, I was not the only one to force to game at my second turn and end up in slam. The others gave their robots no chance to evaluate, however, as they did not splinter. One other human even jumped straight to slam after partner's response!

Our "Individual" Regional has just ended and I'm happy to report better results from trying to get lucky. But first, which (if any) of these two hands would you be comfortable opening as dealer (playing strong no-trumps):  ♠KJ73 ♥K876 ♦Q62 ♣K2 or  ♠9653 ♥A632 ♦K ♣AT64? What about in third seat?

I opened the first one 1♦ as dealer on the grounds that I had two four card majors, and if partner bid 2♣, I would have something decent for him and if he made an inverted raise of diamonds I would be able to rebid 2NT without undue embarrassment. Otherwise, I considered this hand very marginal. Partner, with a 20-count and five hearts, bid all the way up to 7♥ and made it for a 91% board. Would we get to seven if I'd passed? Partner said no.

I also opened the second hand, although I was in third seat. Would I open it in first or second seat? I think so, based on how much luck it generated this time. The next player passed and partner bid 1♥. RHO now came in with 1♠ and I raised to 2♥, promising four trumps. Partner, with ♠T ♥QJ75 ♦AQJ5 ♣9532 now jumped to 4♥. The lead was the spade ace (a trump would have been better) and, if I recall, another spade. Partner played it very nicely for eleven tricks and a 98% board.

Now that's what I call getting lucky.

High card points

Have you ever heard a bridge teacher start out this way: "An ace is worth four points, a king three, ... etc."?  It's as if those numbers are part of the laws of contract bridge.   BTW, I don't really know anyone who teaches bridge this way – hopefully there is no such person.

I'm surprised I haven't written more on this subject here before because it's one of my hobby horses.  There was a short reference to the inadequacies of the Milton Work scheme of point counting, later popularized by Charles Goren, in my article on Zar Points, but that's all.

But I was reminded of this yesterday by a very ordinary hand that came up at the bridge club: ♠ J64 ♥ AK72 ♦ A987 ♣ 85.  We are red against white and partner deals and opens 1♣ (playing standard 15-17 range for 1 notrump).  How do you evaluate your hand?  Will you force to game or invite?

Do I hear you saying "Well, I have twelve points so probably should be in game unless partner has a dead minimum?"  You don't have twelve points.  You have at least thirteen points.  Huh? 

Much has been written on the subject of hand evaluation.  And there are hand evaluators available on the web.  Try this one for example: Kaplan and Rubens hand evaluator.  That gives a value of 12.90.  Or you can try this calculator at the Bridgeclub Himbuv site which includes a Zar points calculator.  In Zar points, the hand evaluates to 27.  However, you can effectively halve this to give you the equivalent in "normal" terms to yield 13.5.  Yes, a whole point and a half above what you might have thought.

I'm not sure to what extent the K&R evaluator upgrades honors in the same suit, but it seems to me that the texture of this hand is about as good as you are likely to get in an otherwise balanced hand.  The lonely jack of spades certainly can't count more than half a point.  But the ace and king of hearts combine nicely.  In theory, Zar points does adjust for combinations of honors but the value given above is the raw value based on hcp, controls and distribution only.

If you don't want to perform difficult calculations at the table, however, then you might try to follow these simple rules:

• first, calculate your points according to the 4-3-2-1 scheme;
• add half a point for each additional ace beyond the first;
• subtract half a point for each pair of "quacks" (not necessarily in the same suit);
• subtract half a point for a 4-3-3-3 hand;
• add half a point for a decent five-card suit, etc.
• add half a point for good texture (honors in combination) and another if these combined honors are in long suits;
• subtract half a point for each short-suit honor on its own (A, Kx, Qxx);
• when resolving those half-points, round up if you have extra aces and are aiming for a suit contract or if you have extra quacks and are contemplating notrump – otherwise round down.

In reality, I rarely preform this evaluation consciously but I am always doing it subconsciously.  And don't worry about the specifics of half a point here or a full point.  These adjustments are quite "fuzzy".

Let's see how this would apply to the hand given above (♠ J64 ♥ AK72 ♦ A987 ♣ 85). It starts with 12.  Add half for the second ace.  Add another half for the AK combination.  Grand total 13. 

Of course, the whole evaluation game changes drastically as soon as partner bids and we have a notion of whether we do or do not have a fit.  In this case, when partner opens 1♣, our hand does not improve.  Yet it's too early to say that it goes down in value.  We bid 1♥ and partner rebids 1♠ (or perhaps 1NT).  I think 3NT is automatic now. 

So, what happened at the table?  My partner has great potential but is relatively new to duplicate bridge, although she's played quite a lot of rubber bridge and online bridge.  She saw her hand as a balanced 11-12 count and so responded 2NT.  I passed with ♠ KQ85 ♥ Q9 ♦ KQ6 ♣ JT43 (a 12 count according to my methods).  Par on the board is +140 for making 3S (not an easy contract to find or make) and the next best score is +120 from my side of the table.  3NT from my partner's side should be doubled and go for 500 on a club lead.  Needless to say (this wasn't the Blue Ribbon pairs), that never happened.

In practice, the defense at our table was less than optimal and my partner wrapped up 11 tricks for 210, thus exceeding par by 70 points – a triumph you might think.  In practice, five pairs (of eight total) bid and made 3NT for 600, one of these from partner's side of the table where surely the final contract should be doubled for a club lead.  Bottom line?  Our teammates were hopeless on this board, partner did great, and I got an opportunity to talk about hand evaluation. :)

A nice bit of hand evaluation

The setting: a club Swiss – the last of four six-board matches. There are three strong teams, six not particularly strong teams and ourselves. We are not doing particularly well.  We have no chance of winning and if we don't do something good in the last match, we won't scratch.  We've had one very lucky result but a couple of soft boards.  As it turns out, we are ahead by just one imp half-way through.  On the fourth board, all are vulnerable and I pick up ♠QJ982 ♥KT64 ♦75 ♣83 (spots approximate).  Len, my partner, is the dealer and opens 1♣.  I bid 1♠ and partner rebids 1NT, showing a balanced 15-17.  I rebid 2♥, showing no interest in game and offering partner a choice of majors.  Partner  surprises me by jumping to 4♥!  His hand is, literally, aces and spaces.  But he knows the power of aces (his 4333 hand is now worth about 18 points) and with two eight-card major suit fits, and a vulnerable game possibility, he decides to bid it all on his own.  I dare say that I would have raised to four if he'd bid three.

Interestingly, this is a hand where we might actually have a slight advantage over the strong no-trumpers.   I can show both majors with a fairly narrowly-defined sub-invitational range (6-8 hcp).  Strong no-trumpers probably get to use this sequence more frequently but, for them, the range is less narrowly-defined (6-11 hcp or thereabouts).  It really wouldn't make sense to have this auction playing a strong no-trump because the responding hand could easily be much too weak.

Anyway, the opening lead is a diamond and dummy is: ♠AT6 ♥A953 ♦A62 ♣A94.  As long as trumps are three-two (they are), I can make this hand if either the ♠K is onside (it isn't) or if the player with the last heart has four spades (he hasn't).  Fortunately, for me, the defense isn't perfect and I'm able to pitch dummy's two losing clubs before the ace is knocked out.  That's 10 tricks, 10 imps and a win by 6, which is just enough to put us into 3rd place.