Does Your Upgrade Policy Need An Upgrade?

Because of their frequency, balanced hands are an important area of bidding. In simple natural systems, opener usually announces a balanced pattern either right away through a notrump bid or in the second round through a rebid in notrump. (The balanced pattern is not shown if he is raising respoder's major suit.) In the SAYC-based system I currently play, the various ranges of balanced hands are expressed thus (“s” means any suit): 1 s → 1 NT (12–14), 1 NT (15–17), 1 s → 2 NT (18–19), 2  → 2 NT (20–21), 2 * → 2 NT (22–23), and 2  → 2 * → 2 NT (24–25).

Of course, this schedule has an air of sweet simplicity about it, but the ranges should not be considered binding, despite the popular notion that notrump ranges are rigid. Three types of adjustments may be necessary.

1. 1 point for a reasonable 5-card suit is automatic. Do not hesitate to count a length point for, say, AQxxx, and do this consistently. Many will do it with Jxxxx too, but that is up to you. An ordinary 4-3-3-3 hand is in general noticeably worse than one of the other balanced shapes. In fact, you can deduct one point for holding a 4-3-3-3, which could be cancelled by a good feature in the hand.
2. The various effects of honour structures are important. This sort of valuation is more difficult than the others, but the familiar general rules are valid, e.g. a KQ or QJ doubleton is bad, whereas AJTx or KQJx is good; AKQ is bad, but AKQx or AKQJ is better. If two hands with abundant high cards afford poor play, it will usually be seen that the culprit is such wastage as KJ opposite Qx or AQ (!) or xxx.
3. A simple rehash of the HCP scale itself is a good adjustment. Everybody knows that aces and kings are more valuable than the 4-3-2-1 scale suggests. Significant improvement will result from simply changing the scale to 6-4-2-1 (to compare the number so obtained with the HCP, you need to divide this by 1.3).
   
   This, however, is unnecessary if you can start thinking in terms of AK controls (to be abbreviated as AKC from now on). Each ace counts as 2 controls and each king as 1. You can train yourself to think of a hand as better than average if it has more AKC than average and vice versa. But how do you know what the average AKC for your type of hand is? One simple rule is to multiply your HCP by 0.3 to estimate the average AKC in a hand with that many HCP. You can therefore upgrade or downgrade by comparison with that average.
   
   This simple rule is quite wrong when the hand has too many points. The following table lists average AKCs for all HCP counts in the range 10–25 in balanced hands (any 5-3-3-2 or 4-4-3-2 or 4-3-3-3 pattern) based on 500 000 random hands generated for each number in the range (except the last one). It also lists the factor by which three-tenths the HCP should be multiplied to obtain the true average in each case. Obviously there is little use for knowing this table by heart, but it is quite handy to know, e.g., that a 20-point balanced hand has on average not 6 but 7 AKC. Familiarity with the trend will, I think, allow opener to judge better which range his hand belongs to.

HCP	AAKC	Corr. Factor	HCP	AAKC	Corr. Factor
10	2.93	0.98	18	6.24	1.16
11	3.37	1.02	19	6.64	1.17
12	3.75	1.04	20	7.05	1.18
13	4.15	1.06	21	7.47	1.19
14	4.58	1.09	22	7.88	1.19
15	5.00	1.11	23	8.27	1.20
16	5.39	1.12	24	8.68	1.21
17	5.82	1.14	25	9.08	1.21

I will give you one example of how correct upgradation can be beneficial. In October, I held the following hand on BBO, sitting second-seat, nobody vulnerable, playing with Prajwal against SP (RHO) and Ravi:  A965  K4  K654  AK4. RHO passed and I had to choose the opening bid. According to the third criterion above, this hand is a prime candidate for upgradation. The AAKC for a balanced 18-count is only 6.24 and this hand has 7 AKC. So it should be a good idea to plan 1  → 2 NT rather than 1 NT, shouldn't it?

Partner turned out to have  83  A763  AQ732  QT. As you can see, 6  is practically a certainty and 7  has good chances.

I was naturally curious to see how others holding my cards had done, and this is what I found: it went 1 -2 -4 -5  at one table and P(?)-1 -1 -1 NT-4 NT at another, but everybody else had started with 1 NT and ended up in some number of notrumps.

If you make the popular choice, though you would like to believe that a good partner will sense slam with the 12-count 5-4-2-2, in reality it will mostly be missed, because you have “29 HCP at most and you need about 33 points for a small slam”. From partner's position, it's really hard to imagine that you will have such a cracker of a 17-count. If you're not convinced, notice that the combined hands may quite easily produce a grand slam, though I'm not sure if it's a good proposition to bid it (because diamonds cannot break worse than 3–1 and if they're 3–1 you can't have the long-trump hand sit over  K4 and be short in hearts).

There was another time, quite recently, the same players in the same positions, when I held  AQ5  K85  AK7  AK43. 23 HCP and 9 AKC—another upgrade-worthy hand. I did not have the Kokish or the Multi-inversion agreement with Prajwal at the time, so I opened 2  and only showed 22–23 with 2 NT after receiving the 2  waiting response, because 3 NT makes exploration quite difficult. I had every intention of accepting the mildest invitation.

None came, however, for partner bid 6 NT next. I did wonder if 7 NT was a possibility but passed with a sigh after realizing how foolish it would be for me to bid it. Luckily, partner held  K632  AQT  T93  QJ6, so that 12 tricks were guaranteed and maybe there were 40 % chances for the thirteenth trick (yes, a small chance of a squeeze in diamonds and spades apart from 3–3 spades). Anyway, the point is that if I had had the Kokish relay, I would surely have upgraded.

I don't remember ever deducting points for anything other than a 4-3-3-3 (don't we all like to overbid?), but surely there are examples. Here are ten hands for you to practise fitting into one of the ranges:

1.  Q543  AT3  AK  KQ94
2.  A865  K875  AK4  AK
3.  K6532  KJ  AQJ  KQ7
4.  A54  AK53  A986  A9
5.  AK5  AT653  KQ8  72
6.  AQ  AJ86  A72  AJ73
7.  AKT  AJ4  QT82  K98
8.  QT85  QJT  A93  AQT
9.  AK94  A3  KJT  KJ64
10.  K3  AQ865  KQ3  KT6

What's the Biggest Swing You've Been In?

DON'T look at the whole deal below. See only the North–South cards and observe the bidding, whether you agree with it or not.

Assume you are North and the lead is ♠ 8. You play the ace and throw your diamond. The contract is watertight if only you could avoid losing two hearts. Plan the play.

The “normal” play, i.e. absent any bidding or lead inferences, is pretty obvious: take ♥ A and follow with &hearts 5, planning to finesse the ten. This play, it turns out, would be successful no less than 87.6 % of the time. It loses only when the hearts are 5–0 or East holds ♥ Q J x x. You can do nothing about a 5–0 break, but you can remedy the latter, by coming to hand (preferably via a diamond ruff) and running the ♥ 10. The question is: Should you?

When this deal was played on BBO, declarer rejected the “normal” line in view of the double, and—you can see the East–West cards now—went down, to bag −14.73 IMPs, generating a swing of 27.93 IMPs. (Scoring was by cross IMPs.)

As dummy, my first reaction was that declarer had made a horrendous mistake. You, however, can see that declarer's line is not absurd. That notwithstanding, I am of the opinion that the “normal” line was the correct line here, because the double merely suggests a strong heart holding with East, and the alternative line fails against any other 4–1 break. Second, East's profile marked him as an expert (not that that necessarily means anything); could he have doubled (on a hunch) merely to deflect declarer from the normal line? Third, he could have read the auction as gone awry or have expected to get a spade ruff after leading his singleton spade to partner's (phantom) ace, despite South's 5 NT. Or he may belong to the school of thought that demands doubling slams because of the a priori improbability of a hand being a slam hand, especially “since partner has nine tricks in his hand”.

To elaborate a point about deflecting declarer from his normal line of play, one should always be suspicious of indications from the opponents that direct one towards an unnatural action which fails against a normal lie of the cards; it could be a falsecard or have been an intelligent psych. That said, can one humanly resist the temptation to expose a sucker double? All in all, I don't think it was a big blunder to play East for ♥ Q J x x.

If you think people don't double on the “a priori” theory, let me tell you that the same East, two boards later, doubled 7 NT on an auction that began on his left: 1♣ –1 ♥–2 ♦–4 NT–5 ♥–5 NT–6 ♦–7NT, holding ♠ Q 5 2 ♥ J 8 7 6 4 ♦ 10 7 2 ♣ 5 4—perhaps heady from his earlier victory, not recognizing that the contract had been very sound.

Let's consider the auction now. What are your feelings on North's 4 ♥ overcall? I think it's an unwise call, though I cannot claim to know a good solution in this situation. I'd be very uncomfortable hiding the clubs. Let's look at the options.

3NT: Are you nuts? 4 ♣: A distortion of course, but 5 ♣ may be the best spot, which can now be reached. 5 ♣: slightly better than 3NT, but not much else. 4 ♥: Fine except that it completely buries the club suit. Dbl: Represents the best chance of finding the correct spot, but partner may jump in diamonds (you'll correct 4 ♦, of course); also, your hand is aceless and has only 2 AK controls. Pass: Though partner rates to have some points, he will also likely have spades, in which case he might not balance and a cold game might be missed.

My choice would be to double. Please note that, holding hearts and diamonds, you will definitely double. If you're wondering why, you better read about the Equal Level Conversion principle. Even if you don't want to play it at lower levels, to my mind, it would be insane not to play it in this kind of situation.

Next, how do you in general show two-suiters over an enemy 3-level pre-empt? One idea would be to use the cue-bid as a top–bottom cue-bid, i.e. to show the lowest and the highest ranking of the unbid suits; the double should be used in accordance with the equal-level-conversion principle (i.e. the highest ranking unbid suit and diamonds or, in case 3 ♦ is the pre-empt, clubs) and flexibly whenever the alternative action takes the partnership too high. 4NT should show the two lowest unbid suits. Please do share your opinion on this.

[Update: In these last minutes before posting, clarity hits me. As declarer on this deal, if you rule out a 4–1 where West has heart length, odds are actually 3:2 against West having a singleton honour, assuming exactly four hearts with East and taking no inference about suit quality. Added to that, East is surely more likely to have doubled holding the Q–J than not. Since you can overcome any 3–2 break, I now think the percentage line is to try the finesse. Declarer did, however, make a minor tactical mistake, in my opinion. He tried to run the seven instead of the ten. The ten is more likely to induce a problem-solving cover.]