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