Controlling Uncertainty

Beginners are taught to bid according to a set of rules that constitute a system in which the various bids fit together like pieces in a jigsaw puzzle. One thinks of bids as the means of telling partner about the hand one holds, so that together, following the rules, one’s partnership will usually arrive at a good final contract. Failing to do so implies one has made a mistake. However, one soon discovers that it is not just what one knows, but also what the opponents don’t know that affects the outcome. Often there is value in disclosing less. The uncertainty that is inherent in a system may work in one’s favor. To remind ourselves let’s look at a simple example of how it works.

		Bob1	Bob2
♠ KJ84	♠ 732	1♣	1♦
♥ AKJ2	♥ Q96	2NT	3NT
♦ AQ	♦ KJ843	Pass
♣ 962	♣ J8	Lead ♠6

Playing standard 5-card major methods, Bob1 opens 1♣ and Bob2 responds in his 5-card suit, and accepts the invitation to bid 3NT. The ♠6 is led to the ♠A, declarer dropping the ♠8, and a spade returned. Ten tricks are taken where a club switch from ♣AT43 would have led to down 1. Some critics would claim the good result is undeserved as the defender should have found the club switch, however, built-in uncertainty played a part and the defender, unable to penetrate the smoke screen set up by the ‘natural’ 1♣ opening bid, followed his partner’s chosen path.

In every session we come across part-score deals where uncertainty can prove advantageous. In such cases it is not the aim to provide a complete and accurate description from which the opposition may benefit. It may important to compete in hearts, say, without the necessity of disclosing a supporting minor, potentially revealing to the opponents the condition of a double fit in both directions. However, when one holds the preponderance of power, more information is better, because one wishes to bid to the full capacity of the hands, and possibly to catch the opponents if they overstep their bounds.

Accuracy comes to the fore when one contemplates bidding a slam. Players devoted to bidding according to probable outcome will often miss slams that a more informative style may reach. In some cases the bidding system they employ fosters that approach when the emphasis is entirely upon the total number of high card points held rather than on the specific location of suit controls. Let’s give Bob2 a much better hand.

		Bob 1	Bob 2
♠ KJ84	♠ Q32	1♣	1♦
♥ AKJ2	♥ Q96	2NT	3NT
♦ AQ	♦ KJ843	Pass
♣ 962	♣ A8	Lead ♠6

After counting his points twice, Bob2 decides not to proceed to slam on just 3 controls and less than 33 HCP. Declarer makes 12 tricks on a heart lead.  More accurate bidding might lead to a 4 NT contract, held to 10 tricks on a marked club lead after a revealing auction that pinpointed the weakness in clubs. Bob2 bid so as to avoid such a result.

Playing standard methods it is hard to judge early in the auction whether or not the hands in combination have slam potential. Barry Crane is often quoted as telling a partner, ‘don’t play me for the perfect fit’. He may have thought that partner should play him for normal expectations instead. Most often one is not in the slam zone. In the above case, responder makes a judgement based on HCP content without exact knowledge of where those HCP are located. In fact, slam makes because of the unusual circumstance of the side holding two 7-card suits each containing AKQJ, which is very much against the odds. Unexpectedly, it is the club suit that represents the weakest holding.

Some players like this style. If everyone bids in the same way, shrewd guesses come to the fore. There is a rush in making 3NT holding ªT in the dummy and ♠Q6 in hand, as I did last week. Others prefer to attempt to bid as accurately as possible using many conventions that allow for the disclosure of otherwise hidden assets. They may stop in 2NT on the first hand (below average) and reach slam on the second (above average), in the end achieving little for their mighty efforts apart from satisfaction of a task well done. The ideal situation is to bid 3NT on the first hand and make it as a result of non-disclosure and to bid and make a cold slam on the second as a result of full disclosure.

Economical Bidding after the Start 1♣ – 1♦

In his book ‘Building a Bidding System’ Roy Hughes makes interesting general comments on the structure of bidding systems as means of exchanging information. In particular, he notes that the lower the bidding is kept, the more bidding sequences remain from which to describe the partnership holdings. To preserve bidding space maximally, each higher bid should be half as frequent as the bid below it. Thus, a 1♣ opening bid should be twice as frequent as a 1♦ opening bid, which should be twice as frequent as a 1♥ bid, and so on up the line. It is important to note that according to Shannon’s Law of Information, the amount of information in a bid is minus the logarithm of the probability of the bid being chosen, thus the most frequently chosen bid is automatically the least informative.

Hughes notes the consequence of this type of allocation is, ‘the higher the call, the more specific and less frequent it should be.’ Because flat shapes are the most probable, the corollary to this conclusion is that in general, ‘the lower the call, the flatter the hand.’

If a jump response of 2♦ to 1♣ is less frequent than a simple response of 1♦, of necessity the more informative it must contain. With regard to saving space, jumps as wasteful, but compensation is derived if the information provided is of a particularly useful kind. If the 2♦ response shows weak hand with a 6-card diamond suit with 2 top honours, that is indeed informative, but is it better to use the jump in a constructive sense to show a good hand with such a diamond suit? If as a consequence of their definitions the strong response and the weak response are equally likely, the amounts of information in the bids are the same.

The Consequence a Forcing Rebid

Let’s consider the following sequence:

1♣ (least well-defined opening bid)     —   1♦ (least well-defined response)

1 ♥ (least well defined forcing rebid)   — 1♠ (now what ?)

Three bids have been exchanged, and the least possible amount of information has been disclosed. It is possible to design a system along these lines, the Polish Club, for example, having a structure where the 1♥ rebid may include a hand with 3 or 4 hearts that qualifies for a weak NT. Responder will not pass with 5+HCP. The bidding seems to be going nowhere fast, but significant information can be deduced from the bids that were not chosen, which makes it hard for the opponents to judge what is going on here.

In a constructive auction sooner or later someone has to make a bid that gives precise information unless they simply decide the final contract on the basis of probable outcome. Does the fourth bid represent the time when responder must come clean? Not necessarily. In a 2/1 structure 1♠ is usually defined as being 4th suit forcing, a vague bid that requires the opener to make a descriptive bid with game in mind. Responses of 1NT, 2♣, 2♦, 2 ♥ , 2NT are nonforcing, limited, and descriptive, and opener is left to continue as he sees fit.

The second hand discussed above must be bid more descriptively if slam is to be reached. Let’s consider how it might be done.

1♣ (least well-defined opening bid)    —   1♦ (least well-defined response)

1♥ (least well defined forcing rebid)    — 1♠ (tell me more, game forcing)

2♠ (4 spades, forcing)    — 3♦ (forcing)

3♥ (strength showing)    — 4♣  (control slam try)

4♦ (control)    — 4NT  (sign off)

6♦ — Pass

Thanks to the use of an artificial 1♠ bid, the players have ample bidding space available for a sequence of forcing bids that allowed them an exchange precise information that could be interpreted in the context of a slam exploration. Both players were able to avoid the removal of bidding space through the necessity to jump to 2NT to show strength. A certain momentum was established that prompted the opener to go to slam on the basis that his diamonds represent excellent support within the established context. In a cooperative mode both players can contribute to the evaluation of slam potential taking into account secondary honors that can’t be shown explicitly with the methods available. This is an especially desirable feature when both hands are balanced.

Next we consider the information in opener’s rebid in the sequence:  1♣ – 1♦; 1NT. In standard American practice, 1NT shows a balanced 12-14 HCP that may include a 4-card major. With Polish Club 1NT has the range of 18-20 HCP, which is ¼ as likely to have been dealt. The Polish 1NT rebid is much more descriptive. It is bad practice to use up space to describe a common occurrence. Here is a nightmare scenario for standard.

		Bob 1	Bob 2
♠ J753	♠ QT42	1♣	1♦
♥ KJ8	♥ AQ	1NT	2♠
♦ A3	♦ QT872	3♠	???
♣ QJT4	♣ K8

The spade fit wasn’t established until the 3-level, and responder has to make a decision on whether to bid 3NT or 4♠ without much evidence one way or the other. To avoid this nightmare, a responder may choose to bid an anti-systemic 1♠, postponing problems until the next round. Upon getting a raise to 2♠ he might bid 2NT, which he doesn’t expect to be passed, suggesting 3NT as an alternative contract, while hiding his diamond suit. That would work, when opener has the type of hand that would make 3NT attractive.

Flexibility is a desirable feature when it allows for the exercise of judgement within the context of a meaningful exchange of information. Bids that show shortage should not be defined in terms of HCP, but in terms of losers and controls. The perfect fit, although rare, does sometimes exist. Wouldn’t one like to bid the following slam on just 25 HCP?

		Bob 1	Bob 2
♠ 3	♠ QT42	1♣	1♦
♥T974	♥ AQ	2♠*	3♠(controls?)
♠ AK3	♦ QT872	4♥ (5)	6♦
♣ AQJT4	♣ K8	Pass

This is not the most efficient auction possible, and the splinter bid is not ideal, but it gets the job done. The opener holds an exceptional club suit in a 5-loser hand, and responder’s controls are well placed. The minor suit fits are unusual with opener’s 3-card diamond support containing the ♦AK and responder’s doubleton club being ♣Kx. It is possible to define 2♠ as a splinter bid only if a rebid of 1♠ by opener is forcing, a splinter being defined as a jump one level above a forcing bid in the same strain.

A Different Criterion in Competition

If one takes into account that the opponents will often enter the auction and take away bidding space, the criterion for bid definition is changed – now one wants to choose an opening bid according to the amount of information it contains on its own. The average amount of information in an opening bid at the 1-level is greatest when those bids are equally likely to be chosen. The message sent is, ‘this is my best suit.’ An overcall (presumably) sends the same message. Once the opponents enter the auction, there are 2 bids that take up no bidding space, pass and double. Pass is the most common competitive bid of all, therefore, the least informative, and therein lies the weakness of a wait-and-see pass. From information-theoretic considerations, it would be ideal if the 2 calls were equally likely, hence contained the same amount of information. The modern trend has been to abandon penalty doubles, which are rare, but informative. Now we double often with flat hands and hope it works out later. In theory this is a sound informative strategy, so the trend to flexible doubling should not be at all surprising.