Bids and Expectations

When it is not in our power to determine what is true, we should act according to what is most probable  –   Rene Descartes (1596 – 1650)

When partner opens the bidding he creates a first impression that may be difficult to correct. Suppose partner opens 1♠ within the context conservative 5-card major system. Although there are no guarantees, one expects, on the basis of probability, that he has at least one honour card in the suit, unless we ourselves hold all the top spades. How should one react to the bid? Of course, we should react according to what is most probable given what we can see in our own hand, but temper our actions according as the known variability. The bidding system may have solved that problem for us. It requires that we raise to 2♠ with 3 spades and 6-9 HCP. That is designed to be on average the best we can do given the expectations. The question is, what if, due to inherent variability, the hands do not conform nicely to expectations? In that case problems are likely to arise.

One may expect that partner will have opened 1♠ with 5-3-3-2 shape and (roughly) 13 HCP distributed between the suits in proportional to their lengths, that is, 5 in spades, 3 in each of the 3-card suits, and 2 in the doubleton. Here are some possible 1♠ opening bids.

Most Likely	I	II	III
♠ AJxxx	♠ AJxxx   (0)	♠ Jxxxx    (4)	♠ Axxxx   (1)
♥ Kxx	♥ Kxx       (0)	♥ KQx      (2)	♥ Kxxx     (0)
♦ Kxx	♦ Kxx      (0)	♦ Kxx      (3)	♦ Kxxx     (0)
♣ Qx	♣ xx         (2)	♣ AK        (5)	♣ —         (2)
13 HCP	11 HCP	13 HCP	10 HCP
Departure   0	Departure   2	Departure  14	Departure   3
Zar Pts     28	Zar Pts     26	Zar Pts      28	Zar Pts      28

The departure is the sum of the absolute differences between the number of HCP actually held in a suit and the expected length of the suit. Hands I and II have the most likely shape, but they are vastly different in their HCP distributions. If one opens a ‘light’ 1♠ with Hand I one may feel that the bid gives a good description of the holding as it is pretty much what partner can expect. The lack of an honour in the short suit is of minor concern. If one opens Hand II, there is a need for further clarification. Even though the HCP total is up to snuff, the distribution of HCP is far different from what partner will expect. It could be a case of ‘nothing wasted in spades’ in a heart contract, a fact that will require several bids to establish firmly. Despite encompassing only 10 HCP Hand III is the best offensive hand and fits well the expected distribution of HCP. In the subsequent bidding responder should be able to reveal the shortage in clubs in order to clarify the full playing strength of this combination without promising extra HCP strength. That facility is up to the system designer to provide, or not – the 5-4-4-0 shape is rare.

On opening bids with hands low on HCP but with good distribution, for constructive purposes it is important that the HCP be well distributed in the long suits – the short suits don’t matter as much. In a traditional bidding system where extra bids show extra strength, the hand may be worth one bid but not a continuation, so it is difficult to correct first impressions without overstating the overall strength. In a system where opening bids are limited and subsequent bids are ‘competitive’ in nature, there is more scope for painless clarification. (In the next blog we consider a bad arrangement – self-preemptive intermediate two bids as used by the Italian pair, Fulvio Fantoni and Claudio Nunes.)

When Push Comes to Shove
There is a great advantage to opening light with length in the spade suit, because to compete the opponents have to bid one level higher. It may be negative thinking to ask this question, but what happens if they win the contract? Obviously one of us is on lead, and the question arises as to whether we should lead a spade, the suit we bid so optimistically. Before we look at the probabilities, let’s look at a couple of hands where spade leads proved disastrous. The first comes from our local game.

 

Dealer: West Vul: North	North ♠   — ♥   A862 ♦   KT985 ♣   AT32
West ♠   JT832 ♥   Q7 ♦   Q ♣   KQJ96		East ♠   K74 ♥   KT43 ♦   A62 ♣   854
	South ♠   AQ965 ♥   J95 ♦   J743 ♣   7

West	North	East	South
1♣	1♦	Dbl	3♦
3♠	4♦	Dbl	All Pass

The West hand has 26 Zar points, so is deemed worthy of an opening bid. North has his bid, and East won’t be criticized for wanting to compete, and South has a legitimate 4-card jump raise. West expects 4 spades opposite, so he bids to the level of his assumed fit. North continues his good work and East surely has the stuff to double. So by modern standards here is a perfect auction, so far. But it is wrong. The Total Tricks add up to 17, which one should expect to sit 9 with NS and 8 by EW. So EW do well to compete to the 3-level. Even though the tricks sit 10 with EW and only 7 with NS, down 2 undoubled should prove profitable. So the only error one can point to is the final double by East.

To be fair, can East expect the opening bidder to hold a topless spade suit after he has freely bid at the 3-level? More likely he holds 4 good spades and a doubleton diamond, reducing the number of Total Tricks. It appears then that this is the time to strike at those who bid on nothing. The next question is: what to lead? From East’s point-of-view a spade lead is surely safe, but in fact it is the only lead to allow declarer to pitch 2 losing hearts on the ♠AQ and cross ruff for an overtrick. The double didn’t cost, the lead did.

Let’s now go to the Seniors KO Semi-Finals at the 2011 Nationals in Seattle. Here we can expect reason to prevail, or can we? Might we not find that the Seniors are afflicted by the same disorder we observe at our local club, namely, undue affection for the spade suit regardless of its defective structure? You know it’s true.

 

Dealer: West Vul: NS	Schermer ♠   J6 ♥   J9652 ♦   AKQ5 ♣   52
West ♠   T4 ♥   Q43 ♦   JT7 ♣   KQT98		East ♠   K9872 ♥   A87 ♦   963 ♣   73
	Chambers ♠   AQ53 ♥   KT ♦   842 ♣   AJ64

West	Schermer	East	Chambers
Pass	Pass	2♦ *	Dbl
2♠	3♦ (->♥ )	Pass	3♥
Pass	3NT	All Pass

John Schermer and Neil Chambers were cited by Bobby Wolff as being one of the best seniors’ pairs at the recent world championships in the Netherlands. They are the antithesis of the overly active players of the younger generation we see emerging on the scene. They may lose out by not acting when perhaps they could do so to advantage, but they gain by the trust partner can put in their action when they do act, as in the deal above.

East-West are up-to-date in their competitive structure which allows them to preempt with a multi-2♦ bid in 3rd seat with the garbage hand dealt to East. The bid promises at least 5 cards in a major- really. Well, Schermer is known to pass on some very good hands, so maybe a bit of preemption will have good effect. A BBO commentator claimed this convention has been shown to possess a 57% success rate. OK, but doesn’t the quality of the suit come into it? Apparently not, if the main aim is disruption.

Chambers has enough stuff to double without length in hearts, as he expects hearts to be the suit in which East is preempting. The preemption may about to work, or at least break even, but here comes West getting active and bidding what he hasn’t got, perhaps in a ‘pass or correct’ mode that risks misinterpretation. Schermer can transfer to hearts on the assumption that spades is the opponents’ best fit, and later suggests 3NT as the final contract. Necessarily brave bidding by a passed hand, based largely on partnership trust, partly on knowledge of the opponents’ proclivity towards light preemption.

One can hardly blame East for leading a spade, thus giving away the contract and losing 12 IMPs. At the other table, North opened 1♥ , East overcalled 1♠ and South ended up as declarer in 3NT. The contract can be defeated on the ♠T lead, but West felt no compulsion to lead his partner’s suit, not when he held such good clubs. At this table it all seemed reasonable, as it so often does in a seniors’ event. It was a difficult hand to play even with help from the opening lead – the hearts weren’t well placed for declarer.

The Honour Structure in an 8-card Fit
If one aspires to follow Descartes’ advice and play according to what is most probable, then it pays to know the odds when partner shows a suit of a given length. Let’s first consider the case where a player opens 1♥ and responder raises to 2♥ . What are the expectation that he holds at least one honour, A,K, or Q (denoted by H)?

If the opener has Hxxxx, the chances that responder has raised on Hxx or HHx is 64%, if we take the suit in isolation. One should play for that possibility. From the other side, if the responder holds Hxx, what are the chances that the opener has at least one honour? 78%. So when defending it is even more likely that a lead in the suit is called for from responder’s side. On the other hand, if responder holds xxx and opener has a 5-card suit, the opponents also hold 5 cards in the suit. It is even odds whether opener holds none or one or that he holds two or three honours. That could make the lead ineffective, so alternatives can be considered. In cases where a player considers bidding a 5-card suit without a top honour, he should take into account the resulting uncertainty in partner’s mind, as partner may not look for alternatives when he should. This applies more to overcalls than opening bids, however, with borderline opening bids the quality of the suit is an important consideration, if one is aiming to elicit cooperation from one’s partner.

If the aim is to disrupt, then one takes one’s chances without expecting partner to get it right. The more levels taken up by an overcall, the more disruptive it tends to be, an overcall of 1♠ over 1♣ being the most space consuming, so the most suspect. If it is judged that the overcaller is weak in HCP, the overcall should show a good suit, but if he is judged to have a good hand, the overcall may be of necessity in a weak suit. In short, the lighter the bid, the better the suit. 

If a pair has an 8-card fit, the chances are 69% that they hold 2 top honours, but the a priori odds change according as an opponent’s holding. If an opponent holds Hx, his partner will hold Hxx or HHx 49% of the time strictly on an a priori basis, which may encourage some and discourage others when contemplating a NT bid. Usually a top honour in the opponents’ suit is a bad omen for those who contemplate bidding one more.