Hand Evaluation

In a world where everything is relative it is a mistake to think in terms of absolutes. Nonetheless, some players are wedded to the ideal of high card points as a means of evaluation of their hands. They think that in order to make a normal opening bid one needs points that translate into tricks whether one declares or defends. That is a comfortable thought, but sometimes a hand comes up that can take many tricks on offence and few on defence. It pays to open such hands.

The number of tricks one can associate with a given deal is huge. There are 5 strains and 4 potential declarers for each strain, 13 tricks for each contract. Some are not worth considering, but there may be a fair number remaining that can be usefully subjected to a double dummy analysis through the application of Deep Finesse. The remaining cases of interest can be multiplied by the number of different possible outcomes that arise from the bidding process. It is not surprising that there are few deals played in the same contract with the same number of tricks taken at every table. The result on any deal has to be thought of as a statistic outcome subject to random variation.

It was the genius of Jules-Renè Vernes that he came up with the Law of Total Tricks to reduce the mass of possibilities to 2 main outcomes, the number of tricks played by each side in its best contract. It is a simplification, of course, but it got players to thinking about the variability of the value of queens and jacks, useful on defence, but potentially worthless on offense. To be valuable on offence, they must be matched happily with cards held by one’s partner, or be part of a long suit that can serve as trumps on its own. Here is an example from last week where lonely queens, accompanied by their ladies in waiting (ten’s), were upgraded purely because of their offensive value.

The ♣K was led, RHO following with the ♣2. The opening leader was very surprised when I ruffed this. I played a trump to the ace, felling the king, making 11 tricks. The opponents had missed a good save in clubs. The number of Total Tricks available was 21 and the number of total trumps, 20, so the outcomes were well approximated by the Law and would have been exactly predicted if I hadn’t dropped the singleton king.

On sorting my hand my first reaction was to open 1♥, but then I had some second thoughts. In this (mostly) friendly game among seniors would it be fair to my current opponents to open 1♥ in first seat on just 8 HCP when every other South would be passing? I don’t like to psyche bid and ruin an opponent’s game as a result, but here I was not deliberately misrepresenting values, I was giving a true description of the offensive value of the hand, as I saw it. Of course, the HCP total alone did not do that. One has to take into account the distribution points, as Goren recommended. In the Zar points scale I had 18 distribution points and 8 HCP, for a total of 26, enough to justify opening 1♥.

My second thought was to open 2♥ as the 8 HCP fell within our announced range of 6-10 HCP, but I rejected that approach. A 6-loser hand is too good for a preempt, the probable effect of which would be to embolden the opponents in a search for a game in spades. Opening 1♥ gives my LHO an easy entry into the auction, but my ♠A may act as a deterrent to high adventure. On the other hand, the chance of finding a fit in one of the red suits in partner’s hand was high. So it turned out. Few reached 4♥, none scored 650.

Although I bought a good dummy it would be wrong to think I was extremely lucky in that. Partner had a 4-4-3-2 shape with more black cards than red cards. With 22 HCP placed in the 3 other hands, I could expect on average that he would hold 7 HCP. With 10 control points missing, on average he would hold 3.  Bad splits with extreme distributions all around the table are against the odds. The chance that partner held at least 4 red cards was over 70%. The odds favour the bold bidders: at least an 8-card fit was likely.

I made reference to Zar Points, but I am not a great believer in any points system. It is better to think in terms of the basic probabilities, on which the efficiency of a point systems depends. Where points may be useful is in the design of bidding systems. The greatest threat to light opening bids comes not from opponents, but from partners whose expectations may be lifted by a vulnerable opening bid on garbage. One needs a way to distinguish between strong flat hands and weak shapely ones. The following hand is also characterized by 26 Zar Points, but this time with the reverse composition: 18 high card points and 8 distribution points: ♠ K65 ♥ AQ43 ♦ A32 ♣ 864. This hand may not play well if there are no control entries in the dummy to facilitate finesses, whereas the previous hand can play well opposite a couple of fillers. This property is reflected in their respective loser counts: 8 for the flat hand, 6 for the shapely hand.

 On the hand where declarer was able to make 11 tricks in 4♥, responder gave a limited raise on a flat hand, which left declarer in control of the auction. With the 4-3-3-3 hand it is better if partner determines the degree of fit, which he can do by asking the right questions. With such a wide range of possibilities for an opening bid, some form of a Drury bid is needed to sort out the mixture of the points. In a way this is not fair as the opponents have no way to discover whether or not an opening bid has any defensive potential, whereas a responder can always ask if he so desires. The best the opposition can do is act upon the probabilities based on the small amount of information available to them. Obviously, they may have to enter the auction in order to provide their own information, and the auction then becomes competitive. The trick is how to do this in an efficient manner. Generally the captain of the side is the one with a shapely hand.

One effect of light opening bids upon the defenders is that the takeout double is used on a greater variety of hands than previously allowed. With opening points and a flat hand one has to make a noise if in danger of being shut out early. With shape one overcalls on a garbage suit in the hope of finding a fit. This need to act sooner rather than later annoys some conservative observers who feel they have to change their systems to cater to undisciplined bidders. My answer is this: do what you have to do.

Let’s return to the above hand and assume that my LHO doubled instead of overcalling.

Rather than put the emphasis on a bad suit, if my LHO had doubled to bring clubs into the auction, his partner may have dredged up a 4♣ bid. Once we reached 4♥, my LHO could have raised to 5♣ as a 2-way shot on the assumption that his partner must be short in hearts. Now with his balanced hand Bela would have to show some defensive values with a double, leaving me with a tough decision. The void tells me to bid 5♥, a contract that is in jeopardy. What was their problem has become my problem.

Information Content
Which of these 3 rounds of bidding give the blindfolded observer the greatest amount of information concerning the placement of the cards around the table?

A) Pass 1♠ Pass 1NT (forcing)
B) 1♥ 1♠ 3♥ Pass
C) 1♥ Dbl 3♥ 4♣

I think you would agree that the auction C in which all 4 players made a bid is the most informative. This in spite of the fact that 1♥ and Dbl may be wide-ranging and somewhat poorly defined. There is a wide difference between a narrowly defined bid and a pass. By reducing the difference we improve overall performance of the bidding system being employed, even though there is a loss of definition in the individual bids being made. Only with auction C will the players have a fair chance of achieving the par result, 6♣* minus 1 for -100. So one should not be put out by the fact that 1♥ is light and Dbl is off-shape. At least they have opened the gates for the partners.

On the other hand it is not an objective of the bidding process to guide the opposition to their par contract. The aim is to beat par, so one must be selective in what information one passes across the table. This week in a team game I was dealt: ♠ KJT43 ♥ QT9865 ♦ 54 ♣ —. I passed in opening seat, LHO opened 1♣ on 9 HCP without ♠AQ. Partner bid 1NT. Eventually I reached 4♥ opposite: ♠ 75 ♥ AK3 ♦ AQJ ♣ AJ874. Twelve tricks were made, but 12 IMPs lost. The player with my hand at the other table opened the bidding with 1♥. His partner eventually took charge and bid 6NT, defeatable only on an impossible club lead. My teammates fumed until I confessed that I was very close to opening the hand myself. I lied, as I am just too disciplined – only 24 Zar Points! Actually, I blame my partner for underbidding 1NT with 19 HCP and 7 controls, then simply raising to game. Major suit slam are worth bidding at 50% Plus.

A further loss occurred when the opponents bid a slam missing 2 aces, which we doubled for down 1. The loss occurred when our teammates went down 2 in the same contract. We gained when our teammates stopped in game and we defended a slam from the right side for down 1 after the auction 2♣ – 2♥ (2 controls) – 6♥. Declarer tried for a strip and endplay when a simple finesse would have worked. The game was looking less and less like a Jeff Rubens’ Swiss Match LXXIX, but I am happy to report successes followed. Partner made 3NT when my RHO led the ♦K, in the suit his partner had overcalled – declarer held the ♦AQ. Good defence capped by a necessary, albeit unintentional, Crocodile Coup against 4♠ produced a happy ending for our side.

Transferable Values
Aces, kings, KQ combinations, think of these controls as being transferable values useful on offence or defence. On the other hand small cards in a long suit can be valuable as trumps, and worthless on defence. Their value may never be realized if one doesn’t get into the auction and submit them to partner for consideration. That’s it in a nutshell. The overcall is the classic action which can be made on few HCP. Why wait? If one can overcall on 7 HCP without feeling guilty, why not open light on the same cards? The light opening bid, like the overcall, doesn’t promise transferable values. In fact, it has become common that these actions don’t even promise a good suit. If an opponent assumes otherwise, so be it.

The question one must consider is how to operate in an atmosphere of uncertainty in a competitive auction where everyone (else) is talking nonsense. As the auction develops probabilities change according to what the other players have bid. The less information one can draw from such actions, the more one must rely on the a priori probabilities. Rather than rely on the opponents to tell one what one needs to know, it is better if partners get it together as the auction develops. Showing a limited, flat hand is important in the process of estimating the number of total trumps. Also, it indicates the presence of transferable values useful on defence. The flexible competitive double can be usefully employed towards that end.