The Second Law of Total Tricks

Bridge players are quick to quote the Law of Total Tricks to bolster their excuses for overbidding. In fact, this Law has become the foundation for a new approach to bidding which makes little reference to the high card content of the hands being bid. Of course, it is known that The Law is subject to many conditions and restraints, a major proviso being that the trumps suits represented are well stocked with honours, which they usually are on the basis of probability. On the occasions where they are not well stocked, The Law may overestimate the total number of tricks available. That has been the observation of experts, including Larry Cohen. On that basis we propose a Second Law of Total Tricks, subject to verification that goes as follows.

The Second Law: The more controls one holds in the opponents’ trump suit, the lower the expected number of total tricks.

That appears to be common sense, but the history of science has taught us not to put too much faith in common sense and logic. First and foremost one must collect and examine the data. The key word is ‘expected’, implying Law2 is not always true, but that it is true more often that not. I suspect it is most appropriate when both ‘best’ trump suits are 8 cards in length. Think of it as akin to the observation, ‘gentlemen prefer blondes’. Not always true, of course, but generally something a girl can work with.

We shall examine the effect at work in hands played in the recent 2012 USBF Trials. First a deal where NS bid and made game missing the AKQ of trumps. With inescapable losers in the trumps suit, the HCP evenly divided at 18 to 22, and a division of sides of 8-7-6-5 one would expect that there was no way declarer could emerge with 10 tricks.

 

Dealer: South Vul: NS	North ♠   AQ ♥   KJ642 ♦   8 ♣  JT432
West ♠   T632 ♥   AT9 ♦   AKJ62 ♣  K		East ♠   J974 ♥   84 ♦   T9 ♣  AQ986
	South ♠   K85 ♥   Q73 ♦   Q7543 ♣  75

Hampson	Hamman	Greco	Zia
—	—	—	Pass
1NT	2♥	Dbl	Pass
2♠	Pass	4♠	All Pass

In theory the game should be defeated with a heart trick added to the 3 certain trump tricks, but on the auction that defence is impossible to find. Hamman at some point has to lead a heart away from KJxxx. He began with the ♣J and Hampson failed to rise with the ♣A in order to pitch a heart from his hand. He won the ♣K and led a trump. Hamman still had time to play a heart, but he continued with a second club expecting to give Zia a ruff. Surprise! An impossible game made against a credible defence.

The point of this demonstration is that there is a difference between theory and practice. Players bid and play according to the odds one encounters in practice. The bidding has a great deal to do with the outcome, as the bidding provides the information on which the decisions of the defence largely depend. Logic doesn’t work in a vacuum.

One may consider Hampson’s choice eccentric, but experience has shown that opening 1NT with a singleton ♣K can win points. It is a common practice in China, where Hampson may have picked up on it. Perhaps more significant is the poor defensive bidding by Hamman-Zia. As we discussed in a previous blog with regard to a 2♣ overcall, the effectiveness of  certain bids depends on the efficacy of countermeasures available. If Zia had been given a chance to show heart support, the heart lead would have been easier to find. Suppose Hamman had bid an Astro 2♣, showing hearts and a minor, and Zia had bid 2♥ over a Greco double. Then there would be no story to tell.

During the Trials we observed many pairs making game on a major 4-4 fit missing high honours in their suit. It didn’t appear to be a concern. As in the above example, success often depends on having a good minor suit to provide discards. Here is another.

Zia	Hamman	Milner	Zia	H. Lall	Hamman
♠ 8642	♠ QT95	—	1♣	1♦	1♠
♥  3	♥  AKJ	4♥	4♠	Dbl	All Pass
♦ Q9	♦AK3
♣ AK9765	♣ J84

This looks bad for whoever wins the contract. The spades are missing AKJ, the hearts are missing AKJ, the diamonds are missing AKQ. Only the clubs have a high degree of quality. We guess Zia’s game bid in spades was based primarily on his holding in clubs. The division of sides is 9-8-5-4, with the expected total trumps being 18. So what are the total tricks according to Deep Finesse? West can make 1♥, 7 tricks and theoretically South can make 10 tricks in 4♠. The Law appears to be fairly accurate despite the disparity in HCPs, however, to avoid 3 trump losers, Hamman playing in 4♠ must lead a low trump from dummy and put up the ♠Q when East follows low. In practice Lall went up with the ♠K from AK3 on the first round and gave Hamman no choice but to make his doubled game.

What is most significant about this deal is that Zia-Hamman had no means available by which to punish 4♥, down 3, against a dubious 4♠. How much better if in a forcing pass situation Zia can bring himself to pass with bad spades so Hamman can double 4♥ and make it stick.  Otherwise, a double must of necessity cover a wide range of holdings, and a game bid becomes a shot in the dark. Here is another example from the Semifinals of a 4-4 major fit missing top honours being used successfully as a trump suit.

Hamman	Zia	Milner	Zia	H. Lall	Hamman
♠ AQ5	♠ KJ	—	—	Pass	1♣
♥  J965	♥ Q432	Dbl	1♦	Pass	1♥
♦ 6	♦AT9872	Pass	4♥	All	Pass
♣ AQJT9	♣ 8

This time Zia-Hamman’s 4-4 major fit was missing ♥AKT, and the Lall-Milner 4-4 major fit, ♠AKQJ. Despite the lack of controls, and in the face of Milner’s double which presumably promised 4 hearts, Zia jumped to game on ♥Q432. The bidding was the same at the other table where Rodwell doubled and Justin Lall put Bathurst in game. From this we gather that the experts don’t put much weight on the need for a good trumps suit –  any 4-4 fit will do, provided one has a long minor that hopefully will provide tricks. In fact the heart game is better than 3NT which is vulnerable to an attack on the diamonds. The heart trumps provide protection in that area, while the club suit provides tricks.

Takeout doubles are non-descriptive these days, that is, they don’t promise favorable distribution. That is why they tend to be ignored by the opponents who bid their own values regardless. Here is an example from the Round of 16 featuring a solid citizen where getting into the auction with AK in an opponent’s suit proved expensive.

 

Dealer: West Vul: None	North ♠   A53 ♥   J72 ♦   AK84 ♣  Q64
West ♠   KT76 ♥   A9 ♦   QT73 ♣  A73		East ♠   QJ ♥   KQ854 ♦   J92 ♣  K52
	South ♠   9842 ♥   T63 ♦   65 ♣  JT98

Kranyak	Rosenberg	Wolpert	Willenken
1♦	Dbl	Rdbl	Pass
Pass	1♥	Dbl	Rdbl
Pass	1♠	Pass	Pass
Dbl	1NT	Dbl	2♣
Dbl	All Pass

 

Although one may opt to play in a trump suit missing the top honours, it is another matter to attempt to declare a hand when the main feature of one’s hand is controls in the opponent’s suit. Although it may be said that the doubler was unlucky to find the division of sides to be 7-7-6-6, the North cards are highly unsuitable for immediate action. After the redouble the scrambling began with nowhere to go.

The amazing feature of the deal was that the same double was employed by Justin Lall at the other table. He and Kevin Bathurst were successful insofar as they managed to play in a 7-card fit at the 1-level, rather than at the 2-level. Their -300 constituted a good save against a potential 3NT making 4. Bidding 3NT by EW is wrong in theory as the Total Tricks maybe less than 14 – the unexpected 3-3 heart split helps immensely.

A bad bid is less dangerous than it should be if the opponents are making the same bad bid. We see this effect time and again when both sides play the same flawed system. One of my favourite bad bids is 2NT by an opponent. It is a big winner in the long run for the side that can avoid it. Recently in a 7-board Team Match we won 23 IMPs on consecutive 2NT opening bids on my right, and there was nothing lucky about it. In one case the opponents reached 6♥ with 2 inescapable trump losers; in the other, 3NT with ♠x opposite ♠Jx, after a Puppet Stayman auction that failed to reveal the fatal flaw. Our teammates followed a different path and were successful in reaching 5♥ and 5♦, respectively. In the latter case, our teammate opened 1♦ because she didn’t fancy opening 2NT with a doubleton spade. A spade overcall then steered the partnership to the right contract. Information, information …. As David Burn so aptly put it, ‘where there is ignorance there is hope’, but actions shouldn’t be based mainly on hope.

Practical Percentages
It is obvious that there was a lot of hopeful bridge being played during the 2012 Trials, and it wasn’t until the latter stages that good bridge dominated. Earlier the bidding was largely ‘psychological’ in the opinion of a trans-Atlantic observer; it was a demonstration of style over substance. I equate the performance to that of a hedge-fund manager – praised when lucky, condemned when not. Justin Lall in a BBO conversation with ‘Mr Woolsey’ commented that he had learned from Kit’s articles that one should always play the percentages. We assume that his double defined above was considered to be the percentage action. The percentages take into account the possible reaction on the part of the opponents. If the opponents have no efficient way to cope with ill-defined bids, or misinterpret the bids, then the chances of getting away with bad bidding is increased.

A nebulous takeout double has low information content. The same applies to overcalls on bad suits. This means that the competitive bids on the opposition have to be flexible enough to cope on their own merits. One cannot count on the opposition having bid accurately and act according to that. Uncertainty has become their weapon. We see this effect in the hands above where players ignored the implications of a takeout double and bid their major 4-4 fits regardless. Ignoring the opponents’ bidding is not the best way to react – we need better methods than that. Flexibility is the key. I suggest an extension of the ‘forcing pass’ concept to part score bidding. In general that’s not the way it went, with partnerships snatching at games for lack of anything better to do.