Decisions in high-level competitive auctions Larry Hammick larry@hammick.com 2000.02.26 If both sides have bid to a high level, there is a well-known maxim: "When in doubt, bid one more." [S. J. Simon, 1945] Say the opponents go to 5H over your 4S. As opposed to passing, a bid of 5S will show a big profit if _either_ 5H or 5S is on, and a huge profit if both are on. It will show a relatively small loss only if both are down, and even then the opponents might rescue you. Some typical swings at IMP's: Our EW Our NS Our IMP's 500 -420 2 50 50 3 200 100 7 -100 420 8 -200 650 10 500 50 11 420 450 13 620 650 17 So the problem is how to avoid the big adverse swings at the cost of some small swings. Exactness is not possible. If our aim is some facsimile of optimal results in the long run, we will not find every chance to offer the opponents 500 instead of 620; in other words, our bidding is not necessarily bad _in the long run_ we miss some 500- point saves. It probably _is_ bad if we miss 100-point saves. If we aim to find every 500-point save, we will sometimes go for 700 or 800. In addition, if we are determined sacrificers, opponents have a motive to bid an occasional unsound game, hoping for 500 instead of 140 or 130. A remarkable thing about double-game deals is that each side tends to have only about 20 HCP. Consider an idealized example: AJxxx KQxxx xx x xx xxxx KQxx AJx Neither hand is freakish in distribution. Both are average in high cards. The two have a 10-card fit, which is not very extraordinary. Yet this could be a big swing hand: 4S is cold and the other side _must have_ at least 9 tricks at hearts irrespective of how their 26 cards are divided. (They can be held to 9 only if their clubs are 3-3 and their spades 2-1. Even then, EW must take their 4 tricks off the top, else NS will pull trumps and throw a club on the fourth diamond. Even with clubs 3-3 they will probably take 11 tricks if their spades are 3-0 and they get a spade lead.) This demonstrates that it may be possible to diagnose, _from our two hands only_, that both sides have a lot of tricks. This raises "hope for a cure" for the problem of high-level competitive bidding. But the cure must lie partly in the definition of our low-level competive bids. We will make four suggestions. Principle 1: Distinguish HCP from distributional strength (i.e. defensive from offensive strength) early in the auction. Standard practice often fails to respect this basic principle. Consider the takeout double of, say, a 1H opening bid. If the pattern is 4-2-4-3, the minimum HCP is such-and-such, say 12. But if the pattern is 4-0-4-5, the HCP may be fewer, say down to 10. So, although the first hand is "minimum", the second is considerably weaker defensively, both in high cards and in length in the adverse suit. Principle 2: Don't accelerate the auction when you have scattered pictures or relatively balanced (defensive) distribution. You know that in a constructive auction, the strength of any bid is _relative_ to one's previous bidding. If you have shown 23-26 HCP already, and you have 23, then your next bid, if any, should be "weak". The same is true with respect to the "offensiveness" of your hand, i.e. the difference between its offensive and defensive strengths. To illustrate, if you have overcalled on 5-3-3-2 shape, or opened a weak two on 6-3-2-2, your hand is defensive _relative_ to your previous bidding, especially if you have three of the enemy suit. -- A free bid in a competitive situation suggests distributional values, while a pass may suggest or conceal defensive values. -- A NT bid in a competitive auction shows defensive values and a probable balance of strength. When a fit is found and you have scattered pictures: -- Queens and jacks in your side's suit(s) increase in offensive value decrease in defensive value. -- For queens and jacks in the enemy suit(s), the opposite is true. Actually, these two principles are the same: quacks in the trump suit and in the declarer's side suit, if any, are more valuable than other quacks. The principle applies less strongly to kings: if an odd king is a trick on defence it is also a trick on offensive, usually. But a singleton K is much more likely to score on defence than playing the hand, and partner may have Qx or Jxx opposite. Kxx opposite a likely singleton or void is primarily a defensive value, as well. Principle 3: Verne's Law, or Law of Total Tricks Say we have some number A of cards between us in our best fit, and the opponents have B cards in theirs. And suppose we can take X tricks if we play the hand, and they can take Y tricks if they do. Then Verne's Law, also called the Law of Total Tricks, is the equation: A + B = X + Y. Not surprisingly, this equation is not always exactly valid, either at double-dummy or at the table. But the two sides of the equation seldom differ at double-dummy by more than 1, and are indeed equal in a remarkably high percentage of deals. The principle exception is when each side has a double fit. For example, if we have 6-4-1-2 facing 4-6-2-1, and each side has all the HCP in its two suits, each side can take at least 11 tricks. In this case A+B=20 but X+Y=22 or more. The Verne equation is the basis of some systems of competitive bidding, such as those used by bridge-playing computer programs. Principle 4: Double relative to your previous bidding If your side has shown a clear balance of power during the auction, then a pass by either of you (directly over an adverse bid) is forcing. For example, if your RHO says 4S or 5 of a minor over your side's 4H, a pass by you requires partner to double if he cannot bid- to-make. During a competitive auction, however, neither side has the high cards to guarantee a plus score. Therefore a pass should have a different meaning. The options are to bid on, to double, or to pass; a reasonable assignment of their meanings is: Double: defensive hand relative to previous bidding; partner may remove Bid: offensive hand relative to previous bidding; this bid might make Pass: typical hand relative to previous bidding, not forcing