The USBF Women’s Final

August 14th, 2013  ~  Bob Mackinnon  ~  No Comments 

We have to thank the USBF for providing fans with the double dummy results for the hands played in their tournaments. Of course, we have been warned not to judge an expert’s particular play on the basis of a double dummy result, but that applies to the analysis of one hand at a time. Over the long run it is another matter. The double dummy results give us frames of reference that we can apply to the statistical analysis of several hands within the same category, for example, deals that in theory can sustain a game contract on any lead. For an expert pair missing one such game may be forgivable, but missing several is statistically significant and grounds for legitimate criticism.

It has long been a widely held belief that the key to winning a long team event is to bid your games and slams and not get caught in awkward situations where you might get doubled for a huge penalty. The scene has changed. The ability to compete effectively has become a necessity. That entails withstanding preemptive bids by the opponents. Thus the emphasis has moved from the logical (constructive bidding without interference) to the emotional (in-your-face interference). This shift was borne out by the results from the recent 2013 USBF Women’s Final over 120 boards in which the Sonsini team prevailed over the Baker team by a score of 237 to 197, even though the Baker team was much more effective in reaching double dummy games (and one grand slam) the other team missed. 134 IMPs were exchanged over 15 deals, Baker gaining 94 IMPs, to Sonsini’s 40 IMPs. Despite this huge advantage the Baker team lost.

Clearly Baker was winning under bidding contest rules, but this was real life where bad bids can be transformed into good results. On six hands both sides bid to games that can be defeated on a double dummy basis. The Sonsini team scored 56 IMPs to Baker’s 11, recovering partly from the losses sustained for not reaching double dummy games. Any blame attributed to the defenders has to be left to a detailed analysis. Suffice it to say, the Sonsini team had much the better of it and benefited greatly after ineffective leads.

Highly Competitive Hands
I think of this type as ‘chaotic’ as one could hardly predict the results from a preview of the hand records. Such hands provided Sonsini with a margin of 20 IMPs over 5 boards winning on 4, losing on 1. Although one may practice one’s constructive bidding, it is difficult to practice competitive bidding as so much depends on the tendencies of one’s opponents. In highly competitive deals one would expect an advantage to a pair who has a long history of success, so are most familiar with each others behavior ‘under fire’. One should not be surprised that Deas-Palmer excelled in this category.

In order to regulate one’s hopes and fears one needs methods in competition just as one has methods in a constructive auction, but the world hasn’t caught up yet on how optimally to combine accuracy with enhanced uncertainty. Clearly distribution is important and the Law of Total Tricks has to be an integral part of the system, but one must be aware that the placement of the honors has an effect on the efficacy of the Law.  Let’s see if we can learn from a closer look at the following 5 important swing deals.

One advantage of a 1NT opening bid with a 5-card major is that it limits the high card content immediately. As a result the responder, being well informed, has more say in placing the final contract. Given leeway Levitina could make a move on minimal values without fear of being punished subsequently by her partner. Stansby is not known for frivolous actions. Her jump to 4♠ was based on an 8-card suit and a void in hearts. Sanborn could pass and await guidance from her (unlimited) partner who must surely be short in spades. Not knowing of the 10-card heart fit, Levitina was not tempted to take further action. 4♠ was cold. At the other table Wheeler’s opening bid was less restricted.

Bernstein gave a preemptive raise which failed to shut out Palmer’s spade suit. Wheeler was the captain of the hand. She had extras, so felt she couldn’t let 4♠ pass her by. Having described a poor hand already Bernstein let the double stand – even with a void she held some defensive cards in the minors.  Some might say Wheeler was unlucky, 8-card suits are rare, others might say the ♦K, ♥Q and ♥J were marked as being wasted on defence. I prefer to think this pair was disadvantaged by not being able to limit their hands before making the final decision. Wheeler led the ♥A which was ruffed in declarer’s hand, setting up the ♥K in dummy for the overtrick!

After Bernstein’s pass Palmer opened a weak 2 in either major (Multi) leaving some doubt in Wheeler’s mind as what to do. She passed to await further information. Deas was able to find out what she wanted to know, and was left to play in a makeable 3♥. Having got assurance of the opponents’ heart fit, Wheeler belatedly got into the auction. Scrambling above the 3-level was costly: -300 against a heart partial. This was even worse as at the other table: teammate Stansby opened 2♥ which Granovetter raised provocatively to 4♥, doubled and down 1, increasing the loss on the board to 9 IMPs.

Against a preempt a player is advised to get into the auction early, later often being too late. Playing safe is not safe, as Wheeler demonstrated. The purpose of an opening preempt is to remove bidding space and make the opponents guess, but the responder is often in a position of having to guess as well. Even if one gambles a double in second seat, responder may not be able to take full advantage, as when Granovetter misjudged the offensive potential of her hand. (♠ KJT ♥ AQ2 ♦ KT85 ♣ Q82).

How can one defend against the Multi 2♦ if one is not sure of which major is held on one’s right? The simplest solution is as follows: double says, ‘I would double a weak 2♥; 2♥ says, ‘I would double a weak 2♠.’ All other bids have their natural meanings.

The following exhibit illustrates the fact that wide-ranging preempts make everyone guess. There are general principles to follow. Trust your partner, act quickly on what has been promised, but don’t expect perfection. If the opponents have been made to guess, assume they have guessed wrong. Don’t give them a second chance to get it right. Assume your side’s preempt has worked, perhaps in some unexpected way.

McCallum tends to preempt lighter than most against non-vulnerable opponents. The inherent uncertainty puts the onus on Baker to handle the subsequent competition. Radin bid 4♠, obviously a guess, but was it a good guess? Baker had primarily a defensive holding without aces and could expect 3 tricks on defence, but is there a good chance of a 4th?  The primary guideline comes from the Law of Total Tricks. Given McCallum is 5-5 in the minors, Baker can expect the division of sides to be 5=4=9=8, so each side has a double fit with a total trump count of 18. If Radin can make 10 tricks in spades, Baker can expect only 8 tricks in diamonds, so 5♦* looks to be going down 3, for a score of -500. The sacrifice would lose IMPs even if 4♠ were making.

5♦ went down 4, declarer taking just 7 tricks. One way in which 4♠ is a bad guess is that the opponents have a better fit in hearts, as Baker might have guessed.  At the other table 12 tricks were made in hearts, beating the double dummy limit of 11. So, bidding 5♦ was predictably the wrong move, as it was possible to drive the opponents to a slam in hearts makeable on less than perfect defence.

For the winning team Levitina-Sanborn incurred some losses in the game zone due to a herky-jerky self-preemptive style otherwise encountered with veteran rubber bridge experts. We see it again on Board 7 which involved an eccentric weak 2♦.

This 2♦ preempt with a good suit, 6 losers, a void, and a 4-card spade suit was so bad that I hoped to see it fail badly. Initially it appeared I got my wish. Levitina made an impatient jump that so often lets down her side. Undeterred, Stansby raised Granovetter to game with 5-card support. Levitina doubled with a vengeance to no avail. 4♥ made.  So, bad preempt, bad result, but wait! Oh no! Another bad 2♦ this time from Baker!

By agreement the McCallum-Baker weak two’s are wider ranging in shape than is customary after a certain age. Under circumstances of great variability one needs methods for checking back to get more definition. If one allows a 4-card spade suit to be stuck in amongst the diamonds, you have to be especially circumspect. Given the uncertainty McCallum did not self-preempt as had Levitina, being content to bid 2NT and await developments which were forthcoming from all sides. She raised to game largely on the information the opponents had provided. The gain was a whopping 16 IMPs, but this fine result on Board 7 was not to be followed by others of a similar type.

It would have been much better strategy for Radin jump to 4♥ before clarification could be provided making the uninformative nature of the McCallum-Baker weak two a liability instead of an asset. Preempt the preemptors! Has it come to this? In this on-going process we palookas are years ahead of the experts.

Inference after a Weak Two

July 30th, 2013  ~  Bob Mackinnon  ~  6 Comments 

In the USBF Women’s Final the Baker team lost a close match to Sonsini partly due to their losses on boards in which the opening bid was a weak 2. As originally conceived by Howard Schenken the weak 2 augmented the standard US opening bid structure by the addition of a light, constructive call that showed a good 6-card suit without the normal requirement for an bid at the one-level. Many players still adhere to the ‘good-suit’ principle in first and second seat, while allowing for more freedom, and hence for more uncertainty, in third seat. Karen McCallum of the Baker team believes that strong suits can be opened light at the one level, so even in first seat there is no promise of a good suit being held.

There are players who allow themselves to open a weak 2 with a bad suit, but prefer to have some back-up in the form of a high honor in a side suit, maybe even with a king and a queen outside. This dubious practice is protected to some extent by the degree of uncertainty with which it operates. It is the task of a declarer to plan her play according to the tendency of the preemptor. Here is an example from the Baker-Sonsini match.

McCallum-Baker are vulnerable against not, so Radin’s raise of Soncini’s 2♦ opening bid can be expected to be weak and adding to the preemptive value in line with the ‘last-guess’ principle. When considering Baker’s options with regard to McCallum’s power double, one should consider the most likely number of total trumps available. Following the suggestions of Larry Cohen in this regard, Baker should assume her partner holds a 4=4=1=4 hand, making the division of sides 7=7=3=9. That turns out to be the exact division. The number of total trumps is 19, so if 5♣ makes, 4♦ can be expected to be down 2, doubled for a score of +300. This would be an insufficient return against +600 at the other table.

From Baker’s hand a conservative estimate of the number of tricks available against 4♦ is 5, one in each minor and 3 in the majors. If clubs are divided 2-2, there are 6 losers in 4♦ but no more winners in 5♣, making the Law suspect. Now 4♦* would yield +500 making the decision much closer.

Baker bid 5♣ and was faced with the task of avoiding 3 losers in the majors. The lead of the ♦4 to the ♦K was taken by the ♦A, a diamond was ruffed, and trumps were found to be split 2-2 with the ♣J on the left. Sonsini holds 5 cards in the majors and Radin holds 7. The hearts could be split 3-3 and spades 2-4, or the hearts could be 2-4 and spades 3-3.   Which is more likely? The success of the contract will depend on which view is taken.
If there were no bias to be applied to the major suits, the number of combination for each situation is 20 of a 2-2 split and 15 for a 2-4 split for a product of 300 combinations. In a case where the decision appears to be a toss-up, it behooves one to look for a clue that might tip the balance in one direction or the other. The clues come from the bidding and the opening lead.

Sonsini has opened a weak 2 on a bad suit. Suppose we assume she is the type who feels more comfortable opening a weak 2 with an outside top honor. Which major suit honor is she likely to hold? The missing majors are ♥ KQT963 and ♠ QJT853. Assume she holds the ♥K. How does that affect the numbers of card combinations? We have the following numbers of combinations.

Sonsini has opened a weak 2 on a bad suit. Suppose we assume she is the type who feels more comfortable opening a weak 2 with an outside top honor. Which major suit honor is she likely to hold? The missing majors are ♥ KQT963 and ♠ QJT853. Assume she holds the ♥K. How does that affect the numbers of card combinations? We have the following numbers of combinations.

Under this assumption the odds are 3:2 that the hearts split 3-3. Carry it a step further: suppose Radin holds the ♥K.

Now the odds favor the 3-3 in spades in a 4:3 ratio. Overall if one thinks there is better than a 50% chance that Sonsini holds the ♥K, one should play for hearts to be 3-3. To put it even more roughly, which holding looks more likely:
♠ Qx ♥ Kxx ♦ Qxxxxx ♣Jx  or ♠ Qxx ♥ Qx ♦ Qxxxxx ♣ Jx ?

Here is the full deal.

The winning decision is to play for the hearts to split 3-3. Duck a heart. The losing spade eventually goes away on the 4th heart in dummy.
The double dummy analysis tells us the number of total tricks was 18. In the same situation at the other table Beth Palmer passed Lynn Deas’ balancing double and collected a penalty of 500. This would have represented a loss on the board if Baker had played for hearts rather than spades to be 3-3. As it was Palmer’s pass resulted in a 12 IMP gain. In effect she took the sure plus rather than face what might be a tough play problem at the 5-level.

If the preemptor were a disciple of Karen McCallum, it may be assumed she holds one or the other heart honor to make up the minimum number of HCPs needed for a first seat 2♦. Here are the combinations for the condition of split honors.

Putting a restriction on both the LHO and the RHO reduces the odds of a 2-2 heart split to 9:8, but it is still better to play for the even split in hearts. This also covers the case where it may be assumed that the LHO must hold either the ♥K or the ♥Q, but not both.

The above analysis is a simplification to illustrate the method, the full implementation of which would require a computer program to weed out the impossible heart-spades combinations. At the table one can’t perform an exact calculation, but one can assume the preemptor holds at least one top heart honor whereas there is no restriction on the spade honor locations. As shown above that suggests hearts are more likely than spades to split 3-3.

Disclosure and Uncertainty

July 29th, 2013  ~  Bob Mackinnon  ~  4 Comments 

There is no escaping death and taxes, however, death is pretty well a cut and dried affair, whereas tax laws are subject to interpretation. Recently when I discussed estate planning my lawyer commented, ‘you just want to escape paying taxes.’ I replied, ‘no, I just don’t want to pay more than I have to.’ I have a new lawyer now. It is not a crime to ask questions and take advantage of loopholes that have been provided for the friends of lawmakers. The same applies to bridge laws. Why be a chump?

I am happy to pay my fair share of taxes, and I am also happy to follow the rules laid down by the bridge authorities with respect to full disclosure of my partnership bidding practices, but I don’t see why I should provide more than what is required by law, unless I choose to do so at my own risk. A bidding system is an imperfect set of guidelines. It is not defined by sharp boarders; there is redundancy and overlap. A good hand for a bidding quiz is one that offers 3 possible bids, all within legal bounds. A system is defined for the normal circumstances that arise most frequently, so a player may make an unusual choice when he feels the obvious bid is inadequate for the purposes at hand – in the same way for good reason he may choose an unusual lead.

We have to state the obvious again because of the Vanderbilt affair where the champions won a match on an appeal citing misinformation. This case is very interesting and significant, but before we get to that here is a problem hand from my local club.

Partner opens 1NT (15-17 HCP) and you hold: ♠ QT3 ♥ J ♦ KT652 ♣ Q842.  How can you use the 2/1 system to explore the possibility of 3NT, when 2♠ is a transfer to clubs and 2NT is a transfer to diamonds? Most pairs were stuck in 1NT making 9 or 10 tricks. Those playing a weak NT could open a ‘natural’ 1♣, after which the path to 3 NT is cleared marked after responder bids 1♦ – there would be no need to distort the auction.

My partner suggested he should have bid 2♣ and followed with 2NT, invitational. Invite with a singleton heart? I do not like inviting without attempting to reveal the nature of the hand so that partner can make an informed choice. Here is my suggestion.

What are we trying to do? Reach 3NT. So, it is important for responder to reveal his minor suit orientation. This enables the opening bidder to show his major suit stoppers. As responder has help in both majors, he can pass 3NT.  Lucky perhaps, but, as Jeff Meckstroth says, there is a bonus for making game. The players at the table rejected my suggestion on the grounds that the diamonds are longer than the clubs, however, I feel the minor suit concentration was the essential feature of the responder’s hand, the relative length of the suits being a minor consideration in a limited context.

Our 2/1 bidding system was an imperfect mechanism for arriving at the optimal contract. No system is perfect. It isn’t reasonable to consider system rules as inviolable and to adhere to system guidelines in the strictest sense under all circumstances. So, one may use Stayman without a 4-card major, or transfer into a 4-card suit, canapé style. Also, one may respond with a 3-card major, prefer a short major to a long minor, bid NT without a stopper, and so on. The point is that a player can bid around the system, as long as the opponents are aware of the uncertainties involved. It can be a mistake to claim, ‘we never do this’, or ‘we always do that’, when adaptability is the keyword. Such broad statements may punish partner for his initiative. An auction is not a simple game of show and tell. The purpose is to arrive at a good contract with all participants duly informed.

The Auken-Welland Appeal
During the 2013 Vanderbilt Roy Welland won an appeal on the grounds of misinformation. This turned a loss into a win, and the Auken-Welland team went on to win the event. The details are of interest to us non-experts, as there are many implications with regard as to how to play the game properly according to the regulations. Let the experts be our guides. Here are the hands for that famous deal.

The Norwegians employ a largely natural bidding system which to me implies a good deal of judgment and flexibility is involved. Helness held the type of hand I dread when playing 2/1, nonetheless a rebid of 2NT shows a flat hand featuring diamonds and the requisite number of HCPs leaving partner in charge of the auction. Helgemo was able to transfer to 3♥ to show length in the suit, and Helness interpreted this as a forcing bid denying 4 spades. He signed off in 3NT missing the 4-4 fit. Helgemo for his part thought Helness had denied 4 spades. He later admitted this was wrong. Bearing in mind that Helgemo might hold 4 spades while wishing to emphasize his hearts, Helness might have said that 3♦ usually denies 4 spades. That would leave left him with the freedom to bid 3NT if his judgment led him to do so. He could still bid 3♠ to show 4 spades if his holdings pointed in that direction.

There are combinations where playing in 3NT is better than playing in 4♠. For example, suppose Helness held ♠ xxxx ♥ Kx ♦ AKQJ ♣ KQJ. There are 4 inescapable losers off the top, and 9 winners, but if Helness must bid 3♠ because he has 4 spades, the pair will reach a bad game. The characteristic of this hand is that the concentration of HCP does not match the distribution: too much in the minors, not enough in spades. On the basis of probability Helgemo would rightfully expect better spades for a 3♠ bid. I suggest 3NT is a reasonable choice even when holding 4 spades. It could turn out badly, but freedom of choice is the fundamental virtue of a natural system.

Welland’s primary grounds for appeal was that he would have led a heart through the long suit in the dummy if he had been properly informed. There are two questions possible with quite different implications.

Question 1: Did the misinformation unduly affect the choice between reasonable alternatives?
Question 2: Given the correct explanations would the majority of experts have led a heart?

The committee asked itself Question 2 and rejected the appeal on the grounds that most experts would not lead a heart. This brings up an interesting point: a player is protected if the action taken is what the majority would do, but he is not protected if he uses his judgment to go against the majority, even if he is right and the majority are wrong, as they often are. This is largely a matter of judicial convenience which favors conventional behavior. Original thought is ever suspect notwithstanding that today’s blasphemy is tomorrow’s sermon.

Let’s consider the subsequent play. Auken won the first trick with the ♠A and advanced the ♦8. She had a second entry to her hand, so we may take it that this play was an attempt to obtain some indication from partner as to the best continuation after winning the ♥K. Welland’s play of the ♦6 was described by him as being encouraging in diamonds. He would have discouraged with the ♦T if he had known declarer could have held 4 spades. As it was he feared Auken would not switch to clubs, the suit he wanted.

If we apply the majority criteria to this explanation, would most experts given the correct information have encouraged in diamonds? No. Given a discouraging signal in diamonds, would the majority of experts with the North cards switch to clubs rather than persist in spades? I strongly feel I would have discouraged in diamonds and my partner would have switched to the ♣J, but, then, we are not experts.

Although the explanation of the bidding after 2NT was inaccurate the bidding was sufficiently informative that given a discouraging signal in diamonds, I feel Auken would have switched to clubs. She had available at the time a view of the cards in the dummy, so there was much more information to guide her than Welland had had on the opening lead. Given the encouraging signal she continued diamonds later which showed a lamentable faith in her partner’s signals. To encourage a hopeless continuation when you really want a switch doesn’t seem to me to provide sufficient grounds for complaint. Contrary to the committee opinion, I think Welland had a better claim for damage through influence on the opening lead. I like his choice, but the law doesn’t work that way. Maybe, in years to come after exhaustive computer study, a 3-card heart lead will become the universally accepted recommendation against 3NT.

All That the Law Allows
Auken-Welland have had a fabulous run recently in high profile international events, topped by their win in the 2013 European Open Pairs. It is fair to say that their success is due partly to their unusually aggressive bidding style in which many bids have meanings quite different from normal expectations. Opponents must be prepared to study the small print on their convention cards. Conservative commentators may be appalled but the law allows it. Here is an amusing example from Slutspil DM Hold 2013 reported on BBO where the opposition could claim to have suffered as a result of misinformation.

The opening 1♠ bid promised a distributional hand, and 1NT was a nebulous game force (according to their WBF convention card.) The saying goes, ‘come alive with 6 and 5’, but the lively Welland doesn’t have need for even that degree of encouragement. His hand is worth 27 Zar Points, so those who place great emphasis on distribution would not find his action in the least alarming. The red tens make this 6-loser especially attractive.

2♦ was a transfer to hearts, but Auken forgot this agreement and did not alert. Rather than reveal his fine diamond suit in an exploration of 6♦, Welland made the practical bid of 3NT. According to the BBO broadcast before the lead this information was offered.

Welland: I showed hearts     Auken: I didn’t know that. Sorry.

A diamond was led and the heart finesse lost to the ♥Q. The contract can be defeated with a switch to a low club, which would be rather obvious if the defender had known the red-suited nature of Welland’s hand. Instead, diamonds were continued twice (Welland ducking once, ha-ha), so 3NT made comfortably with 2 overtricks. One might argue that Welland had obtained unauthorized information when Auken failed to alert and bid 2NT, showing a heart stopper and a lack of support for diamonds.

Income taxes are not always fair, nor are bridge laws. Bidding 1NT, then 3NT on 1=5=6=1 is unusual. Welland was not required to reveal his holding more than he had, but if Auken had known that 2♦ showed hearts, the subsequent auction would have been much different and it is most likely that more information about the 1NT response would have been forthcoming. Likely, but not proved. Nevertheless, saying you’re sorry doesn’t seem to cover it fully, does it?  

PS I just witnessed this action on Board 30 of the USBF Women’s Final. After the auction 1NT (weak) – 3NT,  Beth Palmer led the ♥4 from ♠ 9652 ♥ K54 ♦ A4 ♣ KJ72. She gained 11 IMPs for finding the killing lead from her 3-card heart suit. At the other table the ♠6 was led and declarer, given the timing, made 2 overtricks.

The Pendulum Swings

July 3rd, 2013  ~  Bob Mackinnon  ~  2 Comments 

In the USBF Final the Kranyak team of 4 young players came out victorious against the Fleisher team of 6 seasoned veterans. When I first played a team game, an experienced teammate advised, ‘bid your games and slams, and don’t double part scores’. That was good advice, and most experts have been following that path with the result that players have been entering the auctions without fear of being doubled for penalty and games are bid on a hope and a prayer. This may be about to change due to the successful doubling of the poster boys.

As in the semi-final match against the Nickell team, the younger players had a penchant for doubling part scores for profit, although in this match the effect was not as great. Nonetheless, they came out ahead on such doubles by a margin of 37 IMPs, a significant portion of their overall margin of victory, 68 IMPs. Here is an example from early in the match. The division of sides was 7-7-6-6 making it an ideal situation for a penalty double against a vulnerable contract even at a low level.

Overcalling 2♣ used to show a good 6-card suit within a good hand, but the standards have fallen considerably as one must act quickly in case the opening bid was light, which it certainly was. With shortages in diamonds and spades, Martel could reasonably sure there would be more bidding to follow. Wolpert’s double showed affinity for the majors. Kranyak could see there was no major suit fit. In fact he could conclude that there was a high probability of a 7-7-6-6 division of sides. Leaving in the double might not be successful if South held 3 or more diamonds, a chance Kranyak was willing to take. His pass resulted in a score of +500. At the other table the auction took a more traditional turn.

Rosenberg shunned opening on a 6-loser hand that was short in the majors. Dwyer, playing Precision, opted for a lumpy 1NT. EW found their best 7-card fit, 2♥ was makeable, and Rosenberg found himself in a good position for balancing into a minor. Willenken had no option but to bid clubs. Mercifully he wasn’t doubled, however, the penalty for playing in the same suit in both directions was a whopping 13 IMPs.

Late in the match Dwyer showed the same tendency as had Kranyak in seeking a vulnerable penalty at a low level.

Dwyer’s pass of the double was based on good trumps as well as an apparent lack of a fit in the majors. Doubling on a trump stack may mean that the opponents can escape to a better strain. The division of sides was 8-7-6-5 so it was possible for EW to escape to their 8-card fit in hearts where 7 tricks were available, but they stayed fixed for a loss of 500 on the board. One could say that Martel paid the cost of opening a natural 1♣ with a good suit and nowhere to go – a rare occurrence. The doubleton kings were a bad feature indicative of wasted values. At the other table all went according to custom.

Once again Rosenberg did his bidding later rather than sooner, reaching the optimal double dummy contract in their 8-card fit while losing 9 IMPs in the process.  On Board 103 Fleisher got some of its own back by doubling part scores at both tables for a gain of 13 IMPs. Were the old dogs learning new tricks? If so, it came too late.

An Early Game Swing
The opportunities for penalty doubles are few and far between, whereas the opportunities for game swings are common. Throughout the match of 120 boards there were 22 swings of 9 or more IMPs, due to one pair bidding and making a game or slam missed at the other table. These were evenly divided between the teams. Some triumphs were due to inaccurate defence, some were justifiably bid on a double dummy basis. Board 38 provided a simple bidding problem that one pair solved and the other didn’t due to a difference in approach. I think the difference holds significance for us all as it involves a choice between bidding shape or showing suit strength.

Many would consider this a perfect auction in a 2/1 context; only the outcome was bad.
Unlucky? Both players were able to bid out their shapes without revealing the fatal flaw in the club suit. Over 2NT Martel might have opted for 3 of major, but why should he? If Zia had doubts about 3NT, he might have corrected to 4♠. But why should he? On a different lie of the cards and a different lead they might have got a magnificent matchpoint score.

There are fundamental features of the auction that need to be considered. It is a happy coincidence when a 2NT bid actually shows stoppers in both unbid suits. With 3-3 in the minors it is usual that honours in the minors be evenly divided between them. With the same honour composition the following hand is more likely than Zia’s: ♠ Jx ♥ AKxxx ♦ KQ3 ♣ Q43. Naturally one wants one’s partner to act according to what is most probable given the information one has provided him, and the ♥Q location was unusual.

Often bidding shape can help a declarer as it may give the opening leader a losing option when a weakness has not been revealed. Uncertainty can work in declarer’s favour. In this case a lead in a minor was marked and a diamond lead would have let the game through. Thus bidding 2NT had chance in its favour, but it was not sufficiently informative with regard to the placement of stoppers.

At the other table a Precision pair reached the best contract in a manner that provoked an observation from a system-sensitive commentator.

It was pointed out that Bathurst’s auction was not shape-revealing, as it was consistent with 3=5=4=1. Bathurst’s priority was to show where his points lay. 3♦ showed values in diamonds and denied values in clubs. It was more informative than Zia’s all encompassing choice of 2NT. When neither player could bid 3NT with confidence, 4♠ became the final contract.

There was difference in approach due to the fact that Dwyer’s opening bid was limited to at most 15 HCP. That put the onus on Bathurst as responder to seek the correct contract as the cards lie. Revealing shape was not a top priority as responder could hardly expect a slam to be in the making. One might reveal a 4-card minor, but where would that lead? Was that information relevant when the real choices lay between 3NT or 4 of a major? Whether or not responder was short in clubs was not the issue it might have become in a slam exploration. No, the useful information that needed to be transmitted was the weakness in the club suit, regardless of the length held. After the 3♦ bid, all realistic options were explored in a cooperative, informative manner so the opening bidder was able to make the winning choice in comfort.

It pays to keep in mind how partner will interpret one’s responses. A system is geared to the most likely scenarios, so making the system bid may actually be deceptive if the hand doesn’t match expectations.  After partner opens 1♣, natural, what is your bid on this collection: ♠ Q53 ♥ QJ43 ♦ T85 ♣ K32? In a recent club game, the winning choice was 1NT, limited, showing a flat hand, scattered values, and club support. Some players, thinking the system required it, responded 1♥, which I think was wrong. If opener has a strong hand responder will hear from him again, and the fact that your 1NT bid has implied club support will be useful in a competitive auction. It may well happen that the opposition will not take full advantage of their 8-card fit if they have one. In fact, the division of sides was 7-7-6-6 with the HCPs evenly divided, so 1NT was high enough. A 7-7-6-6 division of sides is much rarer than 8-7-6-5, but one should be prepared to react appropriately when it does occur, and not blindly follow along a preordained path. That is the example the Kranyak team has set for us.

By way of contrast a non-systemic overcall on a 4-card major (a Marshall Miles favourite) can work wonders. During the same local duplicate game, my RHO opened 1♦ when I held the following collection: ♠ A42 ♥ AKQ7 ♦ T8754 ♣ 9.  Action was called for, but there was no systemic bid available. An overcall of 1♥ worked wonders. In the ensuing auction partner raised hearts on 3-card support and the opposition misread the degree of fit in hearts. Partner was able to double 3♣ profitably on another 7-7-6-6 division of sides. No pair was able to reach the makeable 4♥.

Low Level Doubles in a High Level Match

July 2nd, 2013  ~  Bob Mackinnon  ~  8 Comments 

In the 2013 USBF Trials the young and vigorous Kranyak team came out triumphant. One of the features of their style which sets them apart from the older players is their penchant for doubling part scores, an old idea in a new setting. Over half a century ago S.J. Simon pointed out in his great book, Why You Lose at Bridge, the most lucrative doubles are those where neither side holds a predominance of power. He felt that a low level double could be taken as a suggestion to partner, so that a partner can feel free to pull the double or leave it in knowing the sort of hand the doubler was promising. Until now this idea was not taken up in the modern game. For years experts have been entering auctions on minimal values without fear of being doubled in a part score, while commentators on the sidelines have been pointing out a multitude of missed opportunities. Of course, we observers have the benefit of seeing all 4 hands. The problem is not the concept of doubling on misfit hands, but how at the table to determine when to double.

The results from the recent 120-board matches provide us with the material to study hands where penalty doubles were employed successfully. Patterns emerge. Not surprisingly the best penalty doubles come on hands where neither side has an 8-card fit, that is, on deals with a 7-7-6-6 distribution of sides. The number of total trumps is 14. We can expect such hands at a frequency of 1 in 10 deals. Another prime candidate for punishment is a deal with a distribution of sides of 7-7-7-5. One side has an 8-card fit, the other doesn’t, and the total trumps number 15. Taken together such deals occur with a frequency of 1 in 6. The occurrence is fairly low, so not a great deal of attention is given to the possibilities by system designers, leaving partnerships to come up with their own devices as the difficulties arise. A player may see warning signs in the pattern of cards in his own hand, 4-4-4-1 or 4-3-3-3 shapes, but it requires partnership cooperation to guess with accuracy the division of sides. The primary indication is the absence of an 8-card fit.

When play on Board 26 began during their semi-final match, Kranyak held a 24 IMP lead over Nickell, enough to encourage an adventure in the part score domain. Here was the auction, both vulnerable.

At the other table Frank Nickell passed as dealer but later reached 3NT, makeable on a double dummy basis.  He mistimed the play and failed to bring home 9 tricks. John Kranyak started low and found partner didn’t have a 4-card major. If Wolpert had jumped to a limited 2NT, Kranyak would have raised to 3NT, but here he passed to await further developments on a deal he suspected was of the 7-7-6-6 variety. Levin took the bait and balanced aggressively on points, not shape: ♠ K98 ♥ Q74 ♦ Q5 ♣ KJ653. There was no escape and 1♠ went down 3, vulnerable, for -800 and a loss of 14 IMPs. If Wolpert had reached 3NT he might have made it and gained 700 points in the traditional manner, so doubling 1♠ could have led to a lesser gain, but it often pays to take your plus at teams.

On Board 33 a similar situation arose: Kranyak-Wolpert could make 3NT, as Meckwell had done at the other table, but Kranyak chose to go for the throat with neither side vulnerable. He gained 11 IMPs by defending on a misfit.

Weinstein bid a robust 2NT takeout on ♠ KQ ♥ K8654 ♦ AJ975 ♣ 6, certainly nothing to be ashamed of. It was against the odds not to find a haven at the 3-level, but, unfortunately, this was one of those 7-7-6-6 deals. The main criticism I would make is that his bid was preemptive primarily against spades, a suit in which he held the KQ. In that sense he was too strong to preempt, as this increased the chances Levin would get doubled. Indeed, with nothing in spades and length in diamonds, Kranyak was delighted to double and Wolpert could pass comfortably with his 4-4-4-1 shape and values in the other 3 suits. One might even go so far as to claim this was obvious, but only if one thinks of it first. As with the previous hand, the naturalness of the 1♣ opening bid was an important feature of an auction that became competitive.

By Board 42  Kranyak led by 46 IMPs. The scene shifts to a table where both sides are playing Precision. With both vulnerable Bathurst opens a weakish 1NT with defensive values. As responder Dwyer has a good, balanced hand, but not good enough to invite game, so a perfect hand for doubling.

Meckwell’s division of sides was 5=7=7=7, so Bathurst-Dwyer had an 8-card fit in spades. At the other table their opponents played in 2♠ making. Here the uncertainty with regard to Meckstroth’s takeout reduced the temptation to find a major fit. 2♦* making does not represent a game, so Bathurst was willing to take his chances on extracting a penalty. Meckstroth went down 4, for a loss of 14 IMPs on a part score deal. He had balanced with a weak diamond holding: ♠ 72 ♥ KQ875 ♦ J843 ♣ K2. Not really a 2-suiter, is it? The hanging ♣K is a bad feature. Double dummy analysis concludes 2♥ is better, being just down 1. Of course, it would be much harder to double 2♥, a contract that might produce a game.

By Board 49 the lead was up to 63 IMPs. This board is played in a doubled contract at both tables. With a good 6-card suit, both East players opened a preemptive 3♦ on ♠ J86 ♥ T ♦ KQJ864 ♣ T3. Both Souths doubled protectively with 18 HCP and no 4-card major. Meckwell attempted a vulnerable game whereas John Kranyak tried the effect of a penalty pass. He was right, as the division of sides was 7-7-6-6, and 4♠ was too high.

The double of a 3-level preempt must cover a wide variation of hands, nonetheless it is normal for the doubler at least to have tolerance for the spade suit. For the sake of safety one might take out the double to 3♠ hoping to be left to play it there in peace. Kranyak thought aggressively. With no game in sight he passed Wolpert’s double hoping to extract a doubled undertrick or two in a part score deal. There was little chance that 3♠ would make. He judged well, finding his partner with a doubleton diamond, hence, the desirable 7-7-6-6 division rather than an 8-7-6-5 division. His expectation of down 1 in 3♦ was greatly exceeded as the contract went down 4 for a score of 1100. The key to the defence was to score 3 tricks in clubs, one by ruffing.

In order to opt for a double into game one must trust that partner’s double is backed by full values. Here Wolpert held 3 aces which provided good transportation. To guarantee full values, at times one must pass on moderate values and trust partner will balance freely when appropriate. Light takeouts preclude playing for penalties later. At the other table Rodwell took out the double to 3♠, but Meckstroth raised to 4♠, subsequently doubled, down 2 for a loss of 300. In total the Nickell team doubled at both tables lost 15 IMPs on a part score deal.

The Law of Total Tricks can serve as a guide in these situations. If one thinks one might make 8 tricks in spades, but not 9, and if the division of sides is the expected 8=7=6=5, the number of total tricks rates to be 16. Thus the opponents may make only 8 tricks in their 3♦ contract. If the division of sides is 7-7-6-6, the total tricks number 14, so if one can make 8 tricks in spades on a 4-3 fit, the opponents rate to go down 3 in 3♦.

At the halfway point, 60 boards played, the Kranyak team led by 79 IMPs, 52 of which were gained on the 4 part score doubles discussed above. The effect of these doubles might have been even greater than the numbers indicate, as there is a psychological advantage to be had if one cannot compete with the same confidence one has knowing one won’t be doubled in a part score. Could it be that the pendulum is swinging back towards less presumptive competition? The success of these penalties doubles were no fluke. In our next blog we’ll see how Kranyak on aggregate gained 37 IMPs on part-score doubles against Fleisher in the USBF Final, a significant portion of their overall winning margin of 68 IMPs.

The Great Two-over-One Debate

May 17th, 2013  ~  Bob Mackinnon  ~  21 Comments 

In the May ACBL Bulletin readers were given arguments for and against the concept of 2/1 forcing to game. Larry Cohen approved of 2/1, Fred Stewart didn’t, suggesting Standard American is better. Comparing the two is not like comparing apples and oranges, it is like comparing pizzas. Do you like pepperoni or salami? extra cheese or bacon? Nutritionally the two may be equally harmful. Cohen went so far as suggesting that all beginners be taught 2/1 methods, currently the current standard approach. Apart from the societal benefits of going with the crowd, is there any justification for doing so?

With regard to the education of the naive let’s consider high school home economics. Recently I saw on television the author of a cookbook making the claim that 70% of the North American diet consists of processed foods. Every sensible person agrees that this is an unhealthy trend as processed foods contain far too much salt, sugar, and fat, but what we know is wrong and what we do in practice are often in conflict. Now, in home economics classes, should the students be taught how to prepare a hot lunch consisting of a can of tomato soup, a ham and cheese sandwich made with sliced bread from the supermarket, finished off with a dessert of vanilla ice cream topped with chocolate sauce? I’ve enjoyed lunches like that, so wouldn’t it be mean-spirited to argue that teaching kids to partake of mainstream American fare is wrong? Not at all. Students should be taught to think clearly and to make informed decisions. Bad habits they can learn at home.

‘So,’ a critic may comment,’ you’re one of those dinosaurs from the dark ages who think women should stay at home every Sunday afternoon slaving over a hot stove while their husbands go off to play golf with the boys.’
‘Sounds great to me,’ I would concede, ‘but during my nearly 50 years of marriage I have never been given the option.’ But I digress.

To get down to basics, should beginners be shielded from conventions and led to believe that ‘natural is best’? Cohen goes rhapsodic on the topic, but we all know that the requirement to be natural is technically disadvantageous. Naturalness should not be an aim in itself. Consider the following combination in which to respond with a natural 2♣ bid is not only wrong, it is downright perverse.

A bright beginner is entitled to ask, ‘why must I bid 2♣ when I know I want to play in hearts? He or she may wonder, ‘isn’t it better to bid 2♦ where most of my points lie?’ Or, ‘why must I risk a Semi-Forcing 1NT when I want to be game?’ Is it the time for the instructor to backtrack and talk about ‘support points’? Rather it is a good opportunity for the teacher to introduce the idea that 2♣, like Stayman, is totally artificial and asks for more information from the opening bidder. It is not a radical new idea; for good reason the Drury convention, named after an esteemed member of the ACBL Board of Governors, has played its part in American bridge for over 50 years. Today his convention is needed even with an unpassed hand. Accepting the idea that 2♣ doesn’t say anything about clubs makes sense, rendering the slam much easier to bid. In fact, this combination was bid to 6♥ using a system within which 2♣ was defined as a totally artificial invitational bid without reference to either clubs or hearts. I think young players love conventions, especially the ones that are useful, crystal clear, and part of a pattern.

It’s been a while since I have seen a reference to a ‘biddable suit’. Most of the time long suits are biddable, but freely bidding a topless suit gives the wrong impression entirely. When responder freely introduces a suit, a minor suit especially, partner is entitled to expect values in that suit. The absence of honors could be advantageous in a competitive auction if the opposition is deceived, but in a constructive mode it may turn against the pair looking for slam. On the above sequence the responder will be reluctant to invite slam when he has a minimum for his 2-level response and knows his club suit has doubtful value, when, in fact, the lack of wasted values in clubs is a prime attribute.

1NT Forcing
The difference between 2/1 and Standard boils down simply to the use of 1NT Forcing. The wider the range, the less information the bid contains. In 2/1 the normal range is 6 to 12 HCP; within that range there is a wide assortment of hands allowed. If the bid is ‘semi-forcing’ as Cohen advocates, opener is allowed to pass with a flat minimum. In a contract of 1NT there is value in the uncertainty which works in favour of the declarer. This can be said of any contract: the more the uncertainty in the bidding the greater the chances of making it once arrived. Because a vulnerable game needs in theory only a 38% chance of making to justify bidding it in a team game, it behooves a partnership to blast away without delicacy to such games. Keep it simple, bid what you think you can make, and worry about it later.

Fred Stewart likes to think of bridge as exercise in logic, so he prizes accuracy and exploration. He states, ‘one problem with 2/1 is that responder can’t locate his side strength with a game invitational hand.’ Well, as Cohen suggests, delicacy in the game zone is not needed, so one should just go ahead and bid games hoping for a good fit or a bad defence. He mentions the success of Meckwell in this regard, but fails to mention they play Precision which allows for an opening bid on 10 HCP whereas 2/1 doesn’t.

After a 2-level response in Standard a partnership may decide to play in a suit contract at the 3-level. With 2/1, 3-level suit contracts have been removed from consideration, the purpose of 3-level suit bids being to exchange information in order to determine the chances in a slam contract. Paradoxically, bidding at the 3-level which reveals strengths and weaknesses may result in a reduction of one’s chances of making close games or slams. Consequently, players are reluctant to employ descriptive 3-level bids just on the off-chance that a slam may make. So, although the bidding space has been freed up for this use, players don’t like to use it. Thus, minor suit slams are very rarely pursued, 3NT being the contract of choice. In addition, bids between 4♣ and 5NT are seldom utilized in a natural sense. Cuebidding controls has become a neglected art. ‘Last Train’ is a control bid without a control! Precipitous ace asking bids have taken over the territory, and for good reason: if someone has to come clean eventually and cough up real information, it is better if only one partner does it, rather than both.

A Better Way
There is a significant difference between 2/1 and Standard on the one hand, and Precision on the other, in that many Precision opening bids are limited to at most 15 HCP. This is critical even when bidding slams. Here are 2 examples from recent games at my club involving Precision with a nebulous 1♦ opening bid where the length of the diamond suit may be a little as 2 cards. This is unnatural, nonetheless, the opening bid is the same 1♦ in all methods.  What follows is quite different.

The opening bidder had substantial values, a maximum Precision 1♦ opening bid under the definition. It was more or less incumbent upon me to show a maximum by a splinter in support of my partner’s spades. Two trump honors with 6 controls are worth an equivalent of 20 HCP. John upgraded his hand with its singleton in diamonds opposite the advertised singleton in clubs, but what natural, descriptive bid could he make? None. His solution was to cue bid 4♦ presumably to show a control, but really it was more of a mark-time bid awaiting developments. With an unlimited hand responder was in charge of the auction at this point, a situation made possible by the original upper limit on my HCPs, so he didn’t need to share the decision-making responsibilities, so didn’t need to make a descriptive bid to put me in the picture. His aim was to extract information, not give it. So, a unilateral RKCB easily led to a good slam on 24 HCP.

Let’s consider these results from the point-of-view of all those who didn’t reach the slam. Their failure cost them a mere half-a-matchpoint. This is hardly something one worries about, but more than that, why risk a very bad score when one can stay with the crowd in comparative safety? This approach represents mediocrity for its own sake. Fine, but let’s not pretend that 2/1 is a good system for getting to slams. In the same vein, here is a grand slam from the next week’s action missed by all.

The bidding is simple if the opening bidder is allowed to make a descriptive splinter bid on his 6-loser collection. The number of HCP is non-factor. When a fit comes to light the holder of a 6-loser hand should take some encouraging action. In the 2/1 system where 1♦ is unlimited, a splinter to 4♣ seems rather to overstate the condition. In so doing my Precision partner showed courage, yes, but also judgement as the ♦J and the ♠ T can be seen to be assets more valuable than their HCP assignments indicate. The good trump fit, the potential for ruffs, the long suit that might be developed, the control in hearts all point towards an exceptionally good mesh. It is critical that opener was marked as having less than 16 HCP – he wasn’t claiming slam potential for his own hand. After the announcement of shortage in clubs, responder went through the motions of RKCB to determine ‘how high?’  Finding partner without the ♣K was a revelation that made it especially easy to bid the grand slam.

Conclusion
Bridge is a game of probabilities, not certainties. Slams are rare and competitive auctions are becoming more and more frequent. If one is to consider the practical advantages of a system it is necessary to include not only what the bids tell you, but also what they hide. Double dummy accuracy and full disclosure are not the only virtues. A system should be adaptable, logical, and easy to use. Sticking to a requirement of naturalness complicates matters immensely; it is much easy to be able to ask a direct question and receive a direct answer, than it is to fish around in murky waters.

One last point: 2/1 is not a single system, it is 3 different systems that vary with the seat position. It doesn’t apply after interference. A great number of unrelated artificial bids are needed to patch over the flaws. This is a recipe for confusion.

Restricted Choice: What Lies Behind It

February 25th, 2013  ~  Bob Mackinnon  ~  5 Comments 

This blog is in response to Linda Lee’s post Do you “believe” in Restricted Choice?

Bayes’ Theorem always applies where play probabilities are involved. Restricted Choice as generally understood is an application of Bayes’ Theorem where there is an equal chance of selecting 1 of 2 equal honor cards when following suit. The probability of having chosen that one particular card over the other is ½. There are cases where a player chooses 1 of 3 equal cards, in which the probability of choosing that one card is 1/3. These can be small cards, but we don’t think of that process as a ‘restricted’ choice, although Bayes’ Theorem applies equally to that situation.

By saying there was an equal chance of choosing 1 of 2 cards is equivalent to saying the choice was made randomly without bias. This is a theoretical assumption. Maybe some players will prefer playing the queen instead of the jack because they feel it is more likely to influence declarer’s play adversely. The choice is not completely random. Declarer must judge on the basis of experience whether he believes the choice is random. If not he must assign his own best estimate of the chances of the queen versus the jack, say, 2:1. He still applies Bayes’ Theorem on the basis of that bias.

There is sometimes a case for assuming a player must split his honors in front of a tenace in order to give declarer a guess on the next round. Does one always assume the defender will make the correct play and split? That is an interesting situation. If one believes a defender will always play one card rather than the other, or at the very least have a preference, then there is information to be got from the play other than a simple reduction based on random selection.

Dropping the Jack from Queen-Jack
Suppose declarer holding AT65  opposite K987 plays the ace and the jack drops from the RHO. What are the probabilities the jack was a singleton rather than from QJ? Let’s look at a particular situation and put aside for now consideration of the a priori odds. Declarer reaches 4♥ and a spade is led. They prove to be split 4-4. Declarer plays the ♥ A, LHO plays the ♥ 2 and the RHO drops the ♥ J. What are the odds the ♥ J was a singleton?

There are 2 cases to consider: Quwx opposite J  (a 4-1 split) and uwx opposite QJ. Here u,w,x represent the missing low cards that can be freely played without loss.

Case 1

Case 2

The distribution of the minors is entirely unknown and assumed to be the result of a random deal. The number of combinations on a 6-7 split outnumber those on a 5-8 split in the ratio of 4 against 3, giving Case II an edge in that respect.

The play of the ♥ 2 was a choice of 1 of 3 equals so the probability of the ♥ 2 being chosen at random was 1 in 3. For Case I the play of the ♥ J was forced, probability of 1. The one remaining 3-2 combination is Case II with uwx opposite  QJ. Again, the play of the ♥ 2 was a 1 in 3 chance, the same as with the 4-1 split. The play of the ♥ J was a 1 in 2 chance, as the ♥ Q could have been chosen equally on a random basis. Overall the chance of the appearance of ♥ 2 – ♥ J is 1 out of 3 for the 4-1 split and 1 out of 6 for the 3-2 split. The ratio of the probabilities on the play is 2:1 in favour of the 4-1 split.

We now combine this with the number of combinations of the minor suits yet to be played. The result is 3:2 odds in favor of the 4-1 split. As Reese may have put it, the odds are better that the jack was played of necessity rather than it resulted from a particular choice among alternatives. So on the next round of hearts declarer should finesse for the ♥ Q with a great degree of confidence.  The rule of ‘eight ever’ applies.

The a priori Odds
These give slightly different numbers but the resulting decision is the same because the vacant places are evenly distributed between LHO and RHO. Here we don’t assume any cards have been played outside the heart suit, and that there is no clue as to how the other 3 suits are split.  Outside hearts there are 21 cards in the defenders’ hands.

Case 1

Case 2

Based on the (unrealistic) a priori conditions the odds in favor of the particular 4-1 split after the drop of the ♥ J is 5:3. The assumptions are unrealistic as we always know more than the ‘know-nothing’ odds assume. However, the method is the same and the conclusion is the same, the ♥ Q is more likely to be with LHO by a wide margin, 5:3 against the previous 4:3 where the spade suit was counted out.

The Specious Argument
Now let’s examine the argument based on a table of a priori probabilities that begins with,  ‘the 3-2 split is twice as likely as the 4-1 split.’ The table of odds states these probabilities: 4-1: 28.26%;   3-2:  67.83%. The figures include the number of possible combinations: 10 for 4-1 and 20 for 3-2. That is a 2:1 ratio in favor of 3-2. If we consider the probability of one particular 4-1 split and one particular 3-2 split we find the percentages to be 4-1: 2.826%, 3-2 3.3915%. The ratio is 6:5 in favor of 3-2, as reflected in the Others Weights given above. So comparing one 4-1 split against one 3-2 split is quite different from comparing all 4-1 splits against all 3-2 splits. The 2:1 odds that David G. quotes are largely, but not entirely due to double the number of combinations available for the 3-2 split. His argument is false when one is comparing just one combination against another.

One can say with greater accuracy, ‘3-2 splits are more likely than 4-1 splits largely, but not entirely, because there are twice as many of them.’ The play of the cards eliminates some combinations that were included in the a priori tables, and that basically is why the a priori odds aren’t an infallible guide, and certainly aren’t accurate mathematically after cards have been played.

Probability of Distribution Patterns
The same is true of the comparison of 4-3-3-3 shapes and 4-4-3-2 shapes. Table I in the Official Encyclopedia of Bridge (1984) shows both the total percentages and the specific percentages. We all know that 4-4-3-2 is more probable than 4-3-3-3 at the beginning (or rather before the beginning), however, one particular 4-3-3-3 is more likely than one particular 4-4-3-2. That is, 4=3=3=3 is more likely that 4=4=3=2. If one is down to a choice between the 2, the a priori odds favor the 4=3=3=3 (2.634% versus 1.796%).  So one can say with accuracy, ‘4-4-3-2 shapes are more likely a priori than 4-3-3-3 shapes solely because there are one-and-a-half times more of them.’

Similarly one sees from the table that 5=4=2=2 is more likely than 5=4=3=1, even though there are overall more 5-4-3-1 shapes than 5-4-2-2. This is the basis for the argument that as play progresses, if one has to choose one particular shape over another, always choose the flattest shape regardless of the a priori odds. (Bob’s Blind Rule). There are more 2=2 combinations than 3=1 combinations, and 3=3 combinations than 4=2 combinations.

Matchpoints and Democracy

February 20th, 2013  ~  Bob Mackinnon  ~  3 Comments 

The matchpoint game is the most democratic form of bridge. Like it or not one finds oneself thrust into a mix of humanity of various abilities and mistaken beliefs. It is reminiscent of the week I spent in a hospital bed with a broken leg (my leg not the bed’s). There was ample time to observe a part of the world with which I had previously not been in close contact. We in Canada are very lucky to have a universal health care system, at the core of which are a group of hard-working professionals who have recently immigrated from all over the world to help us through difficult times and share in our democratic way of life.  I remember especially the Philippina who cleaned toilets 8 hours a day so that her 3 little daughters would have the chance of a better life in a colder climate. Like the surgeon, she is a necessary part of the system, a fact established by Florence Nightingale during the Crimean War.

On my last night in the hospital the bed next to mine became occupied by a young roofer who had had a 3-hour operation to restore knee ligaments torn during a foolish prank. Of course, it was the other guy’s fault. Who am I to scoff – wasn’t my predicament the result of a moment of careless inattention at the top of a step ladder? The next day I couldn’t help overhearing the conversations with his visitors: a comical brother, his bossy mother, his wayward father, and 2 dazed girl friends with whom he was been sleeping, their visits well timed so as not to overlap, his brother keeping an eye on the parking lot below just to make sure there wasn’t a further accident. These people live in a world quite different from mine. During one visit I was amazed to learn a woman can get a birth control rod with a 5-year warranty stuck in her arm. Was it 5 or was it 3? I sure hope she got it right.

Bill Clinton, twice elected president of the United States, once said that the American electorate always makes the right decision. Well, he would, wouldn’t he? (What does Al Gore think?) The theory is that the great mass of ignorant voters will split the vote evenly between Democrat and Republican, leaving the discerning few to decide the election after due consideration, presumably after having paid close attention to the boring TV debates. With regard to the numbskulls at the next bed, if the 3 males voted Republican, and the 3 females voted Democrat, that would leave my vote the all-important deciding one. It’s not a theory in which I find comfort – what if they all voted Republican?

The reader can see where I am headed: matchpoint scoring is like a democratic election. Just as the Wall Street banker living his golden pavilion penthouse has the same one vote as his doorman, a frightening concept to some, a false hope for others,  so too a humble +50 may carry the same weight as a stupendous +2220, and there are more of the former than of the latter. On every board each individual by his actions ‘votes’ for the best score. Some make a bad choice, some make a good choice – usually those whose actions closest conform to reality. Your score is determined by where you sit in reference to those diverse outcomes. It is normal to lie above the majority of the players who are worse players than you are, and below the majority of those who are consistently luckier. In other words, most of us belong to the middle class. The process is subject to random fluctuations, but over several boards an averaging process takes effect, and one will normally arrive at the appropriate standing in the end. If one makes consistently sound decisions one can expect to do well. Sometimes the worst pair wins the session, but seldom does the best pair come in last. There is a distinct bias towards excellence.

In the previous blog I described how my partner played in 2 slam contracts and scored tops. In the end we achieved a mere 45% result overall. Terence Reese once warned against being overly concerned with pairs who outscore the field on isolated boards – these are not the most dangerous rivals, he noted. The best pairs work hard for their average plus scores and let the tops take care of themselves. The so-called swinging pairs give away as much as they steal. That being said, it can be annoying if a pair does the right thing against you when most of the field gets it wrong. Here is an example.

As he put down the dummy, Roy commented, ‘I know we have a 4-4 fit, but with 29 points you will usually score the same number of tricks in no trumps’. How true, as on a normal diamond lead Ewa had no trouble scoring 11 tricks to share a top with one other pair. All others were in 4♠ scoring the same 11 tricks. To add insult to injury, the spades split badly. Well, one might think that it was unlucky for us to play this particular hand on this particular round, but that would be wrongheaded. We should accept there is a great deal of randomness in the game, and not only in the lie of the cards. It is a game of probabilities in which good and bad things happen at random beyond our control.

As Nietzsche noted, winners don’t believe in luck. Some losers bemoan the effect of chance. We hear statements like, ‘if I could exchange the ♦7 in dummy with the ♦2 in my hand, I would have made it,’ or, ‘you were lucky dummy came down with such good trumps.’ Such statements border of self-pity. Why should we expect justice on every hand? The fact is that randomness is an essential feature of environment in which we operate. The player who acts against the field may gain on any particular hand, much to our annoyance, but by acting in this manner he gives us a chance at an undeserved bonus.

Defensive Signal
The killing opening lead has been made the subject of 2 books by David Bird and Taf Anthias which provide a survey of results from computer generated hands. Which lead is best when playing the hands double dummy? Of course, there are cases where the standard opening lead will not prove best. The idea is that by studying these exceptions a player may gather a feel for when on opening lead to depart from the norm. As one of our club members remarked, ‘how can you tell when partner has made an unusual lead?’ This gets to the heart of the matter of informing partner.

The common approach is to plug away unimaginatively on defence doing nothing unusual. Most likely there will be others doing the same. By falling in with the majority of players with your cards, you ensure a score somewhere in the middle.  Ayn Rand worshippers might consider this a major flaw in the matchpoint approach because it bears the taint of socialism. One doesn’t deserve a reward just because one has plodded along within the guidelines of mediocrity. Those who deserve reward are those who separate themselves from the masses. That’s the elitist creed as practiced by the Masterminds.

The Mastermind prefers an active approach where pressure is placed on the apparent weak spots, which Bird and Anthias attempt to reveal. Most players realize that if their partners must carry the bulk of the defensive load, it behooves them to try to cater to partner’s best assets on the opening lead. It may be the last time they will be on lead, so they try to make the best of it. Players generally realize that if they have most of the missing HCPs, they should be alert to the possibility of an unusual lead. On the following deal just in case partner had nodded off I left nothing to chance.

After 2 passes North opened 1♣, so it was probable that she and I held the majority of the points between us. I estimated that our partners most probably held 6 HCPs each. As you see this guess was accurate. I bid 1♦ as lead directing. Holding the vast majority of points I could direct the defence from an advantageous position. Of course, if partner had a major to show he could still bid it. The ♦9 was dutifully led, taken by the ♦K. Do you see any hope of beating 1NT?

At the table I switched to the ♥J. Declarer ducked, a mistake, so continuing with the ♦A and a low diamond was all that was needed to sever his communications and achieve the excellent 75% score for +100. What do you think went wrong?

Like Hamlet with dagger poised above the back of Claudius knelling in prayer I began to have second thoughts. Partner had signaled encouragement, so could it be he had excellent hearts? I wavered, then continued foolishly with ♥A and the ♥2. This had the opposite effect to the one intended, as South, thus helped, scored up 8 tricks, a top for him, a bottom for us.

Signals generated by selective carding are the way defenders exchange information. In the absence of a clear signal a defender plans according to what is most probable given the information contained in the bids, what he sees in his hand, and what has emerged in the dummy. It is my contention that partner should not have signaled encouragement with ♥Q75, no matter what he thought I held (he envisioned AJTx). One should indicate what one has, not what one hopes partner has. When the ♥J held the trick, it was obvious West held a high honor in hearts, but there was no need to rush to cash it. So, unless the message is urgent, a signal shouldn’t tell partner something he knows already.

A redundant signal contains very little information. It is like coming home dripping wet and telling one’s wife, ‘I forgot my umbrella.’ Maybe she’ll say, ‘oh, is it raining?’ but an understanding wife will say, ‘Stay there and I’ll bring down some dry clothes before you catch your death of cold.’ A good partner is like that. They can skip the hot soup bit.

One further thought on this hand: it shows I am not a true Mastermind. The 1♣ bid is the most suspect of opening bids.  Rather than thinking defensively from the start, I should have bid 1NT without a club stopper and let the opponents worry about the defence. Scoring 120 our way would have tied for top. Truly, it’s a bidder’s game, besides which it is easier, and sometimes merciful, if one player takes on the heavy burden of worry for both. One head is better than two, as the errors are reduced at least by half.

Too Scientific?

February 19th, 2013  ~  Bob Mackinnon  ~  1 Comment 

Bidding to a contract is a process. At each step more information is made available. At each turn one may ask, ‘do I have enough information to place the contract with confidence?’ If the answer is ‘yes’, then one goes ahead and bids what one thinks is best. Of course, that is a judgment call based on present conditions. Extending the bidding process will get you more information, but will that information increase the chance of your arriving at a better contract, and, having done so, will the additional information exchange decrease your chances of achieving a high score?

The ACBL Player of the Year for 2012 is Zia Mahmood, the fifth time he has earned the award. In an interview published in the ACBL Bulletin he criticizes himself for being ‘too scientific’ on this hand from the Blue Ribbon Pairs: ♠ AKQ982 ♥ K8 ♦ — ♣ AKQJ2. As a scientist I resent it when players use the term ‘too scientific’ when they mean ‘too chicken’. His LHO opened the bidding 1♦ and his RHO bid 1♥. In retrospect Zia thinks that with his cards he should have done what Frederic Wrang did, overcall 1♠ , then bid 6♣. Zia, no hand hog he, is willing to let his partner make the final decision if the situation warrants it. Partner holds ♠ T73 ♥ T74 ♦ J964 ♣ T98, and will correct to 6♠ . There is an entry to dummy in clubs for a heart play towards the King.

Wrang practiced good science when he provided the relevant information and his partner made the choice. The opposition’s bidding increases the probability of finding a useful black card in the dummy, so it is against the odds that partner has a totally worthless hand; even if he has, a heart might be led solving that problem. All in all, given the information he had at the start, Wrang would have been unlucky to go down in 6♠ .

Taking Everything into Account
Very often we read analysis based on a discussion of what can go wrong. A better question is:  what is the probability that something will go right? Here is a hand that came up on the last board of my last matchpoint session.

Looking at both hands, one sees that 6♥ is hopeless on a diamond lead, but how probable is it that a diamond will be led? I maintain a diamond is unlikely to be led unless the opening leader holds both the ace and the king. Otherwise, in the miasma of uncertainty a passive lead is probable. Let’s say the odds of a diamond lead are less than 1 in 3.

If I could have seen partner’s cards I might have bid 6NT to decrease the odds of a diamond lead to the theoretic limit of 1 in 4, but that would constitute negative thinking, more appropriate to IMP scoring where the overtrick is not important. Making 510 in 4♥ was worth a undeservedly high matchpoint score of 5 out of 12 as some were playing in 3NT taking just 12 tricks. Making 1010 in 6♥ was worth 10 out of 12.

A further observation on the bidding: 4NT was a bad bid in theory, the 5♦ response giving my RHO the opportunity to double for a diamond lead. We would be held to 11 tricks, a  bottom on the board. The potential disadvantage bypassing 4NT and blasting to 6♥ is that it increases the chances of the lead of the unsupported ♦A. The opening leader may feel the need to take his trick before it goes away. So, although there is a risk attached, 4NT as a false indicator of balanced power may act as an inhibitor.

If the reader feels that one shouldn’t risk a score of 5 in order to achieve a score of 10 when, in theory, there is an obvious risk of scoring zero on a diamond lead, he should consider a posteriori odds based on what actually happened. The chance of getting a diamond lead was 1 in 13. Yes, of the 12 other pairs in the field, only one was held to 11 tricks –  all others made 13 tricks. If one were in 4♥ and got an inspired diamond lead, one’s score for 450 would have been 1/2 . So, in effect, bidding slam risks half a matchpoint to make 10, because a diamond lead would be disastrous in either case.

The Mastermind
As soon as he gets a good feeling about the hand, the average player is ready to launch into some form of Blackwood – ‘decide not describe’ being the prevailing attitude. Why? The reasons are partly psychological, and partly practical. Players learn that bad bidding pays off due to the uncertainty it creates in the opponents’ minds, especially for those who tend to be passive in their approach through fear of giving something away. The Mastermind is the type who takes things into his own hands early in the auction and places the contract after a minimal exchange of information. He takes his partner out of the loop, because he feels his educated guess will prove better than a partner’s reasoned conclusion.

Where do we draw the line? How much information is enough information? If one considers the Zia hand described above, a successful approach may have been to overcall 6♠ immediately. One might even get doubled. That would rule out getting to 6♣ when that is right, so we can’t say we condone that approach, successful as it may turn out. On a lesser hand where slam is unlikely, players who concentrate on spades and neglect the minors are following the expert’s path, they think, because a spade game both scores more and needs less to make. Slam is different, as merely getting to a makeable slam usually scores well. An inferior game may be reached when it turns out slam in a minor was there for the bidding, but the cost of missing it is minimal at the club level. The players assume that the normal conditions apply and lazily follow the well-beaten path in the game zone leading to 3NT or 4 of a major without looking for the special circumstances that may turn out to be slam-favorable.

Mastermind or Scientist?
Because of the scoring rules bidding systems are eschew from the start tilting the auctions in preferred directions. Information provided is biased towards reaching a preferred goal. Players may add their own bias, as I did on the following deal.

After partner opened 1♦ I felt the primary feature of my hand was the fine club suit. The hearts didn’t appeal, and the hand was worth just the one bid, which served to limit the HCP and described the shape if not the components thereof. Partner did the right thing given what I had told him, but much to my chagrin 3NT was doubled by my RHO. My philosophy is, ‘if you have made the bed, you get to lie in it,’ so I passed and faced the lead of the ♦T, which held the trick. There followed a long pause during which my hopes rose immeasurably. Could it be? Yes! The opening leader switched to a spade, ducked to the ♠ J. When the smoke had cleared, I made 9 tricks, scoring +750, for a miracle top.

 That’s not the whole story or even the most interesting part. Most played in 4♥ from my direction. With the ♣K offside that contract can be defeated easily enough on a diamond lead, however, 3 declarers did escape that defence. What about that opening bid? The control-rich hand is worth more than 19 HCP, more like 23 HCP, so the proper opening bid is 2NT.  This solves a potential play problem by placing declarer on the proper side after 3♣ Stayman from partner. I suppose some who went down in 4♥ felt they didn’t deserve their bad score because they had done nothing wrong, but I think they were unjustly rewarded for joining the herd who rigidly followed the rules by opening 1♦. On the other hand, those who opened 2NT and made 4♥ declared from the right side deserve a reward for their initiative.

A Mastermind thinks his judgment is better than a set of system rules that poorly fit his current situation. It’s not like choosing on which side of the road one prefers to drive today. The late Marshall Miles was famous for suggesting bids that others would miss, and he always had a good argument for doing so. In many aspects of partnership agreement it may pay to be flexible. This reduces the information content involved but that may not be important if the final decision is to left to the player best suited to making it, himself. That approach doesn’t work so well if both players are striving to be masterminds; someone has to be reliable and tolerant.

I saw recently a documentary on the Lindbergh kidnapping in which an ‘expert’ speculated that Charles Lindbergh himself masterminded the crime. Unbelievable! But it turns out that he was a perfectionist, a pro-Nazi racist, and a non-believer in the democratic process, who after the age of 54 fathered 7 children in Germany with 3 mistresses. The secret families weren’t revealed until 2003. One is reminded of another genuine hero, Thomas Jefferson, who also had an emotionally starved relationship with his numerous illegitimate offspring. I mention this as a reminder that although we may pride ourselves on our reasoned, technically sound, and largely successful approach to the external world, our actions are sometimes ruled by undercurrents of emotion that defy logic. Bridge is a pursuit during which we can demonstrate our rationality, but that is only a part of the game. Most of the time we are sane, but there is always a finite probability that even the best players will occasionally fall off their perch for no apparent reason. Luckily, it’s only a game.

Partnership Matters
It is in the nature of things that many of the best partnerships consist of a combination of 2 types, the Mastermind and his Servant. As Terence Reese once commented, don’t underestimate the value of reliability. The flamboyant adventurer need a reliable partner on whom he can count to provide that little bit of undisclosed extra that makes his gambles pay off, a partner who won’t push too hard for fear of getting too high. On the other hand the cautious underbidder needs an active partner to push things along. This is true especially of pairs who play a ‘natural’ system where both players are allowed to made judgmental decisions as the auction progresses.

What happens when 2 highly aggressive players who are fond of making unusual pressure bids, i.e. masterminds, get together? Will it be chaos or can they learn to get out of each other’s way and function as a smoothly operating unit? The latest experiment to watch will be the new pairing of Brad Moss and Joe Grue. Brad Moss became ACBL Player of the Year when playing with the careful Fred Gitelman, and Joe Grue became a feared opponent when playing Precision with Curtis Cheek, a system that imposes a certain degree of discipline. Their maiden voyage in the 2012 Buffet Cup was not a great success when they were outplayed by Nicola Smith and Sally Brock on this deal from the BAM 7-board segment won by Europe 3-1.

Here we have the evidence of a moment of madness. Like Hitler’s invasion of Russia, Grue’s 6♦ bid was far too ambitious. Moss failed to come up with ♣A, along with all the other good stuff. I suppose Brad got to feel something of what Field Marshal Paulus felt at Stalingrad about the paucity of the resources being provided. Sally and Nicola did much better, sedately stopping in 4♠ , making 10 tricks. I imagine they were surprised to win a board that appears routine. Can we attribute the loss to Trendafilo’s innocent 2♣ overcall on ♣ AK8753 which had the effect of a red flag waved in the face of a bull? Just joking. We shall follow the Moss-Grue development with interest to see how they handle the problem of sharing the captaincy.

Mixing It Up

February 11th, 2013  ~  Bob Mackinnon  ~  5 Comments 

Getting into the bidding with a weak hand can cause confusion, and if you can get partner involved, so much the better, confusion-wise. Some believe that distribution is everything, so they will enter the auction on topless suits. ‘I have never seen a 6-card suit I didn’t like’ is their motto. Bidding in this manner reduces the information content of their bids, but that is a small price to pay in their way of thinking. If the opponents are misled, so much the better, as there are 2 of them and only one partner.

The aim of undisciplined preemptive bidding is to have the opposition play in the wrong contract, or to misplay the hand if they reach the right contract. There is an art to this. You mustn’t bid too high, and you mustn’t bid too low. Your aim is to give the opponents a losing option. If you don’t accomplish that, then not only is your effort wasted, it may also aid the opponents in their quest for a good score against you.

One of my rules is: don’t preempt if you have more points outside your long suit than you have within it. So it was with grim satisfaction that I witnessed an undisciplined preempt from my partner that got us the shared bottom it deserved. His second seat bid of a weak 2♦ was based on ♠ AK ♥ 85 ♦ Q96532 ♣ 842. His RHO balanced with 4-4 in the majors and the opponents reached 2♥, their best contract. I raised to 3♦ on ♠ T752 ♥ 643 ♦ A7 ♣ AKT6, a good sacrifice at -50, but a shared bottom, as the deal had been passed out at most tables. Missing the AK in both black suit, the opponents were not about to be pushed to the 3-level.

In a recent issue of Bridge Magazine, World Champion Sally Horton commented that her late husband, the British expert Raymond Brock, felt that the most effective preempts were made in 3 of a major or 4 of a minor, and that her experience has borne this out. Such proved to be the case when later in the session, both vulnerable, my partner preempted to 4♣ over 1♠ on this collection : ♠ Q94 ♥ 5 ♦ J ♣ K9876542. This caused enough confusion to get away with, a rare occasion where -200 represented a good matchpoint score. If the opposition had bid to 4♥ they were in trouble on the 5-1 split, and the LHO was reluctant to raise spades on ♠862, so the ♠Q played its part.

Consider what to bid on this hand, ♠ 3 ♥ 4 ♦ T86542 ♣ JT874, after partner opens 1♣ and your RHO doubles. It seems to me there are 2 options, ‘pass’ because you have nothing, or 2♦, for the same reason. Our opponent chose a middle path, not the best choice as so often the case. Look at the deal from our point of view.

 Before the opening bid on my right I was pondering the best way to approach this 3-loser hand. I had decided to open 2♣ to find out first how many controls partner held. 6♥ was my primary target. I was somewhat surprised to see my RHO open 1♣. Much as I hate takeout doubles dominated by a long suit, this hand did provide an alternative to hearts in the form of a good 4-card spade suit. Over 3♣ Jack bid 3♠, guaranteeing a 5-card suit. After RKCB revealed the ♦A, it was easy enough for me to bid the Grand Slam with confidence. I expected an average result, as it was possible we could make 7NT if partner held the ♥Q. It came as a surprise that only one other pair managed to get as high as 7♠. Definitely North had his 1♣ bid (14 HCP and 3=4=3=3 shape), so what happened?

My feeling is that the 3♣ preempt helped us immensely, as it gave Jack the opportunity to show his 5-card length. If my LHO had passed, a jump to 2♠ would not have guaranteed a 5-card suit. The temptation to bid an informative 3♥ was there, placing the auction in a cooperative mode when really we do best if the doubler can take charge and extract information from his partner. I conclude that the best action by South was to pass. As is often the case, bidding on nothing does very little to hinder determined opponents, and may help them. Doubt must be genuine to be effective.

An interesting point in the play of the hand arises. The ♦K is led to the ♦A in dummy. What is the best way to go about making 13 tricks? Should you start with hearts or with spades? It seems safe enough to start with the ♥A and a low heart to ruff. On the second heart the preemptor ruffs with the ♠T. You must overuff, so what now? Do you play for spades having been dealt 2-2, so play for the drop in spades? Well, the preempt has been informative. It is most likely that the cards are divided 3=4=3=3 in opener’s hand and, therefore, 1=1=6=5 in the preemptor’s. It follows that declarer must immediately finesse the ♠9 through the opening bidder in order to bring in his contract. A second finesse will be needed. Note that if the spades were split 2-2 it is most likely that the honors are split (in accordance with the law of restricted choice), so the same finesse is indicated, although it is not as urgent.

In the old days it was claimed that bad bidding demands good play, and such was the case on the next hand, although bad defence was required as well. I suspect this was always so.

At matchpoints 3NT is the obvious spot, but Jack has been playing a lot of team games recently in preparation for the Regional Knockouts coming up. When he went bypassed 3NT with a bid of 4♣ there was nothing to do other than blast to slam. With only bad bidding to go by, the opening leader chose to lead her fourth highest from a suit headed by a queen.  Hurdle #1 was cleared with flying coattails when the ♠J won in dummy. A plan was formed. Jack played off 4 rounds of clubs. He eliminated the majors and led from ♦ 765 towards the ♦AQ4. North played the ♦8, dummy, the ♦4 and South, the ♦T, thereby forcing herself to lead back into the ♦AQ tenace. South had misdefended earlier when she discarded the ♦3 from ♦KJT3, guaranteeing the endplay.

The perils of the cooperative approach to slam bidding when one player should be the captain were demonstrated a week previous when, using Precision techniques, I was able to score a clear top by reaching a slam missed at every other table. Perhaps 2/1 players might like to try their hand at this combination.

The auction features a myriad of asterisks, but is not difficult to grasp. Basically the stronger hand asks questions about controls and the weaker answers as best he can. 2♦ is a limited NT bid, 8-10 HCP. 2♠ shows a spade suit and asks for support. 3♥ shows 3-card support the transfer allowing opener to ask how good the spades are. 4♣ shows a control honor. 4♦ asks for a diamond control; 4♠ shows the ♦K. 5♣ asks, how good are your clubs? 5♠ reveals the ♣A.  It was at the very end that I made the mistake of bidding 6♠ – the Matchpoint Devil made me do it. The safest contract is 6♦, and there was no need to risk a slam contract that no one else will reach. A bid of 6♦ would have given responder the option of bidding 6♠, but here he would pass as I had bid his best suit.

The main weakness of the asking bids employed is that distribution is left somewhat a mystery until the very end when responder has a chance to get his 2 cents in. With a distribution of 3=3=4=3 two losers could be disposed of on the 4th and 5th spades.

Let’s now speculate on how the hand might be bid using 2/1 methods. Presumably, even today, no one outside China will open 1NT. So we start 1♠ – 2♠. OK, I give up. I can’t see how to reach 6♦.

Highland Village Verses

Fair Mary MacNaughton
Will do what she oughtn’t.
Her head there sits on it
A tam not a bonnet.

She is my blossom,
I am her bee.
She is my apple;
I am her tree.

Ten toes point towards Heaven;
Ten toes point towards Hell.
Which way we are headin’
Nae-body can tell.

Stillman Andy MacVey
Lets a quart go astray,
As the Good Lord intended
When Scotch He invented.