I had the pleasure of having a wonderful regional tournament in Boca Raton from September 6-11, 2005.  I played in 5 different team games (3 knockouts and 2 Swiss) and had 2 wins, 2 seconds, and 1 third.  I won 100.44 masterpoints and was the leading masterpoint winner at the tournament.  The following hand was from the afternoon KO teams on September 8, and it was my favorite hand of the tournament.

The opening lead was the ª10, and my right-hand opponent showed out, discarding an encouraging heart.  You win the spade Jack in dummy.  What do you do now?

We were playing NAMYATS, so my opening 4ª bid denied as many as 8 1/2 playing tricks.  After the opponent bid 5©, my partner made what I consider to be a very questionable 5ª bid.  I don't see why he should assume that the opponents will make their contract, and I think he should expect a 5ª contract to go for a 300 or 500 point penalty.  Therefore, you might expect to save 3 or 8 IMPs if the opponents make their game, or lose 9 or 12 IMPs if they go set in their game.  While I think his bid might be successful at best about half the time, the potential gain vs. the potential loss makes it only correct to bid if the game makes at least 75-80% of the time.  If you analyze his bidding situation using the law of total tricks, you would estimate that we have about 8 spades between us, and that the opponents have 9 or 10 hearts between them.  If there are 18 total trump, and 18 total tricks, then if they make 5©, then we would go set 800 points at 5ª doubled for a net loss of 4 IMPs.  And if they go down one trick and we go down 300, then we lose 9 IMPs, and if they go down two tricks and we down one trick undoubled, then we lose 6IMPs.  I would never recommend bidding with his hand at IMPs.    Perhaps my partner felt that the opponent was very confident when he bid 5©.  Table presence is often a determining factor when deciding whether or not to compete.  If my partner thought that the 5© bidder was likely to have a clear-cut action, that could easily make bidding 5ª a favored action.  Indeed bidding was the winning action on this hand, and I would not have had this interesting play situation if he had passed.

The bad trump break was originally disappointing, but upon closer analysis it is probably good since it should guarantee that the opponents make 5©.  You are now faced with 1 spade, 1 heart, 2 diamonds, and probably 1 club loser, so you expect to go for a 500 point penalty.  You have to be careful to maintain trump control, but you have 2 more trumps than left-hand opponent so unless you are careless, you can maintain control.  If the §K is onside you can get out for a 300 point penalty.  Can you give yourself any extra chances to go down only 300 points?

What did you lead from dummy at trick 2?  Was it the ¨4?  That is what I did.  I figured that leading the ¨Q would not help me since establishing 1 diamond trick would not help prevent a possible club loser. By leading a small diamond I had hopes of establishing 2 diamond tricks.  There are two ways this could happen:  1) My RHO has the diamond Ace and King, and assumes that I have the ¨9, and wins the first diamond lead high, or 2) My RHO has the ¨9 and mistakenly places second hand low.  And that is what happened.  This was the entire hand:

My ¨8 forced out the ace, and my LHO made the normal continuation of a small heart.  I trumped the second round of hearts, cashed 3 high spades, and led another diamond.  I trumped the heart continuation and led a club to the ace, and led dummy's two high diamonds, discarding my remaining clubs.  I avoided losing a club trick, and went set 2 tricks, for minus 300 points.  Once I was able to set up two diamond tricks my only risk was if my LHO held less than 3 diamonds.  If my LHO held only 2 diamonds and the King of clubs, I would have lost one trick needlessly, but that was very unlikely.

What do you think of RHO's play of the small diamond at trick 2?

It is an easy mistake to make.  When one learns to play bridge, you learn to play second hand low.  It is hard to learn when second hand should play high.  You have to reason out all the situations, and that takes both time and determination to think out all these basic situations.  But on this hand it is clearly right to play the ¨9.  That is because after the first diamond trick, dummy will be left with the ¨QJ10, and your ¨9 will have no value.  So you must play it on the first diamond trick in case declarer is making a sneaky play against you. 

When teammates played the hand, my hand opened 4ª, and everyone passed.  They led a heart on opening lead, declarer misplayed the hand and they took advantage, and they beat the contract 4 tricks for 200 points.  My teammate did not bid 5© because he feared he would get doubled and go for a big penalty (at unfavorable vulnerability) and because he thought that 4ª might go set.  That certainly is a reasonable decision.  What do you think of my teammate's decision?

There are two problems.  First of all you need to consider the probability of a good trump fit.  And secondly you need to determine if you will reach that trump fit.  And making an educated guess after the 4ª preempt is very dangerous because whatever you do can easily be wrong.  If you bid 5© and partner is short in hearts, then you can go for a major penalty.  Let us begin by using the law of total tricks.

The opponents probably have at least a 10 card spade fit, if you assume the opening bidder has a 7-card suit and the other two players each have 3 spades.  The opening bidder could have more than 7 spades, and it is fairly random to assume that partner has exactly 3 spades, as he could easily have been dealt 2, 3, 4, or some other number of spades.  But 3 (or almost 3) is the average number of spades that partner will have.

You and your partner will have at least an 8-card trump fit, if the opponents have 10 spades.  Since there are 3 different suits where you and your partner could have 8-card trump fits, it seems likely that you and your partner will have at least one 9 card trump fit or perhaps two or more 8-card fits. 

Therefore it seems likely that there are around 19 total trumps, and consequently about 19 total tricks.  Furthermore, you can hope that there are 20 total tricks.  In Larry Cohen's writings about the law of total tricks, he discussed adjustments to the law, and purity in the suits and double fits are two factors that might produce more tricks than the pure number of total trumps.  So it is reasonable for the East hand to guess that there are around 19 or 20 total tricks on this hand.  If there are 20 total tricks, you want to bid.

But it is more likely that there are only 19 total tricks.  If there are 19 total tricks on the hand, then you could go down two doubled for 500 points when the opponents make 420, or you could go down 100 or 200 doubled when the opponents lose 50, or you can make 600 or 650 when the opponents go down two tricks for +100.  So, in these 3 most likely cases, you lose 2 IMPS, or you lose 4 or 6 IMPs, or you win 11 IMPs.  That is 33% (-2), 33% (-5 on average), and 33% (+11).  On the average, you will gain one IMP by bidding, if you get to your best fit.

But if you bid 5©, you do not get to the best fit when that fit is in clubs or diamonds.  And if you bid 4NT showing a 2-suiter, you errantly get to a diamond contract (and would on the actual deal).  And getting to the wrong suit can be very costly.  That certainly outweighs the value of making a dangerous bid that might make an average 1 IMP gain.

Therefore, if there are 19 total tricks, on the average I estimate that bidding over 4ª will lose IMPs.

On the actual hand there were 18 total trumps and 19 total tricks (assuming best play).

Finally, our teammates were outplaying the opponents, and they did not want to take an unnecessary risk that might let the opponents back into the match.  If you bid 5©, and partner fits in a minor suit but not in hearts, and you get doubled and go for 1100 points, you could easily let the opponents back into the match.   So I support my teammate's decision to not compete over the 4ª  preempt, but I think it is very close.  It is never a mistake if a team member choose wrong in a close decision like this. 

My teammates did realize that they did not get a good result on this hand, and were very pleased when we compared and only lost 3 IMPs on the hand.  It was fun that I got 9 tricks on this hand while teammates held declarer to 6 tricks.  And we easily won the match when the rest of the results were very strong.