The First Bridge Cruise
In the late 1920's the Cunard Lines was
rapidly losing trans-Atlantic business to competitors. Their fleet of pre World
War I vessels was outclassed by modern ships. Company strategists decided to
build two super liners, eventually launched as the Queen Mary and the Queen
Elizabeth. After two years of trials and outfitting, the Queen Mary commenced
her maiden voyage from
Naturally they thought of Culbertson first. But he was too busy enjoying the
fruits of his success and fighting off that newcomer, Charles Goren. Attempts to sign other leading experts also met with
rejection. Eventually they were forced to settle on an accredited Culbertson
bridge teacher and club owner, Ms. Ethyl Whitecross
Despite an aggressive advertising campaign, including half page display ads in both The Bridge World and the official organ of the ACBL, published in those days as The Bulletin of the American Contract Bridge League, the response was disappointing. Only ten additional passengers could definitely be attributed to the enticement of bridge play. There were others who took part, but most of the duplicate sessions consisted of three tables.
The games proceeded smoothly for the first couple of days, but the Queen
Mary met up with the fringe of a
The bridge activities were resumed on the return trip. Despite Ms. Whitecross's renewed efforts there were rarely sufficient players to organize a team game. Usually a five or six-handed rubber bridge game was all that could be mustered. Cunard did not attempt another organized bridge activity for almost 20 years.
When playing at the next Queen Mary Regional, if the air conditioning is not working perfectly or a creak from the bowels of the ship distracts you for a moment, think of the trials and tribulations of Ms. Whitecross almost 60 years ago. Bon Voyage.
Ms Whitecross and her activities are figments of my imagination. The Queen Mary and Queen Elizabeth are certainly not. And it is recorded that in her early years the Queen Mary was quite unstable with rolls of up to 44 degrees. Supposedly water sometimes entered her funnels! This was corrected in the 50's by the addition of stabilizer fins.
A Hand for Deep Blue
In 1997 an aggregation of some of the most sophisticated computer hardware including specially designed components, a computer program which required dozens of man-years to development, and a team of dedicated engineers, utilizing the resources of one of the world's greatest corporations, managed to defeat the undisputed world chess champion in a closely contested match. "Deep Blue", a product of IBM, which is able to evaluate chess positions at a rate of two hundred million a second allowing it to consider up to fourteen moves in advance, edged Gary Kasparov after losing a similar contest the year before. IBM has stated that Deep Blue has retired.
Would IBM be willing to devote such enormous resources simply to win a game of chess? They claim that the principles used to humble Kasparov will be applied to such difficult problems as weather forecasting and designing toxic waste site cleanup procedures. The transition is obscure. IBM has not made their position known regarding another complex issue: How would Deep Blue fare at the bridge table?
Chess is a game of complete information. As such, given any position, there is a "best" move, one which can be played whenever an identical position occurs. (This does not imply that Kasparov, Deep Blue, or any other resource knows or can compute, in general, what that best move is - at least yet.) Contract bridge has a complexity that chess does not. Complete information is usually not available; the "best" play may have to be selected from two or more possibilities according to some probability distribution.
As an example, consider declarer's play of the following suit combination when attempting to win five tricks:
For those not familiar with the representation of bridge combinations, the x's refer to small cards, ones that cannot win a trick (unless all the other cards in the suit have been played); A is the ace, K the king, and J the jack.
The ace is played with both opponents following and then a low card is led from dummy, right-hand opponent (RHO) playing a small card. When RHO was dealt none or one cards, he would not have been able to follow suit at the second trick. When RHO was dealt two or five cards declarer's strategy is immaterial.
The remaining original possible distributions (in which
The strategies for declarer vary depending upon which card left-hand opponent (LHO) plays on the first round:
All three strategies win against A and G. They are shown only for completeness. LHO has two strategies from which to choose when he holds combination B. He can:
The winning payoff matrix for declarer according to the various strategies is:
From the matrix it can be seen that declarer can adopt strategy 1 and insure a relative payoff of 13.00, winning if combination B or F exists and losing against C and E. But if a defender either falsecards all the time or never falsecards an improved payoff can be obtained. The "falsecard window" for the defender is small. He should drop the 10 from combination B (LHO strategy 2) between 5% and 15% of the time. Any less frequently and declarer will gain by adopting strategy 3; more frequently and declarer should adopt strategy 2. In layman's terms LHO must occasionally play the 10 to protect his Q10 doubleton, which will occur slightly more often that the singleton 10. But he cannot play the 10 on the first round (holding 10x) very often or declarer can assume that if he didn't play it he doesn't hold it.
At the top level declarer should play strategy 1 and take his guaranteed payoff. But against a careless or sleepy opponent who is simply following suit, declarer should try 3. My guess is that as a practical matter, most competent opponents will falsecard well more that 15% of the time, making strategy 2 a significant winner.
In case you wish to try a bit on analysis, note that RHO can also falsecard, playing the 10 on the second (or first) round of the suit when holding combination D. How might that affect declarer's play? And are the x's really immaterial or must the defenders vary which small cards are played when there is a choice?
If the calculations based on the a priori distributions are not daunting enough, note that either the bidding or early play of the hand can drastically affect declarer's strategy. In addition, the play of the suit cannot be considered in a vacuum. The contract and the distribution of the other suits must be considered when selecting the best strategy. There are also factors which might affect the defender's strategies. It may be necessary to use the sequence of spot cards played to signal partner about the location of high cards in other suits.
I make no claims regarding the relative intelligence or computing power necessary to play chess and bridge at the top level. I do know that there are any number of computer programs (in Deep Blue's case it is a bit more than software) which play chess approaching or surpassing the expert level. There are no such bridge playing programs. I suggest that the overriding factor is that we, as computer engineers, have not yet developed the capability to effectively define decision making processes in the logical elements necessary to allow a computer to play expert bridge. Isn't it likely that developing such capability might allow us to solve the difficult problems assigned to Deep Blue's descendants more readily that the recursive, non-probabilistic algorithms currently in place to win at chess.
Get yourself a partner Deep Blue and let's deal the cards!
1. In the 1973 Vanderbilt National Team of Four Championship a team
sponsored by Bud Reinhold was hopelessly behind another team sponsored by Sam Stayman. They were so far behind, 69 IMPs, that Reinhold,
who had already played his required number of hands, played the last 18 anyway
despite being the weakest player on his team by a considerable margin. In a
miracle finish, the Reinhold team scored 75 IMPs to their opponents 3, winning
the match by 3 IMPs. One of the pickups was a four spade contract with the
example suit as trumps. Larry Cohen finessed the nine on the second round of
trumps, picking up the suit with no losers when his
Johnny Crawford, one of Cohen's opponents during the fateful last 18 hands, didn't see it that way. Due to this hand and others in which his opponents demonstrated uncanny accuracy, Crawford protested to the American Contract Bridge League's Board of Governors the next morning that his team had been cheated. This was an unacceptable forum for such an accusation. Crawford was barred from tournament play for three months.
A few months later, writing in The Bridge World, Edgar Kaplan analyzed the combination in his article, "The Deep Nine", with the assumption that the defenders would not falsecard correctly.
2. Dr. Matthew Ginsberg at the University of Oregon has developed techniques using artificial intelligence theory and simulation to overcome some of the computational problems associated with exhaustive analysis of bridge problems such as the example above. Using these techniques he has created a program (called GIB - for Goren-in-a-Box) to play as declarer. This program enjoys a substantial edge over any other bridge playing program but remains far below the expert level. However, it seems a good start. Perhaps Deep Blue should seek Dr. Ginsberg for assistance in getting started. GIB can frequently be observed playing on the Internet (OK Bridge).
There is precedence for such a ploy by IBM. The predecessor of Deep Blue, called Deep Thought, was created in 1988 by a team of Carnegie-Mellon professors and graduate students. IBM purchased Deep Thought and hired two of the students and one of the professors who had developed the program. It was a successful venture.
The author of this article is Fred Turner who, in my opinion, has written the two most entertaining articles ever to appear in The Bridge World: "The Grosvenor Gambit" and "Nocturne". The following article, published in the Southern California Birdge News, is an exampe of Fred's elegant style.
Did you ever see the movie, "Twelve o'Clock High"? The film begins several years after World War II. Dean Jagger, who had been the Adjutant of the 918th Bomber Group, returns to England. Journeying into the countryside, he rents a bicycle and rides to a long-abandoned airfield. He stands, musing on the weedy tarmac, looking into the distance. A low rumble builds in the sky, swelling to a deep roar. Then a ragged formation of Flying Fortresses appears above the horizon. The 918th is returning from another bombing mission. It is 1943 and the fate of the world hangs in the balance.
It was the fall of 1947 and I was back in the Men's Clubrooms at Stephens Union--the center of what passed for social activities on campus immediately following the war. Guys in army boots and fatigues. Young men, some with haunted eyes, in parts of uniforms from all the services. Eisenhower jackets, OD shirts, flying jackets with patches from every theater of global conflict. Men with half-drained steins and cigarettes engaged in all sorts of games. Snooker, pocket billiards, chess, gin rummy. And yes, Bridge! Bridge out of and beyond Victor Mollo's menagerie. Bridge surpassing even S. J. Simon's imagination. Bidding compared to which the construction of the Tower of Babel was the highest expression of human intellect.
The usual format was rotation for a tenth-of-a-cent a point, after all most of us were living on $75 a month from the GI Bill. The level of play generally ranged from poor to reasonably good, but some of the guys were fine players. Charlie Drake won an Intercollegiate Championship in the mid-forties, as Mike Lawrence and Lew Stansby were to do 20 years later. Larry Maes, Ted Reed, Jim Pestaner, Bob Sturgeon, Augie Hunt, were regulars. I thought the toughest players were Curtis Smith, Joe Bechely and Bob Rowley. Smith was alleged to be the best rubber bridge player in the state. I was never comfortable in a game with Curt because I'd be sitting against him twice as frequently as not. Curt's table presence was dominating. Sometimes, when we were at different tables, I'd hear his exultant laughter across the room--another sucker had been swindled.
By 1951 I was a graduate student. But instead of reading Dobshansky and Ernst Mayr I was devoting too much time to cards. The next year I was gone. When I returned in 1956 a young man named Ron Von der Porten had started playing bridge in the clubrooms. I remember playing with him just once. We bid to six diamonds and went down a trick. I took comfort from Ron's assurance that it was "a good slam." Von der Porten, Lawrence, and Stansby went on to represent the United States in international competition. Lawrence and Stansby have both won multiple world titles.
One of the 1947 clubroom regulars was Don Lee, a Chinese-American who had been a pilot in the China-Burma-India theater. Don played his cards beautifully, but his bidding was--well, shall we say undisciplined? I guess if you'd flown the Hump an 800-point set was nothing. Playing with Don could be nerve-wracking. One of his more famous flights of fancy at the table resulted in this bidding sequence:
Rubber bridge, NS vulnerable
I held: 43, none, 87642, 976432 and meekly passed. Don was two tricks overboard at 6, so removing to a 7 contract would have saved 20 cents.
The din subsided and once again I was staring at polished doorknobs. It was time for the Golden Bears to take the field.
Dealing Like a Computer
The Laws of Contract Bridge are quite explicit about the manner in which cards should be dealt: "The dealer distributes the cards face down one at a time in rotation into four separate hands of thirteen cards each, the first card to the player on his left and the last card to himself." Like many duplicate players, I use to deal across and back -- it's faster and does implement the concept of randomly assigning thirteen cards to each player. However, years ago in national team games, Canadian opponents (Duncan Phillips and Eric Murray) observed that I was in violation of the Law when so dealing. Shortly thereafter, dealing board one of a National Men's Board-a-Match Team with ex-Canadian Hugh Ross at the table, I dealt clockwise just to avoid an international incident.
The result of my law abiding effort looked like something a berserk computer might produce. The hand produced an interesting series of problems. Consider this opening lead problem. Holding:
The bidding is pass to your left, pass by partner,
seven hearts by Marty Cohn to your right, all pass. (Marty was a bridge icon of
the 50's and 60's - an outstanding player but one who was never particularly
concerned if the cards he held were related to his bid.) Mike Moss, who failed
to solve the lead problem at
If you buy the contract at least you don't have to lead. It could be that Mike Moss really had a bidding problem which, by solving correctly, resulted in a lead problem.
If you prefer dummy play, perhaps you'd like the problem Richard Walsh faced:
The king of clubs is led which draws the three from North. South shifts to the heart king which you ruff. After picking up trumps in one round, you lead the remaining club from your hand, won by South's nine. How do you continue when South continues with a high club?
At our table, Hugh Ross had cashed the spade ace disclosing a four-zero spade break before leading the second round of clubs. Then when South played another high club Hugh pitched a losing spade from his hand. South was left with a choice of eight cards to lead, all of which would present declarer a sluff and ruff.
The six heart overcall should indicate the spade void in view of a diamond singleton. However, if seven hearts by Cohn has one losing singleton, why can't six hearts by Russell have two. The original holdings were:
When the hand was played by our team, both West players bid seven diamonds thereby correctly solving the bidding problem. But neither South solved the defensive problem, a tough play to find at the table. Can you find it?
By winning the second club with the jack and then leading the nine on the third round, South eliminates the endplay threat. It would be tough to find a more interesting hand no matter how the cards were dealt.
Be Careful Whom You Fool
Partner opens 2 Flannery (4 spades, 5 hearts, 11-16 HCP) and you're holding: 1097, 962, K432, AK9. You decide to settle for a quiet 2 bid, apprehensive about missing a game after everyone passes.
You win the lead of a low club in dummy and cash a top heart, felling the queen from West. You try another high trump to find out if West is pulling your leg while you're pulling trump. The club discard confirms the heart situation and even eight tricks are not certain. If you take another round of trumps now, East may get in and play a fourth round making it unlikely that you will ever enjoy a spade trick. Winning one spade finesse isn't going to be any help and suspecting club ruffs just over the horizon, you try a low spade to your ten. East has no particular reason to go in with the jack, so his partner is forced to win the trick. West decides to play "Fool 'em" and conceals the king, winning the ace. The club return is ruffed and East, a thinking player, does some calculations. He knows that you did not try for game, yet hold seven points in clubs and, evidently, the king of spades. The defense is clear. Since you cannot hold any other high honors, he leads a diamond to his partner's presumed king for another ruff. But, oops, the diamond king appears out of your hand. Now a heart to dummy picks up the last trump. You have been fooled also, so instead of leading towards the spade queen you lead another low spade from dummy to insure a trick in the suit. East, not yet recovered from the diamond king showing up in the wrong hand, fails to adjust his count of the high cards, and plays the spade eight. The nine forces out the other top spade and the defense has no more tricks. You have missed a game after all.
Kelsey, Reese, and Turner
In 1995 the world of bridge has lost two of its greatest writers: Hugh Kelsely and Terence Reese. Reese published his first book in 1948, Play Bridge with Reese, and was prolific until his death. It was his effort, Master Play, published in 1960 by George Coffin which, I think, brought him to the forefront of bridge authors. In the book he presents detailed discussion of such topics as "Discovery, Assumption, and Concealment". He also introduced and named the sophisticated squeezes "The Vice, Winkle and Stepping-Stone".
Kelsey came along a bit later. His forte was the presentation of difficult
problem hands in an entertaining format. In Test Your Match Play he
presents 64 hands in 8 hand segments as if the reader was a member of a team in
the Gold Cup Finals,
"The time is as you finish scoring and you have to restart at . Even allowing for slow service in the dinning room there is time for an omelet or something of the sort. You captain orders water all round and waves the wine waiter away. During the meal the talk is about the crazy bids and plays made by the opponents, and the brilliancies that might have been. Nothing is said about the crazy efforts by you own side. That will come later, after the match. As the time draws near, the captain informs you that your services are required for the next eight boards. You step out for a quick breath of fresh air before returning to the playing rooms for the next session."
I sent Fred Turner a copy of the book for Christmas the year that it was published. He really got into the spirit of the book as evidenced by excerpts from letters I received over the next few weeks:
"I finished the first half of the first session at last night, concurrently with a Stanford basket following a missed free-throw which sealed UCLA's defeat. Hence, it was really early this morning when our team compared results… It took me 1-1/2 hours to play the second hand (I received a stern warning about slow play), but I brought in 3NT by not cashing dummy's hearts… So after 8 hands we were +26. Trouble is it had taken us 4 hours and 24 minutes to play these deals and I had accumulated two slow play warnings and lots of dirty looks. I was placed on Red Alert, and my teammates asked one of the Sharples brothers if he might consider joining the team in my place. I may not be permitted to play on… Well, the good news is that they let me play the second half… On the third hand I considered the "obvious" line at first which was not unattractive."
What do you consider the best line after South leads the J against 6:
The simple "obvious" line is to win the K, lead the 10 (unblock the 7) and repeat the finesse if it wins. If it loses hope that hearts are 2-2 or the 8 is singleton so you can reenter dummy with the 6 (after cashing the AK), discard the low spade on theQ and take the spade finesse. One of the problems with this line is that a good defender will duck with the Kxx of trumps and deny you a second entry to dummy. Much better is to finesse the Q. If it loses you have an entry to try the heart finesse. If it wins Kelsey recommends cashing the AK and then leading the Q to force an entry to dummy so you can discard the losing spade. There is one very slight improvement on this line. Can you spot it? Also, could you and your partner bid to 6NT, impregnable if either finesse wins? The slight improvement is, after winning the spade finesse, lead the Q before cashing the top diamonds, just in case someone has two red suit singletons.
A couple of boards later Kelsey presents this hand as a declarer problem. Instead I will show it as a defensive problem:
Both sides vulnerable
Your partner, bless his heart, leads the A and continues the suit which you ruff, declarer following with the K. You return the K to which declarer and partner follow. Dummy wins and leads the Q. Do you ruff?
How can declarer possibly need an immediate discard? If he holds the trump ace he would cash two trumps before trying for a discard. If he doesn't hold it he knows it must be with your partner for the two-level vulnerable overcall. If declarer holds two diamonds he knows your partner is out (besides, partner would have led a stiff diamond). Declarer is leading the Q hoping you will ruff to clear up the trump situation. An expert East will not ruff. However, Kelsey claims that if the Q is not ruffed, declarer should ruff and finesse the 10 (holding-Q1097632, -K5, -3, -AK7). The next hand:
The opponents bid indelicately to 6, partner leads the Q to your ace, declarer contributes the 9. How do you continue? This was Fred's analysis:
"After winning the A I worked very hard at visualizing declarer's hand and finally came up with the following:
It was now clear that I was threatened with a minor-suit squeeze, but it also seemed clear that there wasn't anything I could do about it. But wait. Could I disrupt things by leading a club? It was a little hard to follow the ramifications of the play so I called for a piece of paper and pencil and worked it out like a double-dummy problem. It only took me about 5 minutes to see that, amazingly enough, a club lead was the sockdolager! Declarer cannot win the club in dummy because then he has no later entry. Congratulating myself on a brilliant conception I led back the 8. Declarer called for the director and complained that I had used paper and pencil and caused undue delay. The director ruled that declarer should play out the hand and if he didn't like the outcome to check back with him. It turned out declarer had quite a different hand and made his slam easily…"
This is the hand which Kelsey gave declarer:
If declarer holds that hand you must return a trump to prevent the clubs from being established. It turns out that declarer could make his contract even if he held the hand Fred gave him and a club is led a trick two. Can you determine how with your own paper and pencil?
Declarer wins the K and cashes all his major suit winners bringing the hand down to:
East cannot guard both minors. Declarer must guess which suit East is protecting and cash his top card(s) in that suit, cross in the other minor and cash the last card. This is called a criss-cross squeeze. (But give West the 10 and that line wouldn't succeed). Fred started his third letter with:
"Am I hooked on Kelsey. I am reading those dammed problems when I should be writing scholarly papers, and thinking about them when I ought to be concentrating on the Bruins conquest of Cal. Anyway, I had to play again in the third set when Flint became Ill. (He seems to be an unreliable sort, doesn't he?)…Again there was discussion about how long it took me to defend some of the hands, and it was agreed all around that I should not use paper and pencil any more."
Test Your Match Play is out of print but the hands from three of Kelsey's books have been reorganized into six smaller volumes. You can hardly go wrong with anything written by Reese or Kelsey. Reading letters from Fred is fascinating also.
A Matter of Principle
The 1954 World Championship was contested by a U.S.A. team and France, the European champions. There were a number of unusual aspects of this battle for the Bermuda Bowl including the composition of the teams. The U.S. team members were Doug Steen, Milton Ellenby, Billy Rosen, Don Oakie, and Cliff Bishop. They had qualified by winning the Masters' Team Championship (now known as the Spingold) at the Summer Nationals. Lew Mathe was added as a sixth, a tribute to his bridge skills because he did not have a partnership with any of the other players. During the championship the U.S. team proved their versatility and, I suppose, compatibility by using a different partnership combination almost every session.
It was a young U.S. team with an average age of 34 years. At 27, Steen was the youngest. Also the strangest. Mathe told of one morning during the event when he encountered a disheveled Steen in the hotel lobby. Mathe asked what the problem was. Steen replied, "I got stuck in the wall last night." This is not what one wishes to hear from a teammate during an important event. It seemed that one of Steen's out-of-body experiences had not been entirely successful. Steen retired from competitive bridge a few years later to make a fortune in the commodities market. Richard Walsh told me that he would come into the Bache office in Beverly Hills and perform transcendental chants sitting on the floor to improve his trading insight.
The French team qualified four-handed. Their choice of rounding out the team was remarkable. Rather than adding another French pair they created a true European team by selecting Jean Besse of Switzerland and Karl Schneider of Austria! That would not be possible these days because of sponsorship by national bridge organizations. Besse would go on to represent Switzerland in 10 world championships; Schneider was a proven veteran - he was a member of the 1937 World Championship team from Austria.
The conditions of contest included a strange proviso: If the difference between the two teams was greater than 24 IMPs after 192 boards, only 32 more deals would be played. If the match was closer than 24 IMPs, 64 more would be played. (The IMP scale then is use was roughly equal to 60% of today's scale, thus 24 IMPs then is equal to perhaps 40 IMPs now.) The Europeans must have been regretting this rule for they had gained 45 IMPs in boards 113 through 192 but the deficit was 36 IMPs. The U.S. team halted the slide, picking up 13 IMPs over the last 32 boards to win the title going away. This was to be the last World Team Championship for the U.S. for sixteen frustrating years.
The play and bidding throughout the match was far below what is expected of top players these days. Consider this hand:
Using a range of 15-18 HCP the West hand is surely too strong for 1NT (good controls and a five-card suit). But the awful bid was 4. Despite the narrow range in high card strength defined by an opening notrump bid, there can be a wide variance in the value of a hand in support of a suit. It is a well known principle that the notrump bidder must convey this information to partner when possible. An advanced cue bid of 4 in response to 3 is basic sound bidding (not that Steen could have bid more than 4 anyway).
The French pair did reach the excellent slam despite preemptive bidding by Oakie and Bishop. Marcel Kornblum received a heart lead. How should he play? Win the A and cash the ace and queen of spades (so that the suit can be picked up should North have four to the jack). Trumps split 3-2 so the king picks up the last outstanding trump. Then what? There is no distribution which can defeat the contract at this point. But declarer must be careful to start the clubs by leading low towards the QJ. This caters to either defender having all of the missing clubs. If South holds four clubs declarer has but to lead towards the remaining West honor. If North holds four the king will capture the jack, but declarer can enter dummy with the Q and finesse the nine on the way back, shutting out the ten. Unfortunately for the Europeans, Kornblum started with the A and the contract failed when North proved to hold all four clubs. The 7 IMP loss should have been a 7 IMP gain - and then another 32 boards would have been played.
On the return trip the champions stopped off for a 96 board exhibition match against the top British players: Reese, Schapiro, Meredith, Konstan, and Mayer. The result was a crushing 81 IMP defeat. Reese's report of the match in the February, 1954 The Bridge World included this hand:
Reese stated that, "Oakie knew that we played a fairly weak notrump, not vulnerable, and that accounted for his double." I say there is no accounting for it. Partner is a passed hand; game is out of the question. But Oakie found his partner with a quite suitable hand. It is not easy to see how the British pair defeated the 2 contract, but they played a sparkling defense. Ellenby won the diamond lead and tried the ace and another spade. Reese won and continued with a diamond, ruffed by declarer. Another spade and another diamond ruff left this position:
Ellenby led a heart, won by East who returned a trump. Reese made the critical play of ducking the ace! Another heart, another club, followed by a diamond insured a second trump trick for the defense. Reese noted in his report that if Ellenby had ruffed a spade and then led a heart, East would win and lead a trump. If declarer puts up an honor in an attempt to win and ruff his last spade, West wins and returns a trump. Again the 8 scores a trick. If declarer ducks the club, so does West.
Yet, the contract cannot be defeated. Can you spot declarer's error? It is surprising that it was overlooked by the players at the time and by Reese and The Bridge World editors later. When West leads the second round of diamonds declarer simply discards a losing heart. When a third round is led he discards again. After ruffing the next red card lead he plays a spade. West can win and force declarer with another heart but look at the difference:
Declarer cross ruffs, losing only to the trump ace. The location of the 8 is immaterial. This play should be in every player's repertoire. The principle is to eliminate the opponent's communication and to establish your own. All declarer needs to realize is that the two hearts are losers in any event and that there is no advantage of being on lead now rather than later. It is not necessary to consider the play in detail. The principle will see you through.
Last update: July 1, 2009