Elements of elimination play Larry Hammick larry@hammick.com 2002.02.17 Contents ;Introduction ;Ingredients ;The ruff-and-discard ;Tenaces ;Exits ;;Exit with a loser ;;Exit with a ducking finesse ;;Exits with a semiloser ;;Exit with a loser-on-loser ;;Exit to a blocking high card ;;Exit with a finesse which may lose to a bare honour ;;Exit which creates a ruffing tenace ;No-tenace cases ;Entry-gaining eliminations ;Safety eliminations ;Eliminations with two loser suits ;Ruffing tenaces ;Trump-only elimination ;Bluff eliminations ;;Bluff elimination to provoke a lead up ;;Bluff elimination to provoke a ruff-and-discard ;;Bluff elimination to provoke a duck ;;Bluff elimination to provoke an unblock ;Throwins ;Throwins to overcome blockage ;Squeeze throwins ;Defence ;;Diagnosis ;;Leading ;;Avoiding one-way exits ;;Unblocking ;;Discarding ;;Congestion ;;Breaking a dangerous suit ;Introduction It is usually undesirable for the opponents to be on lead. The exceptions are called "endplays". Bringing about an endplay consists of removing an opponent's safe exit cards and then putting him in. This process is called "elimination play". The theory of endplays is somewhat related to that of squeezes, and hybrid endplay-squeezes are not unusual. An elimination, like a squeeze, combines resources from several suits into one trick, and the opponents get to choose from which suit the new trick will come. But, after a little study and practice, a declarer can often tell at trick one whether a hand is suitable for elimination play, just as he can for squeeze play. But elimination play -- the removal of a defender's exit cards -- is not just about endgames. It is generally constructive whenever declarer's control and entries allow it, and also advances his count of the hand. In all the illustrations that follow, except the notrump contracts, spades are trumps. Whenever more than one suit appears in a diagram, the highest suit is spades, the next hearts, and so on. ;Ingredients A defender finds himself thrown in if, for each of the four suits, at least one of these conditions holds: I) The defender has none of the suit. II) Declarer or dummy has some kind of tenace in the suit. III) Declarer and dummy are both out of the suit, and each has a trump. If the ruff-and-discard threat III is present, the position is called an "elimination". If not, it is a "throw-in". Eliminations are commoner than throwins because the threat of a ruff- and-sluff can disable several cards in the defender's hand; it is not necessary for the previous play to have removed those cards. Moreover, condition III applies to both defenders if it applies to one. Because the conditions II and III refer only to declarer and dummy, some eliminations are quite easy to diagnose and play, whereas throwins require counting by declarer, and may still involve some ambiguity and guesswork. Let's begin with two typically straightforward eliminations. Qxxx KJx ATx Axx AKxxx Axx KJx Kx West leads CQ against 6S, and you win in hand. All follow to the trump ace. You can claim: Pull trumps, cash CA and ruff a club, then play out HAKJ, eschewing the finesse. Either the jack will hold or a defender will be on lead in this position: x -- ATx -- x -- KJx -- Hearts and clubs are controlled by Condition III: if one of those suits is led, declarer ruffs in one hand and discards a diamond from the other. Spades are covered by Condition I, and diamonds by Condition II, as a diamond lead from either side will avert a guess for the queen. The hand would play the same way if the HJ were a small card. KTxx Axx Kxx KJx Axxxx Kx AQx xxx Against 4S West leads DJ up to your queen. Both follow to SA, but West shows out when you continue with a small one. Unless West has seven or eight hearts, the hand is still cold. You take SK, HK, HA, and a heart ruff. Now you try to cash your remaining diamonds. If they go by, you lead a trump to East, who now has no safe exit. You are equally safe if East ruffs the second or third round of diamonds. (Actually, you are safe if West has eight hearts! Figure it out.) The first example hand above was a "two-way" specimen: either opponent could win the exit card (HJ) with equal results. Many endplays are one-way, i.e. such that declarer must exit to, or can only exit to, a specific opponent, as in the second example. If he lacks the trumps or the entries to eliminate all exits, declarer may eliminate what he can and hope for the best: a "partial elimination". A partial elimination is one-way by definition. Aside from I, II, and III, a couple of other kinds of holding sometimes participate in a throwin. We will look at them in the section "Throwins to overcome blockage". ;The ruff-and-discard Declarer cannot benefit from a ruff-and-sluff unless he has a trump in each hand. But that formula is only a convenient aid to planning. A more accurate formula is this: for a ruff-and-sluff to show a profit, the ruff must be made with a trump which is not already "reserved" as a ruffer. If one hand is longer than the other in trumps, that means the ruff will usually be taken in the _short_ trump hand, but there are exceptions: xxx -- xx -- xx xx x -- Spades are trumps and the defence has none left. West leads a club. Declarer must ruff in the North hand (although it is longer) and discard a diamond. Two of North's trumps are spoken for by South's hearts, so North is, in effect, the short trump hand. A ruff-and-discard overcomes one kind of "duplication of values": losers facing losers. x xx -- -- -- -- AK xxx A xx x -- Declarer has a heart loser and, if he leads, makes only two trump tricks. But if an opponent leads a diamond, declarer makes three tricks, just as if he himself had a diamond to lead, instead of a heart. For many reasons, declarer must often work on a side suit before pulling all the trumps. Even if a ruff occurs, it may do no harm, e.g. if it allows declarer to pull trumps in one fewer round, thus leaving himself with an extra ruffer. The same can apply when declarer's "new" ruffer will make possible a ruff-and-discard position. The general principle is that whenever the defence ruffs or overruffs in their _long_ trump hand, declarer gets some compensation in overall control. ;Tenaces All throwins and most eliminations rely on a tenace (condition II) in some suit. That may be a normal high-card tenace, such as AQ or Kx, or a divided tenace such as Ax/Qx. Often it is a holding which will benefit from a lead by _either_ defender; we will call this a two-way tenace. Here are some common combinations and the result of a defender breaking the suit. Qxx Jxx One trick is certain. Kxx Jxx Same as the previous. Kxx Txx If South leads, it is 5/8, as if West held KTx. QJx xxx One trick is certain if North leads or if North has no safe exit elsewhere (i.e. you split if South leads low). Kxx Qxx Two tricks are 50%, assuming you have no information on the whereabouts of the ace. KTx Q8x If North leads, two tricks are certain; if South, about 75%. AQx Txx Two tricks are certain if North leads or if neither opponent has a safe exit. AQT xxx Same as the previous. KTx Q9x Two tricks are certain. ATx K9x Three tricks are about 50%. AJx K9x If North leads, three tricks are certain; if South, about 75%. AJx KTx Three tricks are certain. In every case the chances are better than if declarer had to develop the combination directly. At a trump contract, even with no ruff-and-discard possibility, a throwin can counteract a second kind of duplication of values: strength facing shortness. x x KQ Kx -- -- -- -- -- -- ??? ? AQx x -- AK -- AK x x -- -- xx xx At left, a heart lead by West gives declarer the balance irrespective of the location of the ace. At right, declarer cannot directly develop a trick from HK, even though the ace is under it. But if West is in, the HK is a trick. In such cases, high cards opposite a void make up a sort of divided tenace. A high card opposite a shortage can be put to work also as a one-way exit card. We will see some examples in the section on throwins. ;Exits After bringing about conditions I-III for each suit, declarer needs to put an opponent on lead. We will illustrate the commoner styles of exit, one by one. Declarer may need to make a one-way exit (to a specific opponent) or he may not. If II applies, the nature of the tenace determines which opponent needs to be thrown in; if Condition I is needed to control a suit, and that condition applies only to one opponent, then only that opponent can be thrown in. ;;Exit with a loser This simple type of exit may be available when declarer has a two-way tenace. We saw an example in 6S above. Here is a modification in 4S. xxxx Axx ATx Axx AKxxx xxx KJx Kx West leads a heart to the ace. Declarer cashes SAK and finds the trumps 3-1. He eliminates clubs with K, A, and a ruff, then exits with a trump (leaving the following cards) or with a heart loser. x xx ATx -- x xx KJx -- The defence makes a trump and two hearts, but that is all. This demonstrates that a two-way elimination can take effect while declarer still has several losers. With a one-way tenace or a one-way exit card, declarer must normally have only one loser after the exit, i.e. the loser that disappears as a result of the defender's lead. Several losers are possible if the target defender (i.e. the target of the one-way exit) is the only defender who can cover declarer's additional losers. Very similar formulas apply to squeeze play. When declarer has finesse positions in two suits, but cannot afford to lose the lead, he can play for the drop in one suit before resorting to a finesse in the other. But when he _can_ afford to lose the lead, elimination can give him both 50% chances plus a play for the drop. Axxxx AKJ Axx xx KQxxx xxx Kx AQx Against 6S West leads a diamond. Declarer wins in hand, pulls trumps, eliminates diamonds and plays out HAKJ. The hand is home if West has the HQ or East has the CK or the HQ comes down in two rounds. ;;Exit with a ducking finesse A combination finesse, or ducking finesse, can throw in a specific opponent while retaining a tenace against him. Qxxxx xxx Ax Axx AKxxx AJT Kx KQx 6S is cold enough on a heart lead, so suppose West leads something else. Unless the opening lead is ruffed, declarer can claim: He wins in hand, pulls trumps, and eliminates clubs and diamonds ending in dummy. He now finesses his HT in this position: xx xxx -- -- xx AJT -- -- If West wins the trick, he has no exit. To exit by means of a ducking finesse, declarer usually needs no losers outside the exit suit, or a second tenace. Consider these variations of the above hand, now in 4S: Qxxxx Qxxxx xxx xxx Ax Ax Axx Axx AKxxx AKxxx AJT AJT Kx Kx xxx Qxx Suppose declarer takes CA on the first round and later finesses HT. At left, West can just cross to East in clubs for another heart lead. In such cases declarer may try to concede his sure losers early, just as he does for a squeeze. At right, West has no good exit, owing to a second tenace in clubs. The ducking finesse is one of the commoner types of exit in an elimination. Here are some other layouts to watch for: AQ9 Finesse the 9, ensuring two tricks. With AQT you may equally xxx finesse the queen. AQx Run the 9, ensuring two tricks. 987 AQx Run the 9, getting two tricks is West has the king or if East 98x has the jack or ten. KTx Finesse the ten, ensuring one trick. xxx AJ9 Finesse the 9, getting two tricks if West has the ten. Without xxx the elimination you would need to find him with the king or queen as well as the ten, unless you have reason to play him for KQ. ;;Exits with a semiloser A semiloser is a loser which only one opponent can beat. Such cards are another point of contact between eliminations and squeezes. Here declarer has a one-way tenace plus a semiloser with which to exit. Qxxxx Ax Axx Axx AKxxx Qx KJx KQx In 6S a club lead goes to your king. The diamond finesse will see you home, but an elimination can give you a considerable extra chance. You pull trumps, eliminate clubs, cash DA and HA, and then exit with HQ. You succeed if West has HK, as well as if East has DQ. There is the slight additional hope that East has no more diamonds, which is why you cashed DA. If we improve dummy's diamonds to A9x, you have _three_ chances instead of one, but cannot afford to cash DA. Jxxxx Kx KJx xxx AKxx Axx 9xx AQx West leads a heart against 4S. Declarer wins in dummy and takes SAK, West showing up with Qxx. He now eliminates hearts and concedes a trump to West. Qxxx KJx Axx Axx AKxxx Axx KJx Kx This is the same as an earlier hand except that dummy's diamonds are now a shade weaker. A trump or club is led against 6S. You pull trumps in two or three rounds, eliminate clubs, and play out DA and HAKJ. You have the same chances as without the elimination (HQ with West or DQ with East) plus the chances of a singleton diamond or the double HQ with East. If entries don't permit an exit with a combination finesse, a semi- loser will sometimes do: AQT AJT xxx xxx If the lead is in dummy and East is marked with the king at left, or with the KQ at right, you might exit with the queen or jack. We will see an illustration later. If declarer cannot pull all the trumps without disabling the ruff-and- discard, he may leave one or two out, and hope that the defender thrown in cannot, at least safely, lead a trump: KJTx K Ax -- xxx -- Axxx Axxx xx xxx -- x KJxx xxxx x -- KQx xxxx -- x QT9x xx QT9x xxx AQ9x AQ QTx -- AJx -- KJx KJx Against 4S West leads DK, which holds, and shifts to a trump. Even if two diamonds and a heart are lost, if declarer can make six trump tricks he will not need the club finesse. He wins the trump in dummy and tries HA and a heart to the ten, but West wins with the jack and leads another trump. Declarer wins in hand, ruffs away HQ, and plays out DAJ, hoping that East has the last trump, and leaving the cards at right. West must now give declarer a third club trick or a sixth trump trick. A variation, a little subtler: KJTx K Ax -- xxx xx AJxx AJxx xx xxx -- x KJxx xxxx x x KQ9x Txx K9x Tx Txx Qxx Txx Qxx AQ9x AQ QTx -- AJ8 J8 K9x K9x Against 4S West leads DK up to the ace. Declarer starts with HA and a heart to the ten and jack. West shifts to a trump. Declarer wins in hand, ruffs away HQ, pulls a second trump from dummy, and leads a diamond, hoping that East has the last trump and no diamond entry. A semiloser exit generally requires a one-loser position, meaning that you have all but one of the tricks on top, not counting the exit trick. But you will sometimes get by with, say, QJ/xx in the exit suit, when the target defender is burdened with both the ace and king. ;;Exit with a loser-on-loser By discarding a loser on the exit card, declarer may exit at the same time as he completes an elimination, or as much as he can of a partial elimination. Axxxx Axx AQ xxx x J KJ9x Txx Kxxx Txxx KQxx Jxxxx KQxxxx Qxx Jxx A South is in 6S after West has shown most of the missing strength. Declarer wins the club lead, takes SA, and ruffs a club. Next come the diamond finesse, DA, and another club ruff. xxxx Axx -- -- -- -- KJ9x Txx Kx Tx x Jxx KQx Qxx J -- Declarer could ruff DJ but would then be embarrassed by the lead. So he leads DJ and throws a heart from dummy, whether West covers or not. In the extra-chance category, declarer will sometimes lead a loser and _either_ ruff it or discard, according to what comes down from second hand. xx x AQx xxx -- -- x xx -- -- -- -- T9x KJxx KJxxx x -- QT A Kxx QTx -- -- Kx x xx xxx AQ xx xx -- -- Spades are trumps as usual, and South leads a diamond. When West shows out at left, declarer discards a heart; at right, when the ace appears, he discards a club. ;;Exit to a blocking high card In this type the blocking high card is usually in the loser suit. Txxx KJ9x Q Axxx On a low one from North, declarer might duck. 9xx KJT8x Q Axxx If declarer places East with a singleton (perhaps because West bid the suit but did not lead it) he will exit with a low one from hand on the first round. West must go up with the king: the "crocodile coup". If declarer's hands were slightly stronger there might be no defence. But on the other hand, the crocodile coup is sometimes necessary even if it sets up a trick for declarer: when declarer's new winner is a card that he could have ruffed anyway, and on which he has no useful discard. 9xx xxx QJxxx Kx KQxxx Jx ATx AT9 West leads the queen or king East follows small. Declarer might win the first round, hoping to exit in this suit later, and find the cards as shown. It does not help East to unblock, either on the lead or later. Ducking to a high trump is possible, as in this trump suit: ATxxx K Qx Jxxxx Declarer has a tenace in one suit, eliminates two others, and leads a trump toward dummy, ducking when the king appears. The trouble is that the defenders might now score a trump promotion. Therefore this type of exit is apt to be unprofitable unless the bidding has been fairly informative. ;;Exit with a finesse which may lose to a bare honour Eliminating two suits, or even one, will sometimes provide extra chances in the event that a finesse loses to a bare honour. A useful special case is the finesse when missing four trumps to the queen. xxxx xxxxx Ax Ax Qxxxx xxxx Kx Kx AKJxx AKJx Kx Kx Jxx AJTx Axx Axx Against 4S West leads a heart. There is some danger of losing three diamonds and a trump. Declarer wins trick one, takes SA (both following, we assume), cashes the remaining heart, eliminates clubs, and leads a trump from dummy. At left, if East follows, declarer ensures the contract by finessing the jack. At right, the contract is cold even if East shows out, for then declarer takes the SK and exits to West's queen. When missing just Kx of trumps, a simpler manoeuvre may apply: just cash the ace and, if the king doesn't fall, eliminate the safe exit suits and lead out a trump. But when missing Kxx, it may pay to eliminate the hand and then finesse for the king, succeeding if the king is offside singleton. ;;Exit which creates a ruffing tenace KQT KJxx xxx Txx Axxxxxx Axx -- AJx The contract might be 4S, with just an overtrick at stake, or possibly 5S as a result of competitive bidding. West leads a diamond. South ruffs and takes SQ, both following. Eleven tricks are now certain. Declarer pulls the last trump with the K, ruffs another diamond, and cashes HAK. If the queen does not fall he exits with North's last diamond, discarding his last heart, and leaving: T Jx -- Txx Axx -- -- AJx A heart lead from either side guarantees a heart trick, for only the queen and one other are still out, unless an opponent has already shown out. At worst, East will take the third diamond and lead a low club through the ace; but South follows low and the heart "menace" is still effective. Declarer would play the same way if dummy's diamonds were just KTxx, unless the auction had given him some information about hearts or clubs. The elimination still works unless a defender has both heart honours at least 4-long. Even then, he can still play East for HKQ. K9x AJ AJT9x xxx AJTxxx x xx AQT9 West leads HK against 4S. For an extra chance, declarer wins with the ace, cashes DA, and leads HJ to West, discarding his remaining diamond. ;No-tenace cases When an elimination depends on Condition I, declarer needs a count of the distribution, or luck, or some of each. A7xxx KJx Axx Kx KJ8xx Axx Kx Axx Against 6S West leads DQ to declarer's king. On a trump to the ace, East shows out. It looks as if the heart finesse will now be needed, but declarer should let that wait while he does some safe elimination. He takes DA and ruffs a diamond, East showing out on the third round. He now takes CKA and leads a third, on which West discards a diamond. West is 3-?-6-2, so he has exactly two hearts. Declarer ruffs the club in dummy, comes back to his trump king, and pulls West's hearts with AK. Then he exits to West with a trump and claims the rest. Suppose that West threw a heart on the third club. Declarer could cash just one high heart and then exit with a trump, or he could cash SK and play both hearts, for if West ruffs he is stuck on lead as before. On that hand the declarer had a complete count and had a sure-fire exit as well. More often the position will contain some ambiguity. A common setting is this: A specific opponent can be thrown in with a loser in the "exit suit", but will, by then, be void of declarer's "loser suit" (the suit from which he will sluff in a ruff-and-sluff). There are trumps in both of declarer's hands but not in the target defender's, and the fourth suit has been eliminated. Axxx Txx 8542 Ax KTxxx x AQ73 KJx West has preempted in hearts, propelling NS into 4S. West leads D9, on which East plays the 6 and South the queen. As the 9 appears to be a singleton, there seem to be two diamond losers plus a heart and maybe a trump. But there is the prospect of a loser-on-loser elimination, targeting West, with hearts as the exit suit and diamonds the loser suit. Declarer leads a trump to the ace and a low heart toward the closed hand. East goes up with the ace and leads DT, on which South plays the ace. Suppose first that West ruffs. He can only exit with a heart, ruffed by declarer; declarer pulls the last trump, eliminates clubs, and exits to West with HT, throwing one of his two diamonds. A ruff-and-sluff will take care of the remaining diamond. If West unexpectedly follows to the second diamond, declarer just pulls a second trump, because he has at most three losers. If West discards on the diamond, declarer pulls a second trump, takes CA, ruffs a heart while in dummy, eliminates clubs, and exits as before. Can he go down? Only if trumps are 4-0, or the preempt was on KQxxxx or less -- or if West led a singleton holding QJx of trumps and then refused to ruff! Observe that South could not afford to take SAK before conceding the heart. Had he done so, whichever defender had three trumps could win the heart and pull a third trump round, disabling the ruff-and- discard. Partial eliminations are one of several cases in which declarer must foresee the danger that a defender might get in and pull two for one. The above hand illustrated a common manoeuvre by declarer: ruffing away all but one of a suit, to "isolate the exit". Provided that West had seven hearts for his preempt, only he could win the third round. ;Entry-gaining eliminations Most eliminations give the defender only a choice of ways to lose a trick. But sometimes he has another option: to concede an entry or tempo for the development of declarer's side suit. Axxxx AQx K 6532 Kx xxx xx AKQJT8 Against 5C the defence starts with a diamond to the ace and a diamond back, forcing the dummy. As a result of this opening, declarer is a little short of entries for the development of dummy's spades. He pulls trumps in two rounds and takes SKA, both following. When East follows to the third spade, South discards a heart. If West follows, spades were 3-3 and South has a discard for another of his hearts. If West shows out, East's only "safe" exit is a fourth spade, which cures declarer's shortage of entries: declarer ruffs, takes HA, and discards his last heart on the established spade. The loser-on-loser exit just seen is the usual kind for an entry- gaining elimination, but others are possible. Axxxx Axxxx ATx AQT K K 6532 6532 Kx Kx Qxx xxx xx xx AKQJT8 AKQJT8 Again in 5C the defence starts with a diamond to the ace and a diamond back, ruffed in dummy. Trumps come down in two rounds. SKA come next, and a spade ruff, on which West shows out. At left, declarer combines two finesse chances by running HQ. At right, he finesses HT or HQ and is home. ;Safety eliminations In general, elimination play tries to get more work out of high-card (tenace) combinations. But there are a few suit combinations in which a _long-card_ trick can be developed with the aid of the defence's leads. We then use the term "safety elimination", because of a kinship with some standard safety plays. 1) AJxx K9xx 2) AJxx Kxxx 3) ATxx K9xx In the combination (1), there is a safety play for three tricks: cash the ace, and then lead low toward the jack or low toward the 9. Now consider (2). If North's exits have been removed, declarer can still be sure of three tricks (or two tricks plus a favourable lead by North in some other suit): he cashes the king and leads toward the jack; if South shows out, declarer follows low, leaving North endplayed. Now suppose that, in the course of the elimination, the ace was used up, leaving Jxx/Kxx. Declarer can still lead low toward the jack, ducking if South shows out. In (3), if North's (or South's) exits have been removed, there are several ways to ensure a third trick or a favourable lead elsewhere. Txxx A9xx If neither opponent has a safe exit in another suit, and the lead is in the South hand, declarer can ensure two tricks by leading toward the ten. East might capture the ten and then lead through the 9, but if so, either the 9 will hold or the suit will be 3-2. If East wins and leads high, declarer holds up. Likewise: AQxxx Txxx AQJ x Kxxxx Jxxx x AJx West leads SJ against 4S and you put on the queen. If trumps are 2-1, you eliminate the minors and lead a heart toward the ten or jack. You are sure to make a heart honour, a long heart, or a ruff-and-discard, for your tenth trick. If East shows out on SQ, then I think you should just pull SAK and lead a heart through West. If someone has a singleton heart it is likely West, and probably a high one. If you do any crossruffing first, you might lack the time or the entries to develop a heart, even if the suit is 3-2. Kxxx opposite Txx is an interesting special case. xx ATx Txx -- x KJx Kxxx -- Trumps (spades) have been pulled. Declarer can make certain of five more tricks. He exits with a small diamond from each hand. If West wins, no problem. If East, and he leads DQ or DJ, South ducks. (With KTxx/xxx he could cover.) And if East continues with the other quack, or with a small one, declarer puts up the king, for if West wins now it means that the suit was 3-3. Notice that declarer also has five tricks if the defence is already on lead in this diagram, having been thrown in with a trump or a club. ;Eliminations with two loser suits If declarer exits while he still has top losers in two suits, it is usually possible for one defender to take his tricks in one suit and then cross to his partner's hand for tricks in the other. But not always: x xxx Kxx -- x Axx Axx -- Trumps have been pulled. If one defender started with 5+ diamonds and the other with 5+ hearts, they will only take two tricks. Declarer just cashes his three red winners and exits with a _heart_. Suppose East (it doesn't matter which) had five or more hearts and has no diamonds left. If he wins the exit trick, he can cash a second heart but then must yield a ruff and discard; and if West wins the second heart he can only cash a diamond before doing the same. That sort of ending admits positional variations. x xxx Kxx -- -- -- AQTxx Jx xx QJxx -- x x Kxx Axx -- Declarer has four tricks if East has HA and in some other cases too. He takes DA then DK and leads a heart toward his king. If the cards lie as shown, West can win and then cross to East's jack, but to no avail. ;Ruffing tenaces We have mentioned that high cards opposite a void can consititute a sort of divided tenace. We call such a combination a "ruffing tenace", after the standard term "ruffing finesse". A ruffing tenace may come to declarer's aid when he lacks the entries or the trumps necessary to eliminate the suit completely from both hands. ATxx AT9x Qx Qx We assume that the South hand has a trump and the North hand has a side entry. Declarer plays off the ace and exits with the queen. If West has the king, he cannot safely exit in this suit if he has the jack or, at right, whether he has the jack or not. Qxx x The opening lead is the K or A (from AK). West cannot lead another round of this suit so long as North has an entry and South has a trump. If the other suits become unsafe too, West may be thrown in. Txxx AQJ xxx xxx AKxxxx x AKJ AKQ West leads CT against 6S. On SA, East shows out. Declarer lacks the entries to eliminate hearts, but a ruffing tenace will serve equally well. He cashes SK, then HA, then tries to cash his remaining clubs. If they go by, he exits to West with a spade, and claims. Declarer's sequence of play was such that West would still find himself thrown in if he ruffed any of the three clubs. Now suppose North has just AQx in hearts, rather than AQJ. Again a club is led and East shows out on SA. Declarer's sequence of play is the same. This time the endplay is not certain, but it combines two finesse chances: HK with West, and DQ with East. For some fancier illustrations of ruffing tenaces at work, see the article _Avoidance Plays_ at www.hammick.com. ;Trump-only elimination In rather rare instances, declarer's safest line is to cash his tricks in all three side suits, and then let the defence come to him in trumps. Q432 xxx Kxx Axx J8765 Axx Ax KJx West leads a heart against 2S. Declarer wins, cashes CAK, eliminates diamonds, and exits with a heart or a club. He has taken six tricks and is now certain of two more in trumps, or one trump plus CJ. ;Bluff eliminations When declarer can see that his contract is predestined to go down, he must play as if he held something other than what he actually holds: "obligatory deception", one might call it. The same applies to a defender who is certain that the contract is on its way to being made. ;;Bluff elimination to provoke a lead up One such deception is the "plastic elimination play", which usually involves a 4-4 side suit containing a tenace. x ATxx x -- -- -- Qxx Jx Kx Axx x x x K9xx Q -- Declarer exits with his diamond. If the defender who wins this trick has a count of the hand, he will exit with another diamond or a club, giving declarer a profitless ruff-and-discard: the fourth heart round is not a loser. xx ATxx x -- -- -- Qxx Jx Jxx AQxxx x -- xx K9x Kx -- Declarer leads a diamond from dummy, East goes up, and South drops the king, pretending to be out. East can probably see that it is safe to lead back another diamond. DK was a duplicated value in that no loser could be discarded on it; good play, then, to put it to work as a falsecard. There is a little known double bluff on the same theme. xxx ATxx x - Q x Qxx J9x x QJx xxx x xxx Kxx Kx - Declarer's heart tenace is too weak to use, and the bidding rules out the possibility of finding West with only two hearts. So, having arranged the previous play to resemble an elimination, declarer now cashes DK and exits with a trump. Since declarer has not taken a ruff in diamonds, West may well place him with a fourth heart, and lead back a club. In another variety of bluff elimination, an r&d does declarer no good because he has no surplus ruffers. x Qxxxx -- x -- -- KJTx xx xxx xx -- KQx xxx Ax -- Ax West is in and must exit with a diamond. It does South no good to ruff in dummy and discard a heart, for then he will have no ruffer for his club. A defender can come to the right answer in this sort of position if he counts declarer's winners. Four trump tricks (counting the r&d) plus two aces is only six of the last seven, so the defence will take a trick provided that declarer is not allowed to score HQ. ;;Bluff elimination to provoke a ruff-and-discard In this type, the defender must lead up to a tenace, avoiding an r&d. The lead does declarer no good because the defender's high card would have been ruffed out anyway. Again, the defence quickly reaches the right answer if they can count declarer's tricks. xx AQTx Ax -- -- -- 98xx KJx xx KJx xx xx xx xx Qxxx -- Needing seven tricks, declarer finesses HT to East's jack. If East leads a diamond declarer takes the queen, then ruffs down HK, establishing the dummy. If East leads a club, dummy's diamond loser is discarded while South ruffs, and again declarer sets up the board. But if East exits with a heart up to the AQ, declarer has only three trump tricks, two hearts, and DA. ;;Bluff elimination to provoke a duck In this type, declarer simulates an exit via a combination finesse into the closed hand. Jxxx KJ Txxx AKx AKQTxx AKQTxx AQx AQ Kx KQx xx xx At left is the actual deal, and at right is the hand you will pretend to have. Against 6S West leads a heart. You have duplication in hearts: they provide one useless discard. So you overtake HJ with the ace, pull trumps, and eliminate clubs. You lead HQ to dummy's king and only now lead a diamond to your king. West may well duck if he has DAJx(x). Suppose your hearts are just Axx instead of AQx. A heart is led, and East follows small when you play dummy's jack. Again there is a good case for overtaking with the ace, as if you held Ax. ;;Bluff elimination to provoke an unblock Jxx Jxx Kx Txxxx Kx QTxxx AQx Axx At left is a side suit, and declarer has (at least from West's point of view) eliminated the other side suits. Declarer cashes the ace. West may unblock, thinking the position is as shown at right. West will unblock only if he thinks his side needs two tricks from the suit; since his side ends up with none, declarer has presumably gained only an overtrick. One more example: K9x Qx Jxx ATxxx After a mock-elimination, declarer leads low from hand, or cashes the king. Not knowing about declarer's length, West might unblock the queen to avoid being thrown in. ;Throwins In a throwin there is no ruff-and-discard threat, but at least one tenace, sometimes two. Such a tenace may be one which declarer could not directly develop, either because he expects it to be under the opponents' strength, or because he is too short of the suit in the opposite hand. These very problems, when you see them, should steer your thinking toward a throwin. -- -- KJx Kxx AQ AQ -- -- AQx AQx Kx Kx xx xx -- J xxx xx East is marked with strength. At left, North leads HJ and South discards a diamond. At right, a low heart from dummy, or the jack from hand, achieves the same position. In the simpler throwins like the above, the defender is down to two suits: the exit suit and a tenace suit. Usually the exit suit does not also contain a tenace. x AKQJ AQxx xxxx Kxxx Jxxxx xxx xxx xx JTxx JT9x x AQx xxx Kxx AKQx West leads CJ against your 6NT. You take the queen and return the ace, on which East shows out. Thankful not to be in 7C, you test the diamonds, and West shows out on the third round. A throwin against West is now indicated, with clubs as the exit suit. You run hearts, and when East follows twice the hand becomes cold. You throw a spade on the fourth heart, cash CK, and exit to West with the last club. Occasionally the exit suit and the tenace suit are one and the same, as here: Kxx Txx xxx ATxx Jxx x AKx J9xxx K?xx ?xx ? may be the J. Qxx J9xx AQxxxx Qx AQT Kx West opened the bidding with 1D but South is in 4S. The defence starts with three heart rounds and declarer ruffs. Declarer pulls trumps in three rounds, West following, and takes CKA and a club ruff, to exhaust West's clubs. He then exits with DQ to West's presumed king. Other typical exit-tenaces for such an ending are: Qxx Jxx AJx xxx KQx xxx KTx Axx Declarer exits to West Declarer exits with a low with the K. card through West. ;Throwins to overcome blockage A lead by an opponent may overcome a deficiency of entries, such as may occur because of blockage in one suit. We don't have a general theory of these endings, but we will give a few illustrations. Kxxx xx xxxx 743 AQ AKQJT AQx KT8 Against 3NT West leads C5 to East's ace, and East returns the jack. Declarer has eight tricks in his own hand but no entry to the SK. He could lead SQ to the king and try the diamond finesse, but the hand is cold on a throwin if West has five clubs and the hearts are not 6-0. Declarer takes trick two with the king, and runs off five hearts and two spades. Now he exits with his last club. After taking his three clubs West must yield a trick in diamonds or an entry to SQ. If we change the clubs a bit, so that East might have five, or the suit might be 4-3, the play is the same. If East ends up on lead and sends a diamond through, declarer can try the queen at no risk of going more than one down. QJT K K -- Kxx x A -- A -- -- AKQT A -- -- Jxxx At notrump, declarer leads one of dummy's kings and unblocks SA on it, coming to two tricks. Declarer can sometimes unblock on a defender's lead in the same way. If West is on lead in this diagram, cashing either ace costs his side a trick. This example shows why the unblocking discard is a relatively common remedy for blockage: if SA were played off at some point, the lead would be in the hand without the exit card, and we are assuming that the hand with the exit card is short of entries. Qx Qx A A x xx KJx KJTx -- -- A A Ax Axx -- -- xx xx South is on lead and exits with a diamond. At left, the divided tenace in spades now yields two tricks _plus_ access to HA. At right the throwin (as opposed to a lead toward SQ) avoids blockage and yields a third trick. These throwins work equally well if the EW hands are swapped. Naturally, if two or more tricks are isolated, a trick may be sacrificed to get to them. x KQx A -- K -- xxx xx x x -- AK Ax A -- xx The lead is with South. Declarer knows that he can run two spade tricks, but if he has a count of clubs and spades he will cash HA and exit to West with his small spade; this sacrifices two spade tricks to reach three tricks in dummy. ;Squeeze throwins There is a distinctive type of endgame, usually 3-card, known as a "squeeze throwin" or a "strip-squeeze". A defender is burdened with a tenace and with the only card or cards that can cover declarer's exit card. Because of the latter handicap, declarer needs not eliminate the other two suits separately. Instead, he usually runs one long suit, running the defender out of that suit and obliging him to toss his winners or exit cards in the fourth suit as well. K73 -- A43 xx T986 T9 764 -- 5 82 -- KQT975 86 Q KJ 75432 KJ AKQ9 8532 A AQJT964 x J2 J AQ AQ JT -- West opened an Acol 2H and doubled South in 4S. He cashes CAQ and switches to HK. Declarer wins, ruffs a club high, and runs the trumps, reaching the position at right. On the last spade West will, we can assume, throw CA, whereupon he is thrown in with HQ. Observe that cashing the second club cost West's side a tempo. If West switches to HK at trick two (or opens HK), the hand cannot be made. In that example the defender had the minor tenace behind declarer's major tenace. In such cases the defence makes only one of the last three tricks, namely the exit trick. But the defender may equally have the major tenace, and declarer the minor, in which case the defender makes two of the last three. Squeeze throwins are not usually that easy for declarer, even if he can reliably place the crucial high cards. He may also need to take a view on the distribution, and must count the defender's relevant small cards as they appear. ;Defence Foremost, a defender needs to be _aware_ of danger before it is too late to do anything about it. He should habitually take note any stoppers in his own hand which will explode if led away from. A lead by partner, up to such holdings, i.e. a lead through declarer's tenaces, is the most effective defence against endplays. Merely counting the hand will prevent costly mistakes in defective eliminations. KQTx Jx KJx JTxx xx x Kx T9xxxx ATxx xxxx AKQxx xx AJxxxx AQx Qx xx West has come in with the strongest of all simple overcalls: 2C over 1S, vulnerable against not, at pairs. Against 4S he leads AK and another club, ruffed and overruffed. Declarer takes SAK, ruffs dummy's last club, and leads DQ from hand. West counts declarer for two clubs and six spades. If DQ is singleton, therefore, two discards on DKJ are of no use. He therefore takes DQ with the ace and leads back a diamond. West reaches the same conclusion if he counts declarer's ready tricks: 6S+1H+2D. ;;Diagnosis The likelihood of an endplay may be visible to a defender for the same reasons as declarer: declarer has strength facing shortness, or losers facing losers. For an elimination, declarer has ample trump control but no useable side length in either hand. Dummy tends to have four or five trumps but little ruffing value. Dummy is apt to be balanced, but may have, for example, a singleton opposite declarer's doubleton. Declarer's preparations for an elimination are usually rather conspicuous: -- Declarer cashes a winner to no apparent purpose. He may be hoping that the suit will become blocked, later providing an exit to only one opponent. It may be necessary to unblock e.g. Kx behind his ace. -- Declarer ruffs a suit in the long trump hand, although the suit cannot be set up. When a good player voluntarily ruffs in the long hand, you should ask yourself why. Most often he is removing the defence's exit cards. He might also be isolating a menace for a squeeze, or reducing his trumps for a specialized trump ending. Only rarely is he just counting the hand. -- Declarer ducks in a suit which can't be set up For instance, if he hopes to exit by a combination finesse or high loser, he needs all but two of the remainder. It may be vital to attack declarer's tenace at once. ;;Leading On lead, attack the tenace if possible. xxx AJ9 Q8 KTx If East, at some point, leads the queen or the 8, the exit-tenace will be ruined, even though West is unable to continue the suit from his side. When you cannot attack the tenace, you may yet remove entries that declarer needs to eliminate side suits. The usual target will be the hand with fewer entries, or the only hand with losers to ruff, since (usually) neither hand has useable length. Avoid pointless forcing leads. These can give away entries as well as tempos. Eliminations require pretty firm trump control, and if declarer has such control there is no point in forcing him. If dummy is flat there is a temptation to get passive, but a forcing lead may be needlessly unconstructive even then. A flat dummy is not unusual in a dummy reversal, an elimination, or a trump reduction, all of which will be accelerated by a forcing lead. (Cases are known in which a defender gets thrown in specifically to accelerate declarer's trump reduction.) Likewise, it can cost a tempo to cash a winner in a suit which declarer will want to eliminate. Seek a lead up to dummy's weakness, or a play which removes an adverse entry, or a play which is informative to partner, rather than one which is purely passive. ;;Avoiding one-way exits This topic overlaps the one below, about unblocking. Rather often, you can thwart declarer's attempt to isolate the exit. Axxx KJT8 9xxx Q Declarer leads the ace from dummy, which in itself is suspicious to West. If West fears he might run out of exit cards, he follows with an honour, and with honours again when declarer ruffs one or two rounds. Sometimes you can cloak the fact that you are the only one who can cover the exit card. AJx xxxx KQTxx x Declarer crosses to the ace and continues with a small one. If, as is likely, East expects this to be ruffed, he should go up with the king. To play the ten would suggest KQ as well and would therefore make it easier for declarer to plan a loser-on-loser exit to East. If the king unexpectedly holds, East can exit with the queen, destroying the jack. A9x QJTx xxxx Kx Declarer cashes the king and continues with a low card. Diagnosing an elimination underway, West may play the queen instead of the T. He may also play quacks under both the king and ace, as if unblocking from QJx. You can sometimes avert a ducking finesse by going up second hand. Declarer may have a sure-fire exit with AQ9/xxx, for example, but he will frequently try to make do with less. If he has, say, AQx/87x he will lead the 7; then second hand must cover. With AQ8/xxx, second hand must put in the 9, T, or J to prevent the ducking finesse. If declarer's strength is in the closed hand, this defence is harder to spot, but by no means always impossible. ;;Unblocking When threatened by a throwin, a good defender will unblock with grim determination. Bare winners in your hand are a hazard and you should always give some thought to cashing them at an early stage. A bare trump winner, if you don't expect to get in to pull two for one, should be got rid of by ruffing any adverse winner while you still have a safe exit. Near-winners which block a suit, likewise, are sometimes used by declarer to put in a specific opponent; have your thumb waiting on such cards. Doubleton honours are somewhat hazardous; for that reason and others you should often go up with Qx or Kx sitting over small ones in dummy, and should consider unblocking the honour even if you are sitting under dummy's losers. If you have Ax of trumps, give some thought to the danger of ducking the first round, e.g. when declarer seems to be finessing against against the queen. Likwise with Kx of trumps under dummy's AQx or AQT. Unblocking twice in one suit may be necessary, as here: Kxx Qxx QJx Txx KJ8 T9x Axx Axx Be aware that an unblock against an endplay is of no value unless it _promotes_ something in partner's hand, so that he rather than you can capture one of declarer's losers. ;;Discarding In discarding, try not to run out of the tenace suit. The more difficult eliminations require declarer to take a view on the distribution. To a considerable extent you can inhibit his card- placing. For a no-tenace elimination, declarer will want to know at what point the target defender becomes void of the loser suit. For a throwin, he will want to know at what point the defender's stopper becomes unguarded, or at what point he has no more winners to cash when he gets in. AQ x x -- x Kx x Ax x -- x -- xx K A -- Declarer cashes his last diamond and, at double-dummy, East is caught in a squeeze throwin (i.e. a throwin assisted by the semiloser HK). But declarer may well be uncertain of the distribution, particularly if there is a thirteener (West's club) still at large. In the above case East may throw a heart and if declarer places him with the last club, declarer will play for the drop in spades. If the fourth suit (clubs) is all gone, East in such cases may unguard a stopper such as Kx or Qxx, preferably not at the last moment. ;;Congestion The defence has a big problem when all their strength is "congested" in one hand. The strong hand gets into trouble not only with exiting but with discarding -- he gets squeezed as well as thrown in. If you are congested, tend to cover honours, hoping to transfer some of the load to partner. This practice also helps avert squeezes. If partner's hand is congested then you, although weak, may need to diagnose that problem and give him a chance to cover something, thus promoting some card in your hand. To illustrate: Qx Qx T8xx KJxx T7xx K9xx A9x AJ8 In both diagrams, East can discard only twice from this suit, and cannot exit in it. But suppose West leads low and declarer puts up the queen, covered by the king and ace. Now East can discard three times, or discard twice and exit. Declarer does better by playing low from North. Now East finesses against dummy, and can still discard twice and exit. A related phenomenon on idle cards: Qxx AKxx Jxxx xx West, with a congested hand, leads the king against NT, East signalling. It may be right to continue with a low card, preserving the ace as an idle card. ;;Breaking a dangerous suit You know about this position: Txx Axx KJ9x Qxx East, if he attacks this suit, should lead the jack, "silencing" the dummy's ten. East can afford this high lead because he retains a tenace (K9) over the ten. If East led the king, it would not cost a trick but the defence would be unable to continue the suit. The same principles apply when the defenders are obliged to break a suit where declarer is stronger. Jxx QT7 K8x A9x If West leads low, away from two high ones, declarer has two easy tricks. If West leads the queen declarer will win with the ace and now both defenders are burdened in the suit and unable to lead it. But if West leads the ten, the J, K, and A will come out, and now only West is burdened. The lead of the ten silences fourth hand's 9 while retaining a tenace over it. ATx Q96 J7x K8x If West leads the queen, declarer will normally play for split honours and win with the ace, leaving both defenders burdened; he may also win with the king if he can later put East in. But if West leads the 9 (enough to silence the 8), the T, J, and K go and only West is burdened: East can safely discard one and, if necessary, later lead the other. Kxx Kxx Kxx AQT xxx AQx T9x AQx Txx Jxx Jxx J9x If West is stuck on lead, the queen is the best exit. Even if the elimination has succeeded in a double-dummy sense, silencing fourth hand may put declarer to a guess. Txx Kxx AQx J9x AQx J9x Kxx Txx East leads the J. West leads the Q. K9x Jxx Qxx ATx West leads the J or East the Q. Declarer should, by Restricted Choice, guess right. But on some later occasion when a defender has both quacks, the defence will get a trick. Two more miscellaneous technicalities: Kxx T8x Qxx J9x A7x Q9x AT8 KJ6 If East must lead the suit at left, the jack is best. At right, North leads the ten, covered by the queen and king; West may duck if he doesn't have a safe exit. One last merit of a high exit is that it can create blockage. AQx AKx Kxx Qxx Jx Jx West leads the K. East leads the Q. Qx xxx KJ9 xx Kx Jxx ATx AQ If West is in, he must lead SK to avoid a second throwin. On a diamond, declarer takes both diamonds and leads a spade, unblocking the queen if West goes up. On SJ or S9, declarer takes SQ, then SA, and exits with (or cashes) ST.