May 9, 2014 – Should You Risk a Contract Trying for an Overtrick?

My short answer to the title question is – NO. I want you to concentrate on landing your contract, or setting theirs, and not to waste energy on overtricks. Still, bridge is a game of probabilities, and we have to assess the potential gains and losses of every action. What is that overtrick worth? What are the risks? Look at two simple examples:
1.

 

After a trivial auction, both vulnerable, 1NT – 3NT, West leads the spade queen. Plan the play.

This is quite simple. You need only five club tricks for your contract, and can afford to lose a club trick. We can make the contract whenever clubs split 3-2 or 4-1 by winning the spade and ducking a club. That is clearly the right play. If we try to run the clubs, we’ll make an overtrick when clubs split, and win one IMP against the safety play 68% of the time. If clubs go 4-1, our greedy play will mean down two, and 13 IMPs away. We gain 1 IMP 68%, and lose 13 28%.

The math goes like this: The safety play gains 13*.28 and loses 1*.68, for 2.96 IMPs per board.

2. Let’s make one simple change:

 

Again, we can guarantee our contract, even against a 5-0 club split by ducking a round of clubs. However, 5-0 splits only occur around 4% of the time. Paying out 1 IMP on 96 boards to win 12 on four is poor odds. Moreover, if we win the spade and lead a club, we will see West show out, and can duck a club. So the safety play only gains when West has all five clubs, down to 2%. The IMP scale favors playing clubs from the top.

The IMP scale can be quite fickle. Not too long ago, I watched a declarer go down in a four heart game, taking a risky finesse (that definitely rated to be onside). As it turned out, the pair at the other table had a poor auction, and missed the game, finishing up +170. So the greedy finesse turned a 10 IMP gain into a 7 IMP loss. 19 IMPs away. For what? +650 would have won the same ten IMPs. The overtrick was worth exactly zero IMPs. 19 to 0 made for a terrible bet on a finesse.

In practice, I tend to play very safe in any game or slam, but I will sometimes get aggressive in part-scores. I don’t like 10 or 12-1 odds for an overtrick in a game. When the contract is low, the odds might be only four or five to one, and an overtrick might be worthwhile.

These thoughts were spawned by Board 4: With both sides vulnerable, South opened 1NT and played there (hands rotated as usual), at both tables:

 

West led the three of hearts, and proceeded to run off five heart tricks. Plan the play.

You have five obvious tricks, and need two more. You can develop two absolutely sure winners from the diamond suit, with the spade king as an entry. Clubs will usually yield two extra tricks, and may often yield another. Is it worth playing on clubs, rather than diamonds, risking the contract?

No, and not simply because of the threat of a bad club split. We have to discard three cards from hand. If we try to keep all five clubs, what do we throw? Three spades? We may never see the spade king. Two spades and a diamond? The defense might shift to diamonds, setting up their potential seventh winner. No, we will have to throw a club, reducing our potential club winners by one. So we should settle for our seven sure tricks. Discard two spades and a club from hand, and two clubs (or one club and one spade) from the table, preparing to play diamond ace, diamond.

Okay, say you discard two clubs from the table, as East discards discouraging diamonds. This leaves:

 

 West surprises you by shifting to a diamond. Now what?

Well, we can play the eight, win the ace, and return the suit, ensuring seven tricks. Or, we can get greedy, win the queen, and try a club finesse. That will garner an overtrick when clubs are 3-2 with the queen onside, and much of the time when East started with four or five clubs to the queen (on a double squeeze). What are the risks? We could go down, but only if the club finesse loses, clubs don’t split, and the spade queen is off. I make that around an 8% risk. Should we risk our +90 for that overtrick? Maybe.

At both tables, South decided to rely on clubs for the contract, not anticipating the problems discarding on the fifth heart. Both declarers shed a club and a diamond from the table. That was very poor play.

At one table, West shifted to a spade, with the jack covered by the queen, and ace, leaving this ending:

 

Declarer could set up a diamond winner, and bank on the club finesse. Or declarer could hope the diamond finesse was onside, and play out clubs from the top. That would also gain if the club queen were doubleton, so seems better than hoping for the club finesse. Playing for the diamond king onside gives substantial extra chances, but East’s discards suggest that it is off. Declarer chose … the diamond finesse, club play. Unfortunately, this was the full hand,

 

This line fared poorly, and the sloppy discard from dummy cost the contract. West shifted to a friendly diamond, not a spade, at the other table, and South, despite the poor play, emerged with eight tricks, and a six IMP gain.

                                   Unfavorable Vulnerability is a Strange Beast

Now, a bidding problem. Red on white, you pick up:

 

The auction starts out:

 

What do you bid?

Six hearts is almost certainly cold. Even if partner has nothing but a long string of hearts, we will likely survive if the opener has the heart king. I guess I would Blackwood, and play a slam opposite one key card, and a grand facing two.

However, offensive hands like this tend to skew the total trick number. Scoring a silly +680 in five hearts might well beat the +500 against their six spade save. Bidding only five hearts, and getting “pushed” to six could work out very well. That is something to consider:

 

•             Buying the contract on high-offense hands might be better than bidding to the perfect    level, and having them save.

In practice, partner held two keys, so seven hearts was cold, as was 7NT, should they take their cheap seven spade save.

I want to close off with Board 5, a very delicate and tricky defensive problem:

 

North-South were vulnerable, and the auction went:

 

You are hoping partner might find a diamond lead, and, sure enough, your wonderful table-mate tracks the diamond jack. Yay! North covers with the king. You win and return a low diamond, but South’s nine wins. The seven of spades is run to your ten. Plan the defense.

Apparently, partner led from Jx in diamonds, with length in both majors, and, likely, nothing in clubs. Indeed, South almost certainly has the club king and queen for the bidding. Let’s count winners: South has three club winners, a diamond, the heart ace, and the top two spades. That’s seven. The long spade will set up, eight. So we can’t give South another trick. Clearing diamonds, and hoping to get in with our heart king is futile.

To set up the spades, South will lose two tricks, and we have two diamond winners. So, the heart king appears to be the setting trick. Suppose we go passive, and return a spade. Declarer sets up spades, partner shifts to a heart, declarer takes a losing finesse, and we cash our diamond. Can anything go wrong?

 

Here is a possible layout:

 

When spades are established, the position will look like this:

 

North leads the spade as you and South throw diamonds. When partner leads a heart, South might decide that there is no rush to take the heart finesse. North can win, cash the spade, South can take the clubs, and then lead a heart up. In the meantime, after the heart ace and the spade, you are squeezed in all three suits, and will give up the ninth trick on any discard.

This impending squeeze can be prevented, provided the defense play clubs twice. If you shift to a club, and partner continues the suit, there is no squeeze.

 

Excellent! Which club should you try?

Let’s try one small change:

 

You try a club, South plays the seven, and West? West must not play the ten, or South wins four tricks in clubs. You want partner to play low on the first round, yet continue clubs when in. I don’t know any way to communicate all of that. I would probably try the club eight, and trust my brilliant partner to work out the hand.

The full hand was this:

 

On this layout, there was no real defense. Perhaps West should have put up the spade nine on the seven, to gain the lead and play a heart through dummy.