[nielsfoged]

Scoring: IMP

1H-p-1NT-p;
3NT-a.p.

---

Lead: ♠3 (3rd/5th) won by 8 over 7.
What is your plan(s)?
Do(es) it/they depend on the skill-level of your opponents?

Niels

[Fluffy]

there seem to be few legitimate chances, but all of them start with a low diamond.

[nielsfoged]

Fluffy, on Dec 23 2007, 12:00 PM, said:

there seem to be few legitimate chances, but all of them start with a low diamond.

who said anyting about legitimate - this is real bridge!

[dburn]

There are actually quite a number of legitimate chances, none of which starts with a low diamond. I would play a club, intending to put in the seven.

Legitimate chance (1): someone has QJ doubleton in clubs.
Legitimate chance (2): West has Qx or Jx in clubs and East misguidedly wins the first club trick. It is quite hard for the defenders to avoid doing this unless they are both very good players.
Legitimate chance (3): even if West puts in a club honour from Qx or Jx, East might have both top diamonds, when the defence may not be able to beat the contract.

[pclayton]

Fluffy, on Dec 23 2007, 09:00 AM, said:

there seem to be few legitimate chances, but all of them start with a low diamond.

And how do you plan to establish and reach the diamonds even if they are 3-3? You'll burn an entry to knock out the 3rd and the 4th and 5th will be stranded.

There's another idea which fits the title of the thread that David mention in his #2.

[Fluffy]

My plan is an endplay after diamons are cleared so I can make ♥J

[pclayton]

Fluffy, on Dec 23 2007, 04:16 PM, said:

My plan is an endplay after diamons are cleared so I can make ♥J

Lets see, ♠ won, ♦ lost, they continue ♠ won in dummy, ♦ lost, ♠ you win....

You can play ♣, ♣, ♣ and you might get home. They can cash a diamond but RHO could be 2=5=3=3 and forced to lead a heart. Even if they play clubs, they can't stop this as far as I can tell.

I like the ♣ to the 7 myself. Even if it wins, I've retained all of the chances Fluffy is playing for.

[Walddk]

I have much sympathy for finessing ♣7 at trick two. It takes an expert defender in the East chair to duck with Jxx. Most people don't even think about it. Winning a cheap trick is a temptation very few can resist.

Roland

[Fluffy]

I used DF and saw that actually starting with a diamond has very very little chance of success, oppoennts can then never ever play a spade and you can't score ♠J.

This is a double dummy defense of course, more likelly is that opponents decide to open clubs from the wrong side and get a disaster.

To achieve the endplay at double dummy you have to start with spade at trick 2, but it requires some blocking in both diamonds and hearts, this is I think the best legitimate chance, but all in all I don't like the line any more. Low club to the 7 seems best.

[nielsfoged]

Fluffy, on Dec 24 2007, 09:30 AM, said:

..., more likelly is that opponents decide to open clubs from the wrong side and get a disaster.

Notice that the opening of the clubs by the defense is never what causes their disaster, whereas the (mechanical) use of a ♣ honnour in 1st round could be what starts their missery!

[jwmonty]

It seems that there are quite a lot of legitimate chances here.

Return to dummy at T2 with a spade finesse. Now you call for the low diamond. You are hoping for AK onside. A priori this is 24%, but the spade lead indicated a 5-2 split there, so if diamonds are 4-2 or 5-1, RHO is considerably more likely to have the length and this increases his chances of holding both tops. Let's say 30%. (I don't think the spade lead particularly suggests that LHO has a diamond entry. With five spades he would have led one regardless of the rest of his hand.) If RHO does hold both diamond tops, the hand is a guaranteed make. You go up with the queen if he ducks, and if he splits and switches to clubs, you win in dummy, cash the rest of the major suit winners (claiming if the queen of hearts falls), and continue diamonds. East can win, but even if he is able to cross to partner's queen of hearts now and let partner cash the fifth spade, that is only four tricks for them.

Suppose RHO plays low on the diamond, you play queen, and it loses. If diamonds were 3-3 originally, the opponents cannot continue the suit profitably, now or later. If LHO started with AK, AJ, A10, KJ, or K10, he can cash the second honor and establish two more tricks for his partner, but he cannot see your hand and he is very unlikely to think of that. Similarly, if he started with AK10x, AKJx, AJ10x, or KJ10x, he won't know that he can lead a low diamond now to partner's hand. Surely it is most likely that he will simply play another spade.

You win the spade and play a low heart from the dummy. You don't care who wins it. Let's say LHO does and returns the fourth spade, setting up his winner. Now you cash the AK of hearts, to see if the queen falls. If it doesn't, you play the king of clubs, your last chance. You can still make your ninth trick in clubs if there is a singleton honor on your left, or QJ doubleton on your right. (Also QJ doubleton on your left, but presumably you will finesse when LHO drops an honor.)

If LHO switches to a heart when he gets in with the diamond, you play more or less the same way. Win the first heart and then play a low one. You cash the other top heart later.

What are the total chances of making the hand by playing this way? You already have 30% or so from the diamond suit. You also make when an opponent has stiff Q, Qx, or Qxx of hearts. (LHO most likely, but it is not impossible that LHO started with five or six small hearts to go with his five spades, in which case you will have the pleasure of seeing the queen drop on your right.) The hearts will be 5-3 47% of the time. You will get Qxx 37.5% of that 47%, times the 70% chance that you haven't already made the hand with the diamond play, which adds up to a 12% chance out of your initial 100%. So add that to 30 and we are up to 42%. Hearts will break 6-2 17% of the time, and you get Qx one-quarter of those times, for another 4% times .70, for another 3% to the total. That brings us up to 45% overall. The last chance is the club play. Clubs will break 3-2 68% of the time, and a priori RHO will have a doubleton 34% of the time, but RHO is more likely to have the club length (because of the known spades), so let's say actually 28% of the time he will have a doubleton club. The doubleton must be specifically QJ, which occurs 10% of that 28%, for 2.8%, times .7 for, let's call it another 2% overall, which brings us up to 44% making. Clubs will also break 4-1 28% of time, so that a priori LHO will have a singleton 14% of the time, but LHO is more likely to have the singleton than his partner (again because of the known spades), so let's say he has a singleton club 16% of the time. That singleton will be an honor 37.5% of that 16%, or 6% of the time, multiplied by .7 overall, so let's say another 4% there. That gets you up to 49% overall, and you can add a quarter of a percent overall for a stiff queen of hearts.

So it seems that you have roughly a fifty-fifty chance of making the contract legitimately, assuming that the defense lets you try all of your suits one after the other without cashing five tricks first. What can go wrong? Well, there is the possibility mentioned earlier of the diamonds breaking in such a way that the opponents have four tricks in the suit, and have to set them up (by cashing LHO's second diamond immediately) before you have time to try the heart play. I consider this too unlikely to worry about. But it could also happen that RHO has AJ10x(x) or KJ10x(x) of diamonds and plays low the first time. When you try the heart play, RHO can go up and cash the rest of his diamonds. So let's say that you are going to go down whenever LHO started with stiff A, stiff K, Ax or Kx of diamonds originally (with Ax and Kx meaning the low spots, not the 10). I give him about a 10% chance overall of having started with one of these holdings (4/15 of possible original doubletons, times a 30% probability that he started with a doubleton, for overall 8%, plus another 2% or so for stiff ace or king). This ten percent overall of losing cases must be subtracted from the fifty-fifty chance I calculated earlier, bringing us down to about 40%. Another worry is that after you lose the diamond trick to LHO, he will find a club switch that attacks your entries. If LHO has xx of clubs and leads one now, your options are reduced. I don't know what the likelihood is of LHO's finding this play, if indeed it is available to him. However, he might also come up with the clever idea of switching to a high club from Jx, playing partner for club strength, which would give you a chance to make on misdefense. Again, the probability of this is hard to quantify. Let's say your chances remain at about forty percent overall.

How does this compare to the proposed alternative of finessing dummy's club seven at T2? Assuming RHO will always win the trick when he can, you make against Qxx and Jxx in his hand. But if RHO has Qx, Jx, QJx, or QJxx, your chances are now very poor. You are only getting one club trick, the opponents have at least two and perhaps three diamonds to cash whenever they like, and dummy can be endplayed to give up heart tricks. In fact, you will probably go down more than one. So you really need to catch him with that Qxx or Jxx. The a priori chance of a 3-2 break is 68%, half of which or 34% will give RHO three of them, but as noted earlier RHO is known from the spades to be more likely to have the club length, so let's be generous and say he has exactly three clubs 40% of the time. Of these, he will have Q or J but not both 60% of that 40%, for a total of 24%, so you are only going to make the hand about a quarter of the time. (There is also the possibility that LHO will already have played an honor when you led the club from your hand. This will let you play him for a singleton, making when you finesse on the way back, but this risks going down disastrously when LHO started with QJ or split from QJx and you could have made the hand with the diamond or heart plays.)

I think my proposed line is best.

[dburn]

If West plays an honour on the first round of clubs, there is no need to commit yourself at that point. You can win with the king and play a diamond, retaining several options (including the chances you refer to in your post). For example, if the deal is:

Scoring: IMP

---

the defenders cannot beat you even if they try to give you a losing option at once. The play will be: spade to the eight; club to the jack and king; diamond. East wins and returns a club to force you to commit yourself, but you win the ace and play three rounds of spades and a second round of diamonds.

Interchange one of East's top diamonds with West's four, and the defence can beat the contract, but they may not. The play will then be: spade to the eight; club to the jack and king; diamond won by West's jack (East can beat you by rising with ♦A and playing a club, but he may not find this). West now needs to play a red card and not a spade. Interchange East's queen of hearts with one of West's low ones and the defence cannot beat the contract.

It is true that if East has both high diamonds, you can succeed by following jwmonty's line while playing a club to the seven may fail. But it is also true that jwmonty has seriously underestimated the chances of success by playing a club to the seven, as the example I have given may help to demonstrate.