[paulg]

Scoring: IMP

1♦ 1♠
2♠ 3♣
3♥ 3NT

Lead: ♥5

---

As South you stumble into 3NT on the obvious heart lead.

How do you play the contract?

For full marks you need to state where you win the first trick (assuming you want to win it), and why.

No need for experts to answer, even though a good player misplayed it.

[FrancesHinden]

cardsharp, on Mar 7 2008, 09:18 AM, said:

Scoring: IMP

1♦ 1♠
2♠ 3♣
3♥ 3NT

Lead: ♥5

---

As South you stumble into 3NT on the obvious heart lead.

How do you play the contract?

For full marks you need to state where you win the first trick (assuming you want to win it), and why.

No need for experts to answer, even though a good player misplayed it.

It's a nice hand.
Interestingly it took me about 3 times as long to work out where to win the first heart as it did to work out the general approach to the hand.

[han]

This is very nice, it reminds me of a very difficult hand in one of the Falk's trilogy books. If you have read those books as often as I have then you'll know the hand.

I'm willing to place 5-1 odds that no beginner will solve this problem, any takers?

(of course I cannot lose this because when someone solves it I will immediately claim that they are not beginners)

[skjaeran]

Agree with all others that it's a very nice problem. It took me somewhere between half and a full minute to solve it, which means it's far from straightforward (I'm pretty quick normally).

[Wackojack]

Hmmm since this does not look that easy and I class myself as advanced, I will have a go.

There are 7 top tricks and you have to find 2 more. If you go for diamonds immediately by running the Jack, and the Queen is offside you go off. That gives you a 50% chance. Alternatively you can look to see if spades split 3-3. If they do not, you have the fallback on diamonds being favourable and you still make. If spades do split 3-3, then you only need 1 extra trick. So a double hook of clubs now give you better odds.

So which hand do you win the heart lead in? Right now I cannot see that it makes a difference and I haven't any more time. Does this mean that I have to rate myself down? .... Hold on! I have a glimmer. If QJ clubs fall on AK, I get my 2 extra tricks in clubs. So after trying spades and they dont break, I play K♣. If the Q or J comes down I can afford to play the K♣ before trying diamonds. Now if when I play A♣ the 2nd honour does not fall, then I do not have a club as an entry back to my hand to run the diamonds. So I must preserve my ♥A. Thus I win trick 1 with the ♥K in dummy. I must also thwart LHO holding ♦AQx(x) from rising with the ace and putting me in dummy with a heart.

[cjames]

I win the first trick with ♥A, then test the spades. If they are not 3-3, I will play ♣K, if they are 3-3 I will go for the double finesse in ♣.

Anyway, if they are not 3-3 I play my ♣K, and if the Q or J doesn't appear I will sail ♦J.

Probably very wrong

[paulg]

cjames, on Mar 7 2008, 06:53 PM, said:

I win the first trick with ♥A, then test the spades. If they are not 3-3, I will play ♣K, if they are 3-3 I will go for the double finesse in ♣.

Anyway, if they are not 3-3 I play my ♣K, and if the Q or J doesn't appear I will sail ♦J.

Probably very wrong 

Very close to the line I envisaged.

If you play it out, when the spades are 3-3, you will see the slight error (that wacko has noticed).

Playing the ♣K when the spades don't break is something I did not consider. It doesn't cost but gives you an interesting problem of playing clubs to be 5-1 (but not led), QJ doubleton offside, or the international sitting East playing it from QJx. You can play for the QJ doubleton option and still try the diamond finesse first, which might be best.

[vuroth]

I was hoping this would get posted here.

7 top tricks - 3 spades, 2 hearts, 2 clubs. 2 slow diamond winners, but losing the lead twice will be fatal, without some luck.

Win with the K♥, hoping that this casts some doubt about the location of the queen in someone's mind.

Now I play a club to the K. If an honour falls out of RHO, I'll try the finesse back. Two club finesses would give me 9 if they make, 8 if the dropped honour was not singleton. If I'm on 8 tricks, I'll try spades being 3-3 first for the 9th, then diamond king finesse.

Assuming no honour fell, J♦ towards the board, covering only if necessary.

Win the expected heart return, and cash 2 rounds of spades. If spades split 3-3 and the A♦ fell on the third round, I have my 9 tricks.

Otherwise, I drive out the other diamond honour, and hope hearts are blocked (very unlikely).

V

[vuroth]

I take it that the point of cjames line is the following?
- Clubs give 3 tricks 75% of the time
- Clubs give 4 tricks 25% of the time
- Diamonds give 3 tricks 50% of the time (more importantly, only 1 loser on your way to 2 tricks.)

So in order to determine the best line, you need to attack spades up front to know how many tricks you need, and thus which suit will give better odds?

V

[paulg]

This is my line (if it's wrong I'm sure one of the real experts will correct it!).

There are seven top tricks so you need to develop two more. The heart position is unclear, but if you lose the lead twice then the defence should have at least five winners.

The first thought may to be play on diamonds. If West holds the ♦Q then the contract is secure, but if a finesse loses to East then you are almost certainly down.

The alternative is a favourable 3-3 break in spades, and then we only need one more trick. This would come from clubs, rather than diamonds, as the chances of making three club tricks is approximately 50% better than the diamond finesse.

The key to the hand is combining these changes and entry management.

First we should test the spades. If they do not break 3-3, then we abandon this line and have to rely on the diamond finesse succeeding.

If spades break favourably, then we must to play the club suit for three tricks. The best line is cashing the ♣K, intending to finesse twice through West. The double finesse is significantly better than playing for a 3-3 break even if the first finesse loses.

However, this means that you need an entry back to your hand if the first club finesse loses. Remember that you have already cashed the spades and the ♣K, so you better still have the ♥A in your hand.

I think this is the best line.

[cjames]

Yes, that line seems much better.

[whereagles]

Hum.. I would have played clubs AK and a 3rd out. Dunno if this is better than the club dbl finesse, but it means I should take the ♥A 1st trick, not the K.

[gwnn]

ugh this has been discussed a few times before...

Basically the relevant holdings are

xxx HHx (AK and another wins) 4 3-3 breaks =7.2%
HHxx xx (double finesse wins) 6 4-2 breaks = 9.6%
HHxxx x (double finesse wins) 4 5-1 breaks = 5%

So double finesse is definitely superior.

[irdoz]

Im trying to follow this...so this is more in the way of questions...

1. What are the exact odds in the club suit in isolation?

Quote

I take it that the point of cjames line is the following?
- Clubs give 3 tricks 75% of the time
- Clubs give 4 tricks 25% of the time

Looking at the club suit in isolaton assuming no transport problems arent the odds...

I calculate:-
3 or more tricks about 78% (whenever honors split (50%), QJ onside (25%) and QJ doubleton offside (3%))
I calculate the odds of 4 tricks as less than 25% though (QJxx.. onside doesnt always yield 4 when you start with the kc, because presumably you cover any honor with the ace and then lead the 10.)


2. Isnt there a transport problem sometimes getting the 3rd club trick when playing for only one extra club trick

For example lets say theres

QJxx onside and x offside - you start with the Kc then low for finesse and lho rises with a club honor - you have to cover with ace then lead 10cl. If you kept Ah theres no transport to get the winning 9c...

[paulg]

irdoz, on Mar 10 2008, 10:13 PM, said:

2. Isnt there a transport problem sometimes getting the 3rd club trick when playing for only one extra club trick

For example lets say theres

QJxx onside and x offside - you start with the Kc then low for finesse and lho rises with a club honor - you have to cover with ace then lead 10cl. If you kept Ah theres no transport to get the winning 9c...

I was afraid that there was a flaw somewhere. The same problem exists if LHO has Hx in clubs too.

I shall crawl back into my hole and see if I can emerge with some indication of the right line, or perhaps one of the experts who like the hand can tell me!

[paulg]

Apologies that this has become less like a BIL problem, but I hope that the general considerations are worthwhile independent of the more complex solution.

If we leave the entry in the South hand so that we can double finesse in clubs, then we will fail whenever West has Hx, HHx, HHxx or even Hxx (playing H on second round) as we do not have an entry to the fourth club.

So we have to leave the ♥K in the North hand after all.

But this is not the end of the problem. We should now play clubs by cashing the ♣A and then crossing the the ♣K. If an honour drops then we continue clubs and we have the ♥K as an entry to the fourth club, our ninth trick.

If no honour drops, then we must decide what to do. There are 12 combinations of 3-3 clubs (a priori 21%) and 12 combination of 4-2 clubs (a priori 19%) remaining, so the odds of the clubs breaking is 21:19.

We only need a single diamond trick so we could take the finesse, but this is a 50% chance against a 21:19 play.

So, I think, that we should take the heart lead in the South hand. Test spades and, when they are 3-3, play the ace and king of clubs intending to play a third round.

Any flaws in this?

This post has been edited by cardsharp: 2008-March-11, 03:54

[whereagles]

Write this up and send to Kelsey for his "Adventures in card play 2" book.

Ahh.. he passed away? Well, send to Ottlik then

[david_c]

(Deleted while I work out the percentages.)

[david_c]

cardsharp, on Mar 11 2008, 10:30 AM, said:

So, I think, that we should take the heart lead in the South hand. Test spades and, when they are 3-3, play the ace and king of clubs intending to play a third round.

Any flaws in this?

Yes, you can do better. Once you know spades break, you should play a club to the nine. The key is to keep the ♥K as an entry to table and the ♣K as an entry back to hand (to repeat the club finesse).

I must admit I didn't see the problem with cashing the ♣K first, but now we've seen it, small to the nine must be best!

What a great problem!

(This line is 78% given that spades break. ♣AK and another is only 71%, even when you take into account the fact that you can switch to diamonds if clubs break 5-1 or 6-0.)

[FrancesHinden]

I will admit that my original (unspecified) line was A, K and another club rather than 2 finesses.