[Winstonm]

Scoring: IMP

The auction is simple:
N S
1♣ 1♠
2♠ P

Opening lead is the King of diamonds. What is your best line of play to come to 8 tricks?

---

(Problem is for beginning to intermediate levels, so if advanced or better wish to answer please do so in hidden text only. Thanks.)

[Trumpace]

Spoiler

Win the ♦A, ♣A and lead a heart off the table.
Another interesting/(instructive?) aspect of this: I think cashing the ♣A is better than leading a heart a trick 2.

I am intermediate and I think intermediates should get this one quite easily (especially as a puzzle, on the table, it is different), so I am hiding it.

[Wackojack]

I am no expert so I hope this is right.

Spoiler

You have 7 top tricks. You could try coming back to hand with a trump and playing a heart. If the the A♥ is on-side you have 8; 50% odds. If it isn't, good opps will lead trumps at you so that you have none left in dummy to ruff you 3rd heart. So your chance is 50% + the chance that your opps won't play trumps.

On the other hand you could try to establish clubs by first playing a small club from dummy after winning the diamond. If opps win and return a trump you win in hand, play another club to the ace. Then ruff a club high. If they split 4-2 you enter dummy by playing the 2 to the 9, then ruff another club. Then if trumps are splitting 3-2 you can enter dummy once more to enjoy the established club. If trumps are 4-1 it looks like you have a slight extra chance when you throw a losing diamond on the established club and the hand with 4 trumps has only 2 diamonds and the A♥. (It looks therefore that you should duck one round of diamonds initially) .So you come to a heart trick. Odds of 3-3 + 4-2 break in clubs according to my bridge diary is 84% and 3-2 trump break 35.5%. Combined odds are then 57%. Add the few % for the possible heart end-play and you look better than 60%.

Now I will read Trumpaces solution and I hope I don't discover I was wrong.

[Wackojack]

Thanks for the problem. I took the bait. Like you said an excercise in clear thinking.

[ArcLight]

We have 21 HCP so opps have 19 and almost half the deck, and didnt compete.
Probably the hearts and diamonds and HCP are semi-balanced.

Short of entries for a dummy reversal, I'd still try and establish clubs.
Maybe opps will play into your hand and "force" you. Maybe you can establish clubs.

VERY IMPORTANT, RUFF HIGH FROM HAND! You need the lower trumps as entries into dummy.

With that trump holding you can always fall back on the heart finesse.

[Winstonm]

Luckily the opponents did not find the best lead - a spade. So now you have 8 tricks assured. Win the diamond, cash the Ace of clubs if you want, and lead either heart from dummy - the king is fun to see if RHO ducks the Ace.

Point being that you have 5 spades tricks in hand + 2 Aces. All that is needed is 1 extra trick. You are a tempo ahead (a unit of time), meaning you get to act first, so lead a heart; opps win and lead a belated spade. Win the 9 in dummy. Lead another heart. Dummy is now out of hearts and has 2 spades left. If opps lead another spade, win in hand and play a low spade from dummy, then ruff a heart with the King. All the spades left in your hand are now master.

You come to 5 spades, 2 aces, and 1 heart ruff - guaranteed. The point is to keep you eye on the target - here it is 8 tricks. There is something about that "red herring" King of hearts in dummy that pulls the blinders over many players' eyes - that's why this is an excercise in clear thinking. It's not how the clubs might divide, or the odds that the heart finesse is onside - it's about counting to 8 and finding the simplest way to accomplish that goal.

Although a very simple problem, this type of thinking I believe is what makes Bob Hamman the champion he is - it is a type of thinking that looks for the unbiased truth about any bridge situation and acts on that truth - it is the ability to think about the right thing at the right time without being distracted.

It is what I call "Clear thinking."

Winston

[Trumpace]

Winstonm, on Dec 30 2005, 03:30 AM, said:

Luckily the opponents did not find the best lead - a spade.  So now you have 8 tricks assured.  Win the diamond, cash the Ace of clubs if you want, and lead either heart from dummy - the king is fun to see if RHO ducks the Ace.

I am being nitpicky...

8 tricks arent assured yet! What if one of the opps has a club void?

and about the ♣A...

If we assume no opp has a club void, then ♣A must be cashed.

Say East is 5-5-2-1

You lead a heart at trick 2. East wins and returns a diamond. Which west wins. West cashes a third round on which goes East's singleton club. Now West plays the ♣K. You cannot avoid losing 2 club tricks, 2 diamonds and 2 hearts now.

This is in principle similar to the cross ruff advice: cash the requisite number of side suit winners before embarking on a cross-ruff.

So I think the best play is ♦A, ♣A then a heart off the table (you _did_ ask for the best line of play to 8 tricks )

[FrancesHinden]

Harder question: what's the right line at matchpointed pairs?

[Trumpace]

In matchpoints, against expert defence I would probably play safe for 8 tricks (but then I would have gotten a spade lead, wouldn't I?) and collect +110. I expect some tables to go down in 2S, some to be in 1NT. Moreover it seems to be too complicated(for me at least) to calculate the odds for the 2-3 different lines, especially on the table.

Justin, on Sometime in the distanct past, said:

A low club

If I play a low club, opps can cash two diamonds. If clubs are 3-3 they will probably cash their heart tricks now and hold you to 8. If clubs are 4-2, they will return a spade. Well this is assuming 'expert defence', since I am not an expert I can only assume that the expert can 'see through the backs of my cards' and try to play accordingly.

[Trumpace]

What you say definitely make sense, there is probably more than 60% chance of making 9 tricks while < 15% chances of going down. If 2S just making is an average score, going for 9 is probably the right thing to do.

The reason I want to play safe is that I expect Average++ by playing safe (especially in the clubs i usually play), so 60% risk might not be worth it...

[EDIT] The figures above are wrong... Ignore this post.

[Winstonm]

Jlall, on Dec 30 2005, 11:03 PM, said:

Trumpace, on Dec 30 2005, 09:57 PM, said:

Justin, on Sometime in the distanct past, said:

A low club

If I play a low club, opps can cash two diamonds. If clubs are 3-3 they will probably cash their heart tricks now and hold you to 8. If clubs are 4-2, they will return a spade. Well this is assuming 'expert defence', since I am not an expert I can only assume that the expert can 'see through the backs of my cards' and try to play accordingly.

Why do you assume the heart ace is off? That's pretty pessimistic. If it is onside you will make 9 tricks very often. If it is offside, sure they can hold you to 8 tricks but you haven't lost anything. You would need very bad things to happen to not come to 8 tricks after playing a low club, but you need a finesse plus a little to come to 9 tricks after the same play.

As for the opponents being able to see through the back of the cards, if they always defend that well you will never win. Even experts often err, or even make correct single dummy plays that are not right double dummy. Do not make the mistake of giving your opponents too much credit, even if they are meckwell.

I don't view this defense as being all that hard. When declarer ducks a club, both defender's can see if the suit is 3/3 and can be set up. If it cannot, it is not a threat but the doubleton heart and 3 trumps are a threat so it doesn't take expert level play to return a trump when the clubs are 4/2.

If the clubs are 3/3, defender's can see this as well and cash their diamonds and whatever heart tricks are coming.

What it seems to come down to is when the clubs are 4/2 or worse you will go set when the heart is offside: 50% of 63% excluding 6-0 breaks. Call it 31% to go down 1 and 31% to still make 2. 24% if only 4/2 breaks are included.

When the clubs divide 3/3, 36% of the time, half the time the opponents can still take 5 tricks when the heart ace is offside or 18% of the time.

So playing a low club will only gain when the clubs are 3/3 and the heart is onside which is an 18% chance of an overtrick while risking a 31% chance to incur a set.

Seems to me that even at matchpoints ducking a club is a poor risk.

Winston

[Winstonm]

Quote

First: when clubs are 4-2 and the heart is onside, you will have plenty of entries to set up the clubs. You have the ace of clubs, king of hearts, nine of spades, and king of spades. You will make an overtrick in this case.

Hard to argue with you and math never was my strong point. You are right that the 31% figure is simply based on 4/2 and 5/1 breaks, but LHO may certainly have led a diamond from KQJx instead of x in clubs with no trump entry.

You are right that heart Ace onside will make when the clubs are 4/2, provided spades are not 4/1. At this point, my math skills are overwhelmed...maybe even before....

Quote

Third: When clubs are 4-2 and the heart ace is off, you are not going to go set unless spades are 4-1. You still have the CA, SK, and S9 as entries to set up the club and pitch a heart from your hand.

Yes. Dummy reversal will win the day.

So 68% of the time the spades break 3/2, allowing an overtrick possibility. So what are the correct figures for the chances?

On my ACT I scored 35 in English and 16 on math...now you know why.

Winston

[Winstonm]

Quote

JLall: I don't understand your math at all.

My teachers never did either - it was brutal to be so far ahead of them.

Winston

[Trumpace]

Jlall, on Jan 1 2006, 12:05 PM, said:

Third: When clubs are 4-2 and the heart ace is off, you are not going to go set unless spades are 4-1. You still have the CA, SK, and S9 as entries to set up the club and pitch a heart from your hand.

What if East is 3-6-2-2?

East can get a club discard on the third round of diamonds and can ruff your ♣A. Agreed, this is unlikely as East would probably have acted over the 1♣ bid.

(they cash their heart tricks first, go to West hand with a diamond and get a club ruff, but is that giving opps too much credit?)