[inquiry]

Scoring: IMP

West North East South
 -     -     Pass  1♥
 Pass  1♠    Pass  2♠
 Pass  3♣    Pass  3♦
 Pass  6♥    Pass  Pass
 Pass  

Opening lead Diamond King, ruffed in dummy

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Cut to the chase. How do you play hearts in this ending. It doesn’t matter to me what worked on the real hand (I think the right play worked, BTW). The question is how should you play.

[Free]

If we had all our ♥s in the beginning of trick 2, it would be correct to play ♥A and small ♥ to the Q. However, if you do this, and trumps are 3-1 (small singleton), you're screwed since they'll return ♦ and you lose 2 trumps.

This is why I think it's better to play ♥Q at trick 2 and let it run. You can finesse a second time.

[luke warm]

i'd play the ace then low to the board...losing a finesse with the Q seems to put me in diamond danger

[flytoox]

i think finessing h twice is the right play.

[Chamaco]

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It depends on whether we have to play the suit for 1 losers or zero losers.

In the follow up I will assume we can develop clubs, so we have only to consider H losers.
If it turns up we have clubs losers, then we will have to play the trumps for no losers, an there will be no alternative but a finesse.

The only thing I am unsure is whether we have to anticipate CA and club ruff before playing trumps
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2 options:
1) Double finesse starting with HQ or HT (I prefer HQ )
2) A of H and low to HQ


So if trumps are 2-2 double finesse can only gain an overtrick, but will lose 2 trumps with doubleton KJ offside.
In other words, double finesse cannot be a winner at IMPS (at MP, perhaps).

If trumps are 3-1, playing Ace and a small to Q will limit to one losers to all 3-1 breaks with J or K stiff.

Of the remaining 3-1 with KJx held by any opponent, playing A wins with KJx held by LHO, and loses with KJx held by RHO (when HQ lead would be superior).

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All in all, I play Club Ace and a ruff and start trumps with H Ace and low to H queen

[inquiry]

Chamaco, on Dec 2 2004, 10:23 AM, said:

If trumps are 3-1, playing Ace and a small to Q will limit to one losers to all 3-1 nreaks with J or K stiff.

Of the remaining 3-1 with KJx held by any opponent, playing A wins with KJx held by LHO, and loses with KJx held by RHO (when HQ lead would be superior).

I will just point out that you ruffed the first diamond (limit to three hearts in dummy), then you cash heart ACE (down to two hearts in dummy), now small heart.. .now if hearts are 3-1 with KJx in either hand, they win teh king immediately and force you ruff a diamond with the Queen and the jack of hearts will be a winner....if that affects your line of play at all..

Ben

[Chamaco]

inquiry, on Dec 2 2004, 02:35 PM, said:

Chamaco, on Dec 2 2004, 10:23 AM, said:

If trumps are 3-1, playing Ace and a small to Q will limit to one losers to all 3-1 nreaks with J or K stiff.

Of the remaining 3-1 with KJx held by any opponent, playing A wins with KJx held by LHO, and loses with KJx held by RHO (when HQ lead would be superior).

I will just point out that you ruffed the first diamond (limit to three hearts in dummy), then you cash heart ACE (down to two hearts in dummy), now small heart.. .now if hearts are 3-1 with KJx in either hand, they win teh king immediately and force you ruff a diamond with the Queen and the jack of hearts will be a winner....if that affects your line of play at all..

Ben

You are right Ben, as usual.

Well, of all the 3-1 split, I have 2 chances out of 4 to have a a singleton honor (and 2 out of 4 of KJX in either hand).

So it's a 50% of all the 3-1 splits.

Therefore, to remember:

Playing HQ cannot be better than cashing Ace if trumps are 2-2 and instead will gain only 50% of all the 3-1 splits.
It seems to me a case of "heads you lose, tail you draw" :-)

Still playing Trump Ace and small to Q.

[xx1943]

You cannot win against heart 4-0 distribution.

If hearts are 3-1 and opponents gain the lead with the first or second heart trick, a club lead cuts declarer communication with the table.
Therefore you can win only against hearts 2-2 or darwing 2 rounds of hearts without losing the lead.

You win
1) By leading A of hearts and a small against every 2/2 (40,70%) distr. or either opponent having K singleton (12,45%) sums up to 53,15%
2) By playing the Q from the table against every 2-2 (40,7%) and West having J singleton (6,22%) sums up to 46,92%
3) Playing small against the Q wins only against all 2-2 (40,7%)
Therefore line 1 is best.

Al

[inquiry]

xx1943, on Dec 2 2004, 12:10 PM, said:

You win
1) By leading A of hearts and a small against every 2/2 (40,70%) distr. or either opponent having K singleton (12,45%) sums up to 53,15%
2) By playing the Q from the table against every 2-2 (40,7%) and West having J singleton (6,22%) sums up to 46,92%


Al

Hi Al, I get quite different numbers than you, and draw a completely different conclusion. Playing heart Queen first does win against all 2-2 splits includng KJ offside assuming bang the heart ace on the second round. But it wins agianst EAST having singleton King or Jack as well. It also wind asgainst EAST having KJx too, and maybe on trump coup if EAST has KJxx. I get minimum of 71.8% for heart queen lead (ignoring trump coupe)

Quote

3) Playing small against the Q wins only against all 2-2 (40,7%)
Therefore line 1 is best.

Well, like cashing ACE or leading the queen, 2-2 is not a problem however you play. Playing small to the queen caters to West with singleton honor (either), or WEst with three to the KJx... That is 2-2 is not the only play where small to the queen wins. So I get a different percentage as well.

So all three lines (Ace and another, Queen and let it run, and low from hand towards queen) work with hearts 2-2.... So we can remove a 2-2 split from consideration.

So the arguement for and agaist a play is how best to handle 3-1 (or gasp, maybe 4-0... although maybe Al is right that you can not handle a 4-0 split).

Heart ACE wins against singleton honor in either hand, loses to KJx in EITHER hand. Heart queen wins against singleton JACK in WEST hand, or heart KJx in EAST, but loses to singleton King in west unless you give up on 2-2 split. Low heart towards queen wins against singleton King or Jack with WEST, but loses to singleton K with EAST.

That leaves heart ACE and heart (works with singleton K or J in either hand, or 2-2), or low works with singleton king or jack with WEST, singleton Jack with EAST, hearts 2-2, or WEST having KJx.

So, my thoughts are the worse play is heart ACE, and that effectively (almost) heart Queen float and low heart towards queen are "tied". Both work with one player having any singleton honor (WEST K or J in low to queen), East with K or J in queen from dummy. Both work when the other player has the "right" singleton (Jack with East when low towards the queen, jack with West when heart queen from dummy). Heart queen from dummy might when an extra trick if you pin the stiff jack with WEST, but I doubt it.

By my calculations (admittedly maybe wrong), heart ACE and heart works 65.6% of the time, while either heart queen from dummy or low heart towards the queen work 71.8% of the time.

So the arguement here, do you choose the 71.8 that has a chance for all the tricks (if you can manage them (4S, 5H, 2D ruffs, 2C)... or the 71.8% that gives up chance for the overtricks? Well, here is where I thought the problem would creep in. there is a 4.8% chance EAST will have KJ8x of hearts. If you start heart queen, he will cover, you will win ACE, west will show out. So the question, is which play, low to the queen or queen from dummy will handle a 4-0 split with EAST having four the best, and what if the heart SIX was the heart FIVE? Which play would be best. Curious perhaps, perhaps not.

Ben

[PriorKnowledge]

Lead QH... If that loses to KH, lead another heart and finesse the 9. This makes your contract on any 2-2 except KJ offside and all 3-1. If you play AH and small heart, you lose to KJx in either hand.

[inquiry]

PriorKnowledge, on Dec 2 2004, 04:12 PM, said:

Lead QH... If that loses to KH, lead another heart and finesse the 9. This makes your contract on any 2-2 except KJ offside and all 3-1. If you play AH and small heart, you lose to KJx in either hand.

it will not make With KJx in left hand opponent;s hand. When you lead the second heart to "finesse" the right opponent shows out.....you already lost the Queen and now you will lose the jack....

The odds of heart queen and then hook working is 71.2, just short of the other two lines (that are not simply cashing the ace)... (I think)

ben

[PriorKnowledge]

Oops... I have to learn to count to 2

Twice, I have bid slam off 2 aces AFTER bidding blackwood, because I miscounted the number of aces in MY OWN HAND.

[OrShoham]

I doubt we'll be alone in this slam, so I'm floating the queen and hoping to pick up a cheap IMP with the potential overtrick. I don't think there's much of a difference between floating the queen and low to queen, so may as well try.

[xx1943]

Hi Ben

Quote

So all three lines (Ace and another, Queen and let it run, and low from hand towards queen) work with hearts 2-2.... So we can remove a 2-2 split from consideration.

100% agree.

Quote

Playing heart Queen first does win against all 2-2 splits includng KJ offside assuming bang the heart ace on the second round. But it wins agianst EAST having singleton King or Jack as well. It also wind asgainst EAST having KJx too, and maybe on trump coup if EAST has KJxx. I get minimum of 71.8% for heart queen lead (ignoring trump coupe)

You forgot, that you win if WEST has the stiff J too. make 6,217% additional

But:
If you lose the first or second heart trick, defender will play not diamond, not hearts but CLUBS. e.g. if you come to your hand with a spade, lead a heart against the Q and LHO has the singleton J. RHO wins and plays a club, leaving this situation:

---

Here I missed that now a cross-ruff is possible, but to execute that, the spades must be not worse than 4/2, letting away a possible diamond overruff. Or did I miss something again?

Therefore I find as new figures:

line 1: A and small wins against 2/2 (40,7%) singleton K either (13,6%) and singleton J either, if spades are 3/3 or 4/2 (13,6%*0,84=11,4%). Sums up to 65,7%

line2: Lead the Q to finesse wins against 2/2 (40,7%), singleton J with WEST (6,3%), and singleton J or K or KJx with EAST, if Spades are 3/3 or 4/2 (31,1%*0,84=26,1%). Sums up to 73,12%.

line3: Lead small against the Q winsagainst 2/2 (40,7%) and singleton J or K or KJx with WEST, if Spades are 3/3 or 4/2(31,1%*0,355=26,1%). Sums up to 66,8%.

Ben, you are rite as usual line 2: finesse the Q ist best.

Regards

Al

[Chamaco]

inquiry, on Dec 2 2004, 05:00 PM, said:

So, my thoughts are the worse play is heart ACE, and that effectively (almost) heart Queen float and low heart towards queen are "tied". Both work with one player having any singleton honor (WEST K or J in low to queen), East with K or J in queen from dummy. Both work when the other player has the "right" singleton (Jack with East when low towards the queen, jack with West when heart queen from dummy).

Ben, I am sorry but I do not understand why Q lead would be better at IMPS.

Quote

So all three lines (Ace and another, Queen and let it run, and low from hand towards queen) work with hearts 2-2.... So we can remove a 2-2 split from consideration.

I do not think so.
Let us say the Q loses to K offside, when you take the return, are you going for the double finesse or cash Ace ?

I assume you go for the double finesse.
So the double finesse loses in the 2-2 case with KJ offside and it is not true that all 2-2 cases it is equivalent playing A and and small vs double finesse.

In the 2-2 cases A first always limit to 1 loser, whereas double finesse loses to KJ offside (25% of all 2-2 splits).
So the 2-2 split favours A first.

Now let us consider the 3-1 splits.
Playing Ace first succeeds if there is a singleton honor (50% of all 3-1 splits).
It loses with any opps holding KJX (50% of all 3-1 splits).

Now let us consider the chances of double finesse vs 3-1 splits.
It loses to KJX offside (25% of all 3-1 split).
It wins to KJX onside (25% of all 3-1 splits).
It loses to stiff K offside (12.5 % of all 3-1 split)
because a diamond return forces to ruff in dummy. Then you have entry problems: if you use the last dummy trump for finessing the J you have a diamond loser left and not enough entry to set up and cash clubs for a discard.
It wins to stiff K onside (12.5%).
It wins to stiff J in any hand (25%).

so it wins overall in 62.5% of all 3-1 splits.

Given that
2-2 split has 40.7 % prob
and
3-1 split has 49.7 % prob

Option 1
Ace first

works in 100% of 2-2 splits = 1 x 40.7 = 40.7
works in 50% of 3-1 splits (e.g. stiff honor) = 0.5 x 49.7 = 24.85
Total = 65.55 % (of all the 3-1 splits + 2-2 splits; this does not include 4-0 splits)

Option 2
Works in 75% of 2-2 splits (fails to KJ offside) = 0.75 x 40.7 = 30.525
works in 67.5% of 3-1 splits (fails to LHO holding stiff K or KJX ) = 0.625 x 49.7 = 31.0625
Total = 61.5875 % (of all the 3-1 splits + 2-2 splits; this does not include 4-0 splits)

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So if my calculations are right, excluding 4-0 splits, Ace first is better in 4% of the combined 3-1 and 2-2 split cases (which means that overall, the difference between the 2 lines will be lower than 4%).

If the above is true, that should mean that the difference is so small hat ANY indication (including "table presence") will tip the balance in favour of one or the other line.

[xx1943]

Chamaco, on Dec 3 2004, 11:56 AM, said:

Now let us consider the 3-1 splits.
Playing Ace first succeeds if there is a singleton honor (50% of all 3-1 splits).

Hi Mauro

Sorry not rite. If either opponent has singleton J and you play A and another, they will play a third round of hearts and you are a trick short.

You make 4♠+4♥+1♦-ruff+2♣=11 tricks

Regards

Al

[Chamaco]

xx1943, on Dec 3 2004, 11:46 AM, said:

Sorry not rite. If either opponent has singleton J and you play A and another, they will play a third round of hearts and you are a trick short.

You make 4♠+4♥+1♦-ruff+2♣=11 tricks

Are you sure ?
Ace of hearts planning to continue H if no honor drops.

But when a honor drops I have additional chances:
I can ruff 2 more diamond losers and discard the last diamond on clubs, leaving only a trump loser.

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Oh, not true. In this line, 3-1 split with stiff honor still poses problem since ruffing the 3rd diamond with the Q will lose to H8x in either side, so this falls back on deciding for or against the finesse...