[jschafer]

---

♦ lead versus 6NT.

[inquiry]

jschafer, on 2012-January-25, 11:59, said:

---

♦ lead versus 6NT.

Let's assume diamonds are no worse than 4=2, or 5-1 with singleton diamond Ten. In that case, you have 10 top tricks, and can easily win a second heart for 11 tricks. How to get to 12?

OPTION 1 - SPADES 3-3 (35.5%)
OPTION 2 - EAST HAS singleton spade J (1.2%)
OPTION 3 - WEST HAS singlton spade J (1.2%)
OPTION 4 - West is void in spades, and we find out in time to finesse the Jack and get back to dummy to cash spade queen (0.75%)
OPTION 5 - EAST OR WEST HAS JX of spades (16.2%)
options 1 through 5 adds up to 54.8% (if you are willing to play the hand such to discover and take advantage of a spade void with west)

The question is how best to maximize chances when options 1-5. If you manage to win two hearts without giving up a trick, you can always led low towards the club QUEEN, making 1/2 the time options 1-5 fail, and even if that play loses, you have a possible squeeze if west holds four (or more) spades to the jack and the heart king. OR if has five clubs and four spades. The best defense on this line might be for WEST to cover the heart queen (when he holds it). This gives your 10th trick without losing one, but removes the threat of the 2nd heart honor against his king.

Anyway, here I GO....

Win diamond king, cross to spade ace, lead the heart queen, if this loses the king in east, I will play for a potential spade-club squeeze (needs west to have four spades and the club king, or east to have four spades and a buncho clubs (five). IF the heart queen wins, I will play a low club towards the queen (gving up on making all 13 tricks should west have both kings and spades split or west has both kings and four spades to the Jack, where I would have a triple repeating squeeze --- of course, west already misplayed in that case by not covering the heart honor I played).

This line makes easily 1/2 the time you win two hearts without losing one (club king with west), and some of the remaing time on various squeezes. WHEN the heart finesse loses, you simply go for the club-spade squeeze it might work against east if he holds five clubs (because the threat has to be the six in your hand) and four spades, and anytime west has four spades and the king of club.

[whereagles]

I'll do it the simple way: a club up to the Q.

[phil_20686]

whereagles, on 2012-January-26, 05:15, said:

I'll do it the simple way: a club up to the Q.

Yes, this seems better than inquiry's line. Suppose that a club to the Q wins, if this hold the trick i can just play ace and another heart and I am home. If lho jumps in the with the K I can test either black suit for 3-3 before falling back on the heart finesse. If it loses to the K I dont seem any worse placed, I now need the heart finesse and then either spades 3-3 or some kind of positional black suit squeeze on west. Again you can clarify the position by cashing the Q spades and crossing in spades and cashing the club ace you still need the heart finesse onside, but if lho has the heart K and the spades and the clubs, he can be squeezed in an odd sort of way. if he unguards the k low to the ace gives you three heart tricks, obviously for a spade or a club pitch you get what you need. via two hearts and a black suit. You just have to read the position in the 4 card ending when you play your final diamond.

There is also the chance of a double squeeze via a defensive error, as if you play the heart Q and lho covers you might be able to squeeze rho in hearts + a black suit. An ending like this:

---

If LHO lets go a spade or a heart it is all over, so suppose he lets go a club, then rho is squeezed out of a heart, now if lho covers the heart Q, then I have the entry back to hand to score the third heart.

Obviously I could also try the spade-club squeeze on west by taking the heart finesse early and keeping the spade Q.

[inquiry]

phil_20686, on 2012-January-26, 06:27, said:

Yes, this seems better than inquiry's line. Suppose that a club to the Q wins, if this hold the trick i can just play ace and another heart and I am home. If lho jumps in the with the K I can test either black suit for 3-3 before falling back on the heart finesse. If it loses to the K I dont seem any worse placed, I now need the heart finesse and then either spades 3-3 or some kind of positional black suit squeeze on west.

Well the first part is true, if the club queen holds you are home. The part about if west jumps up with the club king is clearly not true. West will return a heart and you have to decide if you are going to finesse in hearts or not right away. If you are, YOU made a big mistake taking club finesse first, because you are down when the heart loses on this line. IF you win the heart ace, your entries are very muddled to as to how you are going to try for different 3-3 black suit breaks. You didn't say if you cashed both diamonds before spade to dummy, if west wins the club king, having the 2nd diamond winner in north is useful. If east wins the club to the queen-king, having the 2nd diamond in dummy is not useful. I might post on this is a bit. If there is no diamond in dummy, you are pretty much screwed if only one suit splits 3-3, as you have to try to guess which one it is (you have only one entry to north, so you can't afford to test the wrong one. For instance if you want to "test clubs" you have to cross to the club ace then cross back to the spade queen -- blocking spades. if you want ot test spades, you have to run your diamonds, and throw all the small clubs from dummy.

So needless to say, perhaps you will suggest leaving a diamond in dummy, so that when the heart comes back, you can cross to the club ace, return to dummy with the diamond, and test clubs. This is better, but leaving one diamond in dummy screws up entries when east wins the club king and returns a club. Now, all your entries to your hand (but one in spades are gone), and you need to cross to dummy in diamonds and use your diamond reentry to your hand. The hand now boils down to do you want to play for 3-3 spades or take the heart hook, no way to test both as dummy has to throw away three cards on the diamonds, coming down to heart ace, spade queen, and just one more card. Do you keep the small heart for the finesse or the last spade for the 3-3 split.

I might write more on comparing the two lines, and how low to the club queen can lose even when there is a doubleton jack of spades some place, and the significance of cashing or not cashing the 2nd diamond before entering our hand with a top spade. But if I do or don't I have to say I still prefer my line, so here is something to think about.

[Zelandakh]

My first instinct was also Ben's line and it still feels right to me to find the ♥K before deciding whether to play the ♣ up. No doubt Rainer will find a line to combine everything in due course.

[phil_20686]

inquiry, on 2012-January-26, 23:49, said:

Well the first part is true, if the club queen holds you are home. The part about if west jumps up with the club king is clearly not true. West will return a heart and you have to decide if you are going to finesse in hearts or not right away. If you are, YOU made a big mistake taking club finesse first, because you are down when the heart loses on this line. IF you win the heart ace, your entries are very muddled to as to how you are going to try for different 3-3 black suit breaks. You didn't say if you cashed both diamonds before spade to dummy, if west wins the club king, having the 2nd diamond winner in north is useful. If east wins the club to the queen-king, having the 2nd diamond in dummy is not useful. I might post on this is a bit. If there is no diamond in dummy, you are pretty much screwed if only one suit splits 3-3, as you have to try to guess which one it is (you have only one entry to north, so you can't afford to test the wrong one. For instance if you want to "test clubs" you have to cross to the club ace then cross back to the spade queen -- blocking spades. if you want ot test spades, you have to run your diamonds, and throw all the small clubs from dummy.

So needless to say, perhaps you will suggest leaving a diamond in dummy, so that when the heart comes back, you can cross to the club ace, return to dummy with the diamond, and test clubs. This is better, but leaving one diamond in dummy screws up entries when east wins the club king and returns a club. Now, all your entries to your hand (but one in spades are gone), and you need to cross to dummy in diamonds and use your diamond reentry to your hand. The hand now boils down to do you want to play for 3-3 spades or take the heart hook, no way to test both as dummy has to throw away three cards on the diamonds, coming down to heart ace, spade queen, and just one more card. Do you keep the small heart for the finesse or the last spade for the 3-3 split.

I might write more on comparing the two lines, and how low to the club queen can lose even when there is a doubleton jack of spades some place, and the significance of cashing or not cashing the 2nd diamond before entering our hand with a top spade. But if I do or don't I have to say I still prefer my line, so here is something to think about.

As long as I leave a diamond in dummy I am fine? Suppose as you say, they return a club, I win the ace, cross in diamonds cash the Q pitching a heart. If clubs 3-3 or JT tight I am home. If not I have a choice of plays available. One is to vienna coup the hearts by cashing the ace and playing for an automatic squeeze in spades and hearts (or spades 3-3) by crossing in spades and cashing the diamonds. In the three card ending I have

---

And get to make any time spades are 3-3, any time hearts are with the spades, and also if west holds both black suits.

You are of course right that I am giving up the chance of Jx spades. But this line will make virtually all the time that the club K is onside. I can obviously do the same thing if a heart is returned.

If the club queen loses to the K, he obviously cannot return a heart, so suppose he returns a club. It must be right now to take a heart finesse, suppose this is not covered but runs, now I can again reduce to the position above. Cashing the two red suit winners in dummy and crossing back in spades. If it is covered, now I have an extra heart entry and can check for Jx spades by cashing the spade K before crossing back in diamonds and again back in hearts. Now I have nothing to hope for but that if the spades are 4-2, there is either 4 spades with 6 hearts, or with west who also holds 4 clubs.

So in total I make when: Kxx clubs onside always, Kxxx (no JT) onside, always, spades 3-3 always, if KJxx(x), KTxx onside, I make if west also holds 4 spades, or if he also holds the K hearts, or if east holds 4 spades and the k of hearts. If Kx K onside, I make if the long spades are with the heart K. If the clubs are unfavourable I need the heart finesse, assuming best defence (covering the heart Q), I will make when it is Jx spades, or spades 3-3, or 4 spades with west with long clubs.

Lets total this up:

By club position with west
Kxx, Kxxxx, JT = 17.75%+3%
KTxx(x) KJxx(x) KJTx(x) = (48.4*2/3+15.4*5/6+1.5)*(35.5%+32%*0.75)
K Kx = (1/3*48.4+1/6*15.4)*(35.5%+32%*0.5)
JTx = 4.5%*50%*(35.5%+0.5*(48.4*2/3+15.4%+1.5)+1/3*48.4%)
xxx, Jx, Tx, xx, x, -, = (13.25+2/3*48.4%+5/6*15.4%+1.5%)*50%*(35.5%+48.4%*1/3+8.5%*(48.4*2/3+15.4%+1.5%))

Which I think covers all of the possibilities, and gives me: 20.75+12.45+7+1.1+16.7= 58%

Is your line better than that?

Your line after the heart wins, you make if the club k is onside, or if the spades are 3-3, or if 4 clubs and 4 spades with west (hearts 6-2 not really worth bothering about), or with JT tight of clubs, giving, giving a total of 0.5*(0.5+0.03+0.5*35.5+0.5*61.5*64.5*0.25) = 37.8%

If the heart finesse loses you make if spades 3-3, or if west has four spades and the club k, which is 0.5*(35.5+0.5*64.5*0.5+64.5*0.5*0.07)=27%, so your line edges ahead if we assume perfect defence. However, my line starts to win if you assume that some % of the time when west wins the club K he does not return a heart, or if some % of the time he will duck the club K. In either of those cases I am close to cold.

[Fluffy]

When I saw the hand I though along Ben´s line, but the problem is I am short of entries to my hand because after ♠A ♥Q covered I have no way to get back to hand and play a club up without ruining my squeeze chances one way or another, that´s why I didnñt post at the start.

A club to dummy is wrong as Ben says, LHO hops and plays a heart and it becomes a ♠3-3 or split heart-club menaces at best when ♣K is onside, worst is RHO wins and spades are 3-3 but you can´t make the hand now.

[phil_20686]

Fluffy, on 2012-January-27, 08:47, said:

When I saw the hand I though along Ben´s line, but the problem is I am short of entries to my hand because after ♠A ♥Q covered I have no way to get back to hand and play a club up without ruining my squeeze chances one way or another, that´s why I didnñt post at the start.

A club to dummy is wrong as Ben says, LHO hops and plays a heart and it becomes a ♠3-3 or split heart-club menaces at best when ♣K is onside, worst is RHO wins and spades are 3-3 but you can´t make the hand now.

The two lines are pretty close, it depends if you think lho is 100% to rise with the club K and play a heart. Also depends whether you think he is 100% to cover the heart Q (J) in the end game, if he does not your chances on my line are much improved.

[inquiry]

Quote

Which I think covers all of the possibilities, and gives me: 20.75+12.45+7+1.1+16.7= 58%

Is your line better than that?

I am not great at estimating percentages, I am pretty sure I have demonstrated my lack of ability in that area many times over the years. However, my line clearly is better than your 58%, lets see how we might be sure of that.

off the top, my line always makes when:
both missing king are with west is 24%
chances for lucky break in spades is 54.8% (see my first post for this calculation)

My line caters to both of those, but they are not mutually exclusive, so you can't simply add them together. However, of the times where no lucky break in spades, you my will make 24% of the time when both kings are with west. So without considering any squeeze possibilities the odds of my line start out at:

54.8% + (.24x(100-54.8) = 54.8% x (.24 x 45.2%) = 54.8% + 10.8% = 65.6%

This percentage is higher than your calculated chances on your line, and we haven't covered all the possibilities yet. Of the times neither of these work, you still have the following chances.

Chance one. heart finesse wins but east has the club king. Now you have the chance of JT of clubs doubleton in either hand or east having doubleton club and west having four spades. IF west fails to cover the heart queen, there is also chances for a heart-spade squeeze against him if he also holds 4+♠s

Chance two. heart finesse loses, you still have the chance that west has club king plus is the hand long in spades.

These will add some percentage to the chance of success of this line of play. The following is my best estimate of what these small chances add to this line.

The small addition of chance one are for JT doubleton are not great, and is not mutually exclusive of all the other lines, so it adds very little to the real chance of making this. Such a doubleton occurs about 3% of the time, but is only helps in th 34.4% fo the time everything has gone wrong, this only adds roughly 1% to the chance of making. The chance east holds singleton K or Kx of clubs doubleton is higher (x can also be J or T), at around 9%. However, this 9% only counts when all this other stuff gone wrong, and west is long in both spades (4+) and clubs (4+). Since either opponent can be long spades when west holds 4 clubs (and no one can have Jx of spades), I estimate that west will be the long in both suits only 1/3 of the time some is long if east has 2 clubs. So of this 9%, only 1/3 of it would count. So this means only 3% of the reaming chances (of around 33%) or we can add one more percent to our chances. This gets it up to about 68% (estimiates used in here). There are some added chances here I will not calculate when the heart finesse wins, and west didn't cover, you can make on heart-spade squeeze against him. WEST can muck with these chances by covering the queen of hearts, so I didn't bother calculating them. Basically, if he failed to cover the heart queen, you will make ~1/2 the time spades don't break for you (when west has the spades). This would be about 8 or 9% to your chances, but i will not factor that in.

When the heart finesse loses, all you need is the club king with west (and chance of that went up a little based on vacant spaces when the heart finesse lost, not much, but when you add to the fact west made a passive diamond lead, it goes up a lot in the real world, we will just use the chance of west having the club king when heart loses at 50%, it is actually much higher because of the choice of opening lead). Now there is no requireent of long clubs with east for the proposed club-spade to work, you make anytime west has the long spades and the club king. west will have the long spades half the time (when they don't break) and the king of clubs half the time. This adds 25% to the remaining chances, or (100%-68%) x 25% = 32% x 25% = 8%, bringing the total to ~ 76%.

This is actually a bit too low, since I ignored the possibility that west with ♥K would duck the first heart when he is long in spades. I think the cover for west when holding four or more spades is clear, so I left that out of the calculations.

Even if I am off a bit in some of the add on percentages associated with additional chance 1 or 2, I start off at a much higher place than you 58%.

Fluffy is on the right track with his comment about being short of entries. Leaving a 2nd high diamond in dummy is useful on some lines (and even necessary to keep all the chances alive) and harmful on others. Still, it seems clear starting heart finesse before low to the club queen still seems very right to me.

[sasioc]

Like Fluffy, my first instincts were to play a line like inquiry's but didn't feel I could fit it all together nicely (entries completely hideous!) or be confident I was doing the right thing. I hope someone will enlighten me

[phil_20686]

I calculated my line to be 58 and your line to be 65.

I forgot stiff J in both cases, though I included JT doubleton in clubs. So both lines are 2.4% better or so.

I did not include Jx on your line as I dont beleive you can pick it up reliably on our lines. Some of the time, if the defence errs, you can, but for example, on your line of taking the heart finesse, suppose that the defence just allows the heart Q to hold? Now you switch to a low club to the Q and K. now the defence will return a heart and you cannot pick up Jx spades without giving up the spade/club squeeze. On the other hand you have an extra threat card in hearts. Or if the heart Q loses and a diamond is returned. Now we just dont have the entries.

Of course, another day they might cover the heart Q (which they should do if there is no Jx) then you have an extra entry back to hand to check so you can check the spades, suppose you now crossed back to hand with a spade and played a club up, this time you pick up Jx trivially.

If we are to assume double dummy defense on whether or not they cover the heart K, they can always prevent you from being able to pick up Jx spades as far as I can see.

On the other hand, if you play a club to the Q at once and it loses, suppose they play back a club now you can win the ace and you can afford to cash two spades before you take the heart finesse, so maybe I should include some Jx layouts in that case, If lho rises with the K and plays a heart at once I obviously have no chance to pick up Jx.

So the Jx layouts are very complicated and too conditional to be the subject of a proper analysis. Its not even clear what the best defence is on some of these layouts.

However, I'm not sure how far I trust my calculuations, its a very difficult hand.

You can see the lines must be very close. You win always when both Kings are onside, I lose when both kings are onside and neither black suit comes in and there is no squeeze. When the club K is offside, but the heart K is in the slot, both lines are identical except that I can pick up JT doubleton in clubs, and also Jx in spades. When the heart K is wrong but the club K is right I gain when either black suit comes in. When both kings are offside I gain on JT club doubleton and the spades come in. All in all I thought these small chances would add up to more than I was giving up in losing sometimes when both Kings are onside, but I was wrong, apparently. There is also a large chance I failed to calculate correctly. Lets try another way:

Both kings are right: You 25%, me 25%*(35.5%+3%+61.5*(35.5+2.4+62.1*.25)=17.8%
Heart K right, club K wrong: You 0.25*(3%+0.97*(35.5%+2.4+62.1*62.5*0.25)=12.3%, me the same = 12.3%
Club K right, heart K wrong: You 0.25*(35.5+2.4+62.1*0.25) = 13.4% me 0.25*(35.5+3+0.615*(35.5+2.4+62.1*(0.5*0.75+0.25))=21.4%
Both wrong: You (35.5+2.4)*0.25 = 9% , me 0

So this way of counting makes your way about 8% better, at 59% to 51.5%, which is the same difference, though different totals, as when I calculated the first time.

I think my first set of calculations are better and the %s are actually 65% for you and 58% for me.

However, there are lots of risks that are hard to quantify, particularly the risk of defensive error. There are lots of ways for the defence to err on this hand, even something as simple as covering the heart Q will help a lot, in your case it will allow you to basically always pick up Jx spade by giving you an entry to hand. In my case they might fail to rise with the K of clubs from KTx KJx or KTxx fearing that they were rectifying the count for a squeeze, or that you might just have a guess after club to the Q and the ace of clubs of playing for clubs 3-3. It might not be obvious that you have 5 diamond tricks. If you need the clubs to come in with ATx in your hand rising from KJxx is a disaster. I dont know how to quantify these risks. SO it remains totally unclear which line is actually better at the table. Also, the correct defence might be much harder for east to find if he wins the first club, if he doesn't play a club back the extra entry to hand allows me to pick up Jx of spades. Its all very complex. The reality of playing these lines at the table is that even for expert level defenders there is a lot you could get wrong. I think there are more ways of going wrong if you play a club first, but that is totally subjective. Does that make up for 8% of hard technical gain? I don't know that either.