[Stephen Tu]

---

Uncontested auction, diamonds are bid and supported, you end up in 7NT with a diamond lead. What end position do you play for?

[Cyberyeti]

Without thinking too hard, I hope whoever controls the spades also has either the Q♣ or 4 hearts if hearts aren't 3-3:

I keep N ♠AKJ, S ♠7, ♥7, ♣J

[HardVector]

My initial thought was play it as a double squeeze. Cash the AK in the black suits and run the diamonds playing one of your opponents for 4 hearts and a black queen. I think this will work if east has 4 hearts and either queen, or west has 4 hearts and the spade queen.

[pescetom]

HardVector, on 2018-September-23, 14:38, said:

My initial thought was play it as a double squeeze. Cash the AK in the black suits and run the diamonds playing one of your opponents for 4 hearts and a black queen. I think this will work if east has 4 hearts and either queen, or west has 4 hearts and the spade queen.

Neat, but are you sure that this is advantageous compared to just cashing the spades ace and then finessing the jack? I haven't done the maths but have some doubt.

[HardVector]

pescetom, on 2018-September-24, 09:48, said:

Neat, but are you sure that this is advantageous compared to just cashing the spades ace and then finessing the jack? I haven't done the maths but have some doubt.

A finesse is 50/50. Cashing the A caters to spades 5-1 with a singleton Q. That elevates it to a little more than 50%. I don't know what the percentage is for the squeeze, but I'd eyeball it to above 75%.

[mikeh]

I want to cater to 3-3 hearts, the spade Queen dropping doubleton or stiff, and some squeeze positions. I can't cater to all layouts.

So assuming diamonds run, and with a small diamond lead they have to run, I will win, cash the club Ace, run the diamonds, pitching 2 spades, then play heart K and low to the A.

I will have reduced to (edit: in my original version I forgot that I had pitched a spade on the club K but this simply gave me one to many cards in dummy and doesn't affect the analysis, which had been done knowing I was down to AKJ))AKJ x void void opposite x Ax void J.

If either player had long hearts and the spade Queen, they are already squeezed out of one of the majors. Assuming the hearts are not good, I play spade to the AK. The Queen may drop, either because someone was squeezed in the major or it was short all along.

Assuming nothing good has happened, on the last spade, in the three card position, with my hand still to follow to the last top spade, I hold void Ax void J and dummy is J x void void.

I am cold if hearts were 3-3, and otherwise I need RHO to have the club Queen and the heart length (edit: obviously, but I should never assume anything is obvious, if RHO doesn't pitch the club Q, I pitch my Jack and hope hearts are breaking).

So if either opp had 4+ hearts and the spade Queen, I make. I also make if RHO had the hearts guarded and the club Queen. In addition, of course, I make on 3-3 hearts or the spade Queen dropping, plus a tiny amount for clubs being 7-2 with Qx clubs (or 8-1, stiff queen).

We have all kinds of ways to make.

I'm not sure of the odds, the calculation is beyond anything I could do at the table, but I think my losing cases is when RHO has short hearts (which is about 32% of the time AND Qxx in spades or better. He is slightly more than 50% of the time to hold the spade Queen when short in hearts, and most of that time he will have 3+ spades. So I ballpark the odds of his holding the danger layout as about 18%.

There is a slight chance that the club queen drops in 2 rounds, but that is likely to be only a rounding error in the arithmetic.

Note that I am not cashing a spade early: I'm dropping the stiff Queen anyway. And I am never taking a finesse. Even if the finesse were equal (but not superior) to a squeeze, I always choose the squeeze. In real life I've seen that arise maybe half a dozen times, because there is usually something going on that tips the odds at least a little. Here, the finesse is way less likely to win than the squeeze.

[pescetom]

HardVector, on 2018-September-24, 10:58, said:

A finesse is 50/50. Cashing the A caters to spades 5-1 with a singleton Q. That elevates it to a little more than 50%.

But of course even a beginner is only going to take the finesse if hearts do not split 3-3, so it works out roughly 68% (1 - 51% * 64%).
Still very unfavourable compared to Mike's squeeze calculation though.

[Cyberyeti]

pescetom, on 2018-September-25, 07:01, said:

But of course even a beginner is only going to take the finesse if hearts do not split 3-3, so it works out roughly 68% (1 - 51% * 64%).
Still very unfavourable compared to Mike's squeeze calculation though.

The problem is that the only way you can know the finesse is favourable also improves the squeeze chances. If W has 1♥/2♦ he's at least 2:1 to hold Q♠, but he's also very likely to hold Q♣.

[cherdano]

I don't understand the advantage of Mike's line over cashing the hearts first. To be precise, cash ♣A, run diamonds pitching two spades, cash three hearts, cash ♣K, then (usually) play spades from the top. This wins
- whenever hearts are 3-3,
- when ♣Q and heart [i]shortness are in the same hand, or
- when heart length and ♠Q are in the same hand.
(There is a very minor improvement in that if we learn that is has quite a bit more length in hearts+diamonds+clubs--cashing ♣K last might help discover that, we can revert to the spade finesse.)

Leaving aside this minor improvement, we can roughly compute the losing cases as
- hearts are not 3-3 (64%),
- club Q in the same hand (45% when hearts 4-2, even less otherwise),
- spade Q in the other hand (58%)
for less than 17%.
If this seems only marginally less than the 18% figure in Mike's calculation, that's because he forgot a losing case - Mike's line also loses when RHO has long hearts and neither of the queens.

By the way, whether I am right or wrong, this would say little about whether Mike or I would play this better at the table - I am sure at the table, we would both stop and think at the point where our lines diverge (cashing the last heart, or cashing ♣K and cashing spades first), and reconsider based on what we learned about the opponents' distributions. It's quite an obvious fork of the road, and we will know at least the diamond count, and perhaps some uneasiness in the opponents' discards.

[mikeh]

cherdano, on 2018-September-25, 08:14, said:

I don't understand the advantage of Mike's line over cashing the hearts first. To be precise, cash ♣A, run diamonds pitching two spades, cash three hearts, cash ♣K, then (usually) play spades from the top. This wins
- whenever hearts are 3-3,
- when ♣Q and heart [i]shortness are in the same hand, or
- when heart length and ♠Q are in the same hand.
(There is a very minor improvement in that if we learn that is has quite a bit more length in hearts+diamonds+clubs--cashing ♣K last might help discover that, we can revert to the spade finesse.)

Leaving aside this minor improvement, we can roughly compute the losing cases as
- hearts are not 3-3 (64%),
- club Q in the same hand (45% when hearts 4-2, even less otherwise),
- spade Q in the other hand (58%)
for less than 17%.
If this seems only marginally less than the 18% figure in Mike's calculation, that's because he forgot a losing case - Mike's line also loses when RHO has long hearts and neither of the queens.

By the way, whether I am right or wrong, this would say little about whether Mike or I would play this better at the table - I am sure at the table, we would both stop and think at the point where our lines diverge (cashing the last heart, or cashing ♣K and cashing spades first), and reconsider based on what we learned about the opponents' distributions. It's quite an obvious fork of the road, and we will know at least the diamond count, and perhaps some uneasiness in the opponents' discards.

Arend, I started by writing that the reason you didn't understand the advantage of my line is probably because there isn't one.

You are in a 3 card ending, knowing who has the long hearts (we both make on 3-3 hearts so there is no edge there).

If LHo has the heart length, he is down to 2 black cards. If one is the spade Queen, we make. But so do I, since in my 4 card ending, he still has to shorten the spade.

If he lacks the spade Queen but has the club Q, then he controls both round suits and you need RHO to have begun life with Qx or stiff queen in spades. So do I.

If he has 4 hearts and neither Queen, you win because RHO, caught with both black Queens, can't guard them in the 3 card ending.

In my 4 card ending, he can keep Qxx void void Q, and is not squeezed.

Meanwhile if RHO has the heart length, and the spade Queen, we both prevail.

If RHO has the heart length and the club Queen, in the 3 card ending he has to have come down to a stiff spade and you have to decide whether to finesse or drop, and will be guessing to some degree.....because it is unlikely that you have a complete count...altho the opps sometimes signal accurately because they are worried about pseudo-squeezes. Does LHO hold Qxx in spades or has RHO been squeezed in the majors?

In my line, if RHO has 4 hearts and the club Q, I will always get it right, since I am squeezing him when cashing the top spades in the 4 card ending. So I think I have the edge on that layout.

What does this mean? Frankly, I don't know. I suspect, but am not sure, that your line offers slightly better odds if only because the opps may give you a good count, and your spade play at the end (finesse or drop) may be one that you can assess with a high degree of probability. In other words, in your winning case, I have no chance of getting it right in the end game but in my winning case, you will have a pretty well-informed guess, depending on how good your opps are and how good your table presence is. So heads you win, tails you have a chance

Also, as a matter of general principle, it is probably better, most of the time, to reduce to a 3 card ending rather than a 4 card one, since you will know one more piece of information. I, for example, am very unlikely to take the spade finesse, while it might be odds on for you, depending on what you know about the hand, which will be one more card than I (probably) know.

As for my 18% estimate, I wouldn't claim that it was precise. Were someone to say it was 16.3 or 18.9, I would merely nod (assuming I thought they know what they were talking about).

I agree wholeheartedly with your comment about our play being influenced by what we learn when we cash the diamonds. It took me a while to map out my suggested line, although I always try to come up with the line in the time I'd take at the table. If I can't...if I sweat it out and make hand diagrams.....I will usually say so (and I almost never do that).

I suspect that had this hand arisen at the table, and assuming I was in a long team game, this would be the slowest played hand of the event.