Best line in 6S slam

[Mbodell]

Apologies for inline hand, but tablet interface doesn't have the insert wizard.

 

Dummy has:

A943 AKQT6 72 A4

 

Declared has:

QJ752 72 AKJ3 93

 

Lead club K.

 

Day 1 of NABC+ mixed pairs. Auction (opponents silent, every one red, declared opens in second seat):

1S - 2H

2S - 3S

3nt (non-serious) - 4C

4D - 4nt (1430)

5C (1/4) - 5D (Q?)

6D (Q+K in D, no K in C) - 6S

[Cyberyeti]

My first feeling is to play 3 rounds of hearts immediately.

[WesleyC]

I like Cyberyeti's line although I think it's pretty close.

 

To expand on the reasoning, the ♠A is a valuable entry so if you're planning to play on hearts then you can't really afford to cash it early.

 

If hearts are 3/3 you'll probably make (ignoring 4-0 trumps).

 

If Hearts are LHO 4, RHO 2 you're in good shape.

If RHO ruffs small you overruff, cross to the ♠A, ruff a heart and then hope to get to dummy with a diamond ruff.

If RHO ruffs with the ♠K you pitch a club and are probably home.

 

If Hearts are LHO 2, RHO 4 you're in slightly more trouble but still not dead. You pitch a club and then probably end up needing to fall back on the spade finesse.

 

I'd guesstimate this line is in the 65% ballpark - slighty better than ♠A and then a diamond finesse.

[greiman]

When first looking at the hand, I was thinking of cashing the SA before playing three rounds of hearts. Compared to Cyberyeti's line, it gains if East is 22 in the majors with the SK. Even if they don't have the king, we might survive if West was 2443. Also gains if anybody has a stiff king since now we know we can afford to draw trump (5 spades, 4 hearts, 2 diamonds, 1 club, and diamond ruff for 12 tricks). This feels like about 75-80%.

 

Of course, the other advantage to Cyberyeti's line is that if hearts are 3-3, now we can try for 13 tricks.

 

 

At least we've established that they're both better than taking a diamond finesse.

[WesleyC]

Hi Greiman and welcome to the forums!

 

My first instinct was to cash the ♠A, but I don't think it's correct. Have a closer look and I think you'll find that Cyberyeti's line will also make if either player has 2 hearts and ♠Kx.

 

The main gain case for not cashing the ♠A early is when LHO has ♠Kxx and a doubleton heart. They can ruff the 3rd round of hearts (after you pitch) but you can fall back on the spade finesse - more likely than stiff King offside.

[Mbodell]

Fwiw my first instinct was also to cash A first. This gains if spades are 3-1 with the short spades having 2 hearts as well as clarifies some kx holdings and wins all stiff k. In quick informal discussion with a pro, the line of immediate hearts keeping the A for later was suggested as better. Both beat the immediate spade finesse, which was the unsuccessful line taken at the table (kx offside, hearts 4-2 with the short hearts in the East kx hand).

[greiman]

Hi Greiman and welcome to the forums!

 

My first instinct was to cash the ♠A, but I don't think it's correct. Have a closer look and I think you'll find that Cyberyeti's line will also make if either player has 2 hearts and ♠Kx.

 

The main gain case for not cashing the ♠A early is when LHO has ♠Kxx and a doubleton heart. They can ruff the 3rd round of hearts (after you pitch) but you can fall back on the spade finesse - more likely than stiff King offside.

 

I took a closer look, but I remain unconvinced. I'm going to ignore the 4-0 splits because both lines are in trouble. Looking at the hand combinations for west, there's spade count (1, 2, or 3), heart count (2 or 4 (a 3-3 split works for both lines)), and SK (yes or no) for 12 different combinations. (Obviously, not all the same probabilities).

 

Cashing the ace before hearts makes on 8 hands, goes down on 2, and gets complicated (usually depending on diamonds on 2).

Cashing hearts first makes on 5, goes down on 3, and gets complicated on 4.

 

Both lines go down if West is 22 w/o the SK.

SA 1st goes down if West is 32 w/ the SK

Hearts 1st goes down when West is

32 wo SK (finesse fails after he ruffs)

12 wo SK (finesse fails after he ruffs)

 

That would seem to favor cashing the ace first. What am I missing?

[Cyberyeti]

I took a closer look, but I remain unconvinced. I'm going to ignore the 4-0 splits because both lines are in trouble. Looking at the hand combinations for west, there's spade count (1, 2, or 3), heart count (2 or 4 (a 3-3 split works for both lines)), and SK (yes or no) for 12 different combinations. (Obviously, not all the same probabilities).

 

Cashing the ace before hearts makes on 8 hands, goes down on 2, and gets complicated (usually depending on diamonds on 2).

Cashing hearts first makes on 5, goes down on 3, and gets complicated on 4.

 

Both lines go down if West is 22 w/o the SK.

SA 1st goes down if West is 32 w/ the SK

Hearts 1st goes down when West is

32 wo SK (finesse fails after he ruffs)

12 wo SK (finesse fails after he ruffs)

 

That would seem to favor cashing the ace first. What am I missing?

 

Part of the problem is where you're not instantly off but are in trouble.

 

Have a look at E has 3♠ with K and 2 hearts.

 

So you cash the third heart and E ruffs, you overruff.

 

Now what ?

 

If you've cashed A♠ already, you need W to follow to 4 diamonds (or have Qx(x))

 

If you haven't you can ruff a diamond, ruff a heart, spade to the A and lead the 5th heart.

[greiman]

Part of the problem is where you're not instantly off but are in trouble.

 

Have a look at E has 3♠ with K and 2 hearts.

 

So you cash the third heart and E ruffs, you overruff.

 

Now what ?

 

If you've cashed A♠ already, you need W to follow to 4 diamonds (or have Qx(x))

 

If you haven't you can ruff a diamond, ruff a heart, spade to the A and lead the 5th heart.

 

You're right, leaving the ace as an entry handles this "in trouble" hands better since it can handle a less favorable diamond layout. But it has twice as many of these "in trouble" hands and it fails more often.

[rmnka447]

At first, I wasn't sure that cashing 3 rounds of ♥ was best. Possible alternatives might be taking the trump finesse first or possibly trying for a discard on the ♦ by finessing and playing for ♦ to be 4-3.

 

The diamond finesse option can be dismissed fairly easily as the conditions necessary -- 4-3 ♦ with ♦ Q onside would be less probable than a 3-3 ♥ break.

 

I think the thing that makes cashing the ♥ so attractive is that it works almost all the time declarer's RHO has only 2 ♥. If RHO ruffs with ♠ K, you pitch the remaining ♣. If RHO ruffs low, you can overruff and play a ♠ to the ♠ A. Then there's only a problem if LHO started with 4 ♥ to the J and ♠ K10x. It seems like the probability of this line is much better than that of the immediate ♠ finesse (about 50%). Something like 36% for 3-3 ♥ plus near 24% for 4-2 ♥ (RHO doubleton) plus some % when ♥ 2-4 (LHO doubleton) AND LHO holds ♠ K (maybe 10-12%?).