[dicklont]

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South is in 6NT, diamond lead.
South took DA and decided to play SA DQ DK and in trick 5: heart 6, small, King, Ace.
That was mistake by East, later West was squeezed in hearts and clubs.
Holding up the ace would have sunk the contract while finessing heart Jack was the winning line on this layout.

Obviously the finesse gives a 50% chance for 12 tricks.
South argued that his line was better for it would win on combined odds:
- clubs 3-3
- heart Jx or AJ somewhere
- heart A plus four clubs in east
- a defensive mistake

In analyses defensive mistakes play no role so my question is:
What are the odds for Souths play?

[phil_20686]

dicklont, on 2012-April-16, 11:42, said:

Obviously the finesse gives a 50% chance for 12 tricks.
South argued that his line was better for it would win on combined odds:
- clubs 3-3
- heart Jx or AJ somewhere
- heart A plus four clubs in east
- a defensive mistake

In analyses defensive mistakes play no role so my question is:
What are the odds for Souths play?

Whomever has the ace, if they hold it up you cannot squeeze anyone, as you cannot rectify the count. Further, you cannot test for Jx hearts either, as if they duck you cannot afford to play a heart honour, as if the hearts are 4-3 they will win the ace and cash the J. So the odds are really AJH or clubs 3-3 << 50%

[Fluffy]

Winning ♦A and going down with ♦Jxxx on west and going down when clubs are 3-3 would be pretty ridicoulous

[MrAce]

phil_20686, on 2012-April-16, 12:06, said:

Whomever has the ace, if they hold it up you cannot squeeze anyone, as you cannot rectify the count.

He can squeeze without rectifying the count of course, but this requires a double dummy line or info from opponent bidding that West has ♥A+4♣. He is wrong that south can squeeze East if he has clubs and heart Ace though.

South can, after winning the ♥K, cash all his winners 2♠+1♥+5♦ and West has to come down to 5 cards (4♣+♥A) then south holds dummy with 3♣+2♥, goes to dummy with ♣ honor and plays a small ♥. As i said this is far from a single dummy line.

[gnasher]

Another possibility is to test clubs and then decide whether to finesse in hearts. Disregarding the cases where clubs are 5-1 (where everyone ends up taking a heart finesse), that's about 50%:
Clubs 3-3: 36
Clubs 4-2, ♥A is with the short clubs and ♥J is onside: 12, plus a bit because of vacant spaces
This line requires us to win trick one in dummy, in order to keep the entries fluid.

It would help to know the bidding. We might be able to infer something from LHO's lead: with xxx in each of the minors he might have led a club. The bidding would also help with estimating the chance that LHO has led from ♦Jxxx.

[dave_w]

You should run the first diamond to hand. A lead from Jxxx is more likely than a singleton! And you can always overtake the ♦Q if they break 3-2.

Win the first diamond and play a Heart to the Ten: wins with the singleton Ace onside or any Jack onside: a little bit above 50%
Win the first diamond and play a Heart to the King (the duck is so obvious that this should win the trick): Now you virtually need clubs 3-3. No squeeze works without the count here + JT doubleton (the entry position works as long as diamonds are 3-2 also). About 38%. Also wins with AJ doubleton on either side (they have to win the Ace from this holding) or Jack singleton offside (about 2% all up) taking us to 40%

Win the first diamond and cash 3 clubs, then take the Heart hook if it doesn't work (clubs 3-3 36%, Clubs 4-2 with ♥A in the short club hand 26.6% (but only half these - so 13%) looks like about 49% to me. Yikes really close!

I'm not sure if there are any squeezes on West without the count. ie cash the ♠Ace and 5 rounds of Diamonds and discarding 2 Hearts. But West won't come under pressure until you cash the SK (they've had to release all their spades by this point if they are getting squeezed). But that's too big of a position to take HA onside plus 4 clubs with West (ie you can make it on that lay out by running all your winners - but it's the only lay out).