play 6S

[kgr]

[hv=d=e&v=b&n=saqhad965cak98532&s=skj7432hkq942dqc7]133|200|Scoring: IMP

1S-2C

2H-4NT

5D-6S[/hv]

Lead ♠5.

What is best plan?

[Foxx]

♠A

♥A

♣A, ♣K (pitch diamond)

♦ ruff

♥ ruff

♦ ruff

♠K, ♠J

 

When clubs are 3-2 you can survive either, but not both of hearts 5-2 and spades 4-1.

 

When East has a singleton club, you still come out on top if hearts are 4-3 and spades are 3-2.

[kgr]

♠A

♥A

♣A, ♣K (pitch diamond)

♦ ruff

♥ ruff

♦ ruff

♠K, ♠J

 

When clubs are 3-2 you can survive either, but not both of hearts 5-2 and spades 4-1.

 

When East has a singleton club, you still come out on top if hearts are 4-3 and spades are 3-2.

Thanks

...1) You can play 2 spades from dummy and ♣A and ♣ ruff: makes if ♣'s are 3-2. (and also if player with 4 card ♣ has a 4 card ♠).

...2) or the line given by you: makes if (♣'s are 3-2 and not both of hearts 5-2 and spades 4-1) OR (East has a singleton club and hearts are 4-3 and spades are 3-2.)

 

How to calculate the probabilities of these 2 lines?

Or even better: How to "feel" (or very rough calculation) which of both lines is best, so you can make the correct play at the table?

[skjaeran]

♠A

♥A

♣A, ♣K (pitch diamond)

♦ ruff

♥ ruff

♦ ruff

♠K, ♠J

 

When clubs are 3-2 you can survive either, but not both of hearts 5-2 and spades 4-1.

 

When East has a singleton club, you still come out on top if hearts are 4-3 and spades are 3-2.

So you make if ♣ are 3-2 (68%) with ♥4-3 and ♠4-1 (17.36% combined) or ♥5-2 and ♠3-2 (21.08% combined) or ♥4-3 and ♠3-2 ((42.16% combined) for a total of 54.8%. In addition if east has singleton ♣ (14%) you make with ♥4-3 and ♠3-2 for an additional 5.9%. All in all your plan give a 60.7% chance of success.

 

The simpler plan, cashing dummy's trumps, ♣A, ♣ruff, draw trumps and use ♥A as entry to the established clubs need ♣3-2 and trumps not worse than 4-1. This adds up to 65.3%.

 

I've used rounded percentages here, so these numbers are just approximate. They'll be so little offset that it's clear that setting up dummy's clubs is the better line.

[kgr]

This was the full hand. I took the wrong line (Discarding ♦ on ♣'s and ruffing a ♥). If I could only do these calculations at the table :D

 [hv=n=saqhad965cak98532&w=st865h75dk832cqjt&e=s9hjt863dajt74c64&s=skj7432hkq942dqc7]399|300|[/hv]

[pretzalz]

 

The simpler plan, cashing dummy's trumps, ♣A, ♣ruff, draw trumps and use ♥A as entry to the established clubs need ♣3-2 and trumps not worse than 4-1. This adds up to 65.3%.

 

This is trivially inferior. Win the ♠A, and cash the top clubs pitching a diamond. If both clubs live you are cold, cash the ♠Q and in the worst case scenario of west having 2 clubs and 4 spades you ruff the third club high and play ♠K, spade. But you still preserve the extra chance when east is precisely 3=3=6=1 or 3=4=5=1 only at the expense of an overtrick when west has 4 spades and 2 clubs[which should be exactly equally likely as you are just mirroring the black suit splits].

 

Incidently, this line even survives 5-0 spades if LHO has 3 clubs[of course you find out about 5-0 spades at trick 1 so you'd hardly take a line that doesn't have a chance of picking up 5-0 spades].