[pclayton]

I think I know the answer here (and I found it funny).

You play in an aggressive 6♠ on:

Scoring: IMP

---

LHO leads the ♥2 (5th best). You hold your breath and the Q wins.

Now what?

[655321]

Spade finesse followed by club finesse gives you (from the trick 2 position) one of two finesses.
That seems a fair bit better than anything you can do by cashing the ♠A and trying to get opponents to lead diamonds.

[manudude03]

Agree that the 2 finesses line is the highest. I think its much closer though.

Heart to the Ace, spade to the Ace. If both follow (and assuming K is still out), cash AK of clubs, ruff a club, exit a spade. You make if they lead clubs or hearts, or you guess the diamonds right (and stiff K of spades- the finesse line also caters for stiff K on). The variation on this is cash AK of diamonds before exiting spades which endplays whoever had the spade K if they had 2 diamonds or less (but you then go off if they can lead diamonds again).

NB if spades are 3-0, you must finesse clubs unless you find an honour drops when you cash a top diamond (play the opp holding 3 spades for this H).

Change the 9 of diamonds to the Jack and the original version only depends on spades being 2-1 or choice of finesse. (and obviously a claim if club J is the Q after T1)

[han]

Hmm, it seems to me that we'll just play for split diamond honors, so that's slightly over 75%. The chance that spades split 2-1 is 78%. 26% percent of that is a stiff king and then we are home. We get roughly 3/4 of the other 2-1 splits so 40.5%. When spades split 3-0 we can fall back on the club finesse so that's another 11%. That makes a total of 77.5%, considerably better than the two finesses (which is only slightly over 75%).

This seems very clear to me but 653321 seems so confident that I suspect I'm making a mistake.

[655321]

han, on Oct 15 2008, 06:32 PM, said:

Hmm, it seems to me that we'll just play for split diamond honors, so that's slightly over 75%. The chance that spades split 2-1 is 78%. 26% percent of that is a stiff king and then we are home. We get roughly 3/4 of the other 2-1 splits so 40.5%. When spades split 3-0 we can fall back on the club finesse so that's another 11%. That makes a total of 77.5%, considerably better than the two finesses (which is only slightly over 75%).

This seems very clear to me but 653321 seems so confident that I suspect I'm making a mistake.

Split diamond honors is 50%

So cashing the ♠A gives you:

26% (singleton K)
26% = (52% * 50%) for Kx of spades and split diamond honors.
11% = (22% * 50%) for Kxx of spades but the club finesse working.

63% approx for this line, instead of the 76% approx for one of the black honors onside.

[han]

Oops, there's my mistake!

If we think that LHO would lead from ♦QJ rather than low from the heart king then we'd be back at 75%, but since we were not given the auction that's hard to say.

[jdonn]

Another way to think of it.

Ace of spades first gains over two finesses when there is:
Singleton king offside and club finesse off = 13%*50% = 6.5%
Doubleton king offside and split diamond honors and club finesse off = 26%*50%*50% = 6.5%
Total: 13%

Two finesses gains over ace of spades first when
Doubleton king onside and diamond honors together = 26%*50% = 13%
Tripleton king onside and club finesse off = 11%*50% = 5.5%
Doubleton king offside and diamond honors together and club finesse on = 26%*50%*50% = 6.5%
Total: 25%

This 12% difference is about the same difference between the two lines that 655321 stated.

It's true not getting a diamond lead probably reduces the chances of either QJ(x)(x) or xx(x)(x) with the leader, which sways things more in favor of ace of spades first. But that is very very dependant on who your opponents are, and I don't think sways things enough in any case.

I think I see a mistake or two in my analysis anyway (other than intentionally not considering QJ doubleton or 6-0 diamonds or stuff like that), but I don't feel like pointing them out to anyone who would have missed them

[FrancesHinden]

Of course you are going to cash the ace of diamonds before taking the spade finesse, in case an honour drops under it. If it does you go back to ace of spades and the elimination.

[655321]

FrancesHinden, on Oct 16 2008, 07:28 AM, said:

Of course you are going to cash the ace of diamonds before taking the spade finesse, in case an honour drops under it.  If it does you go back to ace of spades and the elimination.

Perhaps you are right, I am not sure about 'Of course'.

Could West drop the ♦Q under the Ace from QJx in a hand like x Kxxxx QJx xxxx (or would this hand have led a diamond at trick 1?)

If East played a diamond honor it would be safe enough in real life to take it as a true card (or would East try a cunning Jack from Kx xxxx Jx xxxxx?)

How will you cash the ♦A? If you cross to dummy in diamonds, West might split anyway holding both honors. But if you cross to dummy in hearts and cash the ♦A, it will be clearer to the defenders what you are up to, increasing the chance of a tricky false card.

All these possibilities are quite confusing for me, so I suspect I might stick with the black suit finesses anyway, even though I am not sure how likely these false card positions are (not very, I suspect.)

[pclayton]

Gnome and I were discussing this yesterday. At the table, I'd like to think here's how I would analyze the hand:

Two lines present themselves.

1. Two black suit hooks.

2. Strip out the hand and either try to drop the ♠K offside, or throw in the Kx. An improvement to this would be cashing the ♠A before stripping out clubs. Note that we can't take advantage (that I can see) of ♦QJ(x...) in either hand, since we'll assume that a defender will always exit a diamond honor regardless of his diamond holding.

There are six cases of how the spades can be divided:

A. Stiff King on. Everything works.

B. Stiff King off. #2 works, and #1 works half the time (split diamonds)

C. Kx on (2 cases). #1 works, and #2 works half the time (split diamonds)

D. Kx off (2 cases). #2 works half the time (split diamonds). #1 also works 1/2 the time (club hook - 50%). So this washes.

E. Kxx off. The lines are equal, since the two lines converge. You can either play for split diamonds or LHO to exit a club. Stripping clubs loses when LHO has two clubs (what a nice falsecard if LHO pretends to have Qx by the way), but wins when LHO erringly shifts to a club.

F. Kxx on. This is the only critical case I can see and breaks the tie. #1 works. #2 works half the time.

A, D and E are the same. B and C cancel each other out.

I didn't work out the percentages, but if all spade distributions are equal (I know they are not), that it should be 1/16th better or roughly 6%.

I misanalyzed this at the table by the way.

[FrancesHinden]

Don't understand your E. If there is Kxx in either hand, what are you going to do other than take a club finesse?

[pclayton]

FrancesHinden, on Oct 16 2008, 07:51 AM, said:

Don't understand your E. If there is Kxx in either hand, what are you going to do other than take a club finesse?

Yes, true. But the lines do converge.

[awm]

Your B and C don't cancel each other out.

Situation C (Kx onside) is twice as likely as situation B (singleton K offside). You even mentioned this in your post.

[655321]

pclayton, on Oct 16 2008, 10:36 AM, said:

Gnome and I were discussing this yesterday. At the table, I'd like to think here's how I would analyze the hand:

 [Snip long, messy and incorrect analysis]

I didn't work out the percentages, but if all spade distributions are equal (I know they are not), that it should be 1/16th better or roughly 6%.

I misanalyzed this at the table by the way.

Why on earth would you like to think that is how you would analyze the hand at the table?
And if you did analyze like that, it is no wonder that you misanalyzed.

I say this, not to criticize you for misanalyzing (goodness me, I misanalyze hands all the time ), but to disagree on how to analyze this particular hand at the table.

Sometimes, the simplest way to compare 2 lines is to enumerate the cases which are different, as you and jdonn have done. And often at the table it is very difficult to calculate the actual odds of different lines. But for this hand, it is very simple to calculate the approximate odds of each line and for me, that is much the easiest way to approach this hand.

Taking 2 finesses is about 75%.

Spades can only divide 2-1 or 3-0 (78% and 22%), so the calculation of the elimination line odds, as in my earlier post, is simple enough to do at the table.