[ralph23]

♣♦♥♠

North ♣ A Q 3 2

South ♣ J 6 5 4

South (here, you) needs to take three (3) club tricks. Taking four club tricks gets you absolutely nothing: you’re in a great contract of 6NT and all you need on this last hand of a team match is three club tricks to make the contract, and score a big win. The overtrick which would result from taking four club tricks is totally, completely and utterly meaningless.

a. What layouts of the EW hands must exist for you to succeed? That is, how must the cards be divided? NB - layouts = plural.

b. How does South play so as to maximize his chances of success? (State the simplest line, without unnecessary back-and forth between the hands. The lead is currently in the North hand. NB—Cater to all "good" EW Layouts. Remember, an overtrick is without any value at all, so don’t try for one if doing so in any way jeopardizes your contract)

c. What is the likelihood of NS success here?

For part c., here is the Table of Probabilities (from Richard Pavlicek's web site, which has a cool interactive calculator for this stuff): If you are declarer and are missing five (5) cards in a suit, the odds of how they are dividing are as follows:

3-2: 68%
4-1: 28%
5-0: 04%

Adv & exp, pls hide your answers.

[inquiry]

Hidden answer below....

Spoiler

To win only three tricks, best line is to start with the ACE, to cater to a singleton king offside (which is 2.8%), if that doesn't occur, then you still have the 68% chance the suit is 3-2 or the other 2.8% the singleton king is onside. This comes to 68+2.8+2.8 or about, 73.6%. There is some rounding errors in here, So this could be as low as 73.5 or high as 73.7... maybe someone will do the math accurately (3-2 is really 67.83 for instance).

[goobers]

If you want to pick up 4 tricks, you need to find doubleton K onside, but since we only want three...

I guess we can start by cashing the CA. If the suit breaks 3-2, we always make 3 tricks no matter how we play it. If it breaks 4-1, then starting with the CA picks up the additional 4-1 break with the stiff K offside (where finessing a club honor would lose the suit).

I don't see how you can pick up 3 tricks on any other 4-1 break, your spots just aren't good enough.

So 68 + 28/5. Something like that?

[Echognome]

My hidden answer below:

Spoiler

What Ben said.

[han]

Spoiler

Yep, agree with Ben

[pclayton]

Exhaustive analysis follows as hidden:

Spoiler

Ben, Matt and Han are dead on.

[Quantumcat]

Hmmmmm I'll have a go

• If it's 3-2, lead small to jack, let west have the king if he wants (win A, Q, little), or if it's east, play a round of little ones, then the Ace takes the King, 3 tricks (J, A, Q) or if he takes it before your Jack, 3 tricks (J, A, Q)
  
• If it's 4-1 with the king onside, finesse couple times, lose the last trick. Same if 5-0 (only win if king onside). Low to the jack can only give you 2 tricks unless east is kind enough to take king on first lead.

So finessing wins if 4-1 or 5-0 with king onside: 28% + 4% = 32%, but times a half because king has to be onside: 17%. Also wins when 3-2 and king onside, 68*1/2 = 32%, Both together = 49%

Low to jack wins on all 3-2, 68%.

Low to jack wins 68% of the time, finessing 49%. So choose low to jack!

I hope this is correct. Then I'll be very proud of myself

[DWM]

If you take the finesse and it loses 68% of the time you will still make 3 tricks as you will have the top 2 remaining cards plus the 4th trick.

The way the question is worded the bonus of the finesse getting the 4th trick sort of makes me think that there may just possibly be an alternative line to help secure the 3rd trick at expense of the 4th.

At the table I would like to try and leave this suit till last so I can factor in oposition error (on a good night that makes my line 100% on a bad night makes no difference)

To win 3 tricks when the suit splits 4-1 the king has to be dropped, hence the play of an ace. On this line when the suit splits 3-2 two the AQJ will still make plus the 4th trick.

Down to the maths now

68% for all 3-2's
4-1 split with king singleton = 20% of 28% = 5.6%

73.6% chance by playing ace then queen then jack

[Quantumcat]

Ok I forgot about possibly dropping the king. That makes sense.

[SoTired]

This is too simple to be complex. The only thing you have to think about is getting 3 tricks.

(Actually, if you are good enough to realize the CoC, then you are good enough to solve this problem )

If we needed to get 4 tricks, we would finesse and hope the doubleton K was onside. We still get 3 tricks almost anyway we play the suit.

Finesse won't help because any 4-1 break will stop 3 tricks if you finesse and any 3-2 break will get you 3 tricks no matter how you play.

The ONLY hand where the finesse and playing the Ace first makes a difference is the singleton K offside. In ONLY that case, you get 3 tricks if you play the ace first and don't if you finesse.

So play the Ace first