Martens Declarer Problem - Maths?

[Little Kid]

[hv=d=s&n=sat9752hdk873cj95&s=shakq98742dacakt2]133|200|6♥, lead K♠.[/hv]

This is one of the "easy" declarer play problems in Marten's Declarer Play Book: Virtual European Championship Part 1. The reason I'm posting it is not because of the declarer play problem itself but because I'm curious what people feel is the best line intuitively. I've asked some players and they pretty much all give the same line, not the one I had in mind. :(

 

When I did this problem I thought about it for a bit then decided I would going to ruff a ♠, draw some trumps, unblock A♦, AK♣ and throw RHO in with a club (EDIT: a ♥ throw in!). This was not the same as the proposed line, which is cashing one top ♣, throwing RHO in and finessing if necessary. My judgement is probably a little off but would anyone be able to find how big the difference between the lines is? It would be very much appreciated!

Edited May 31, 2010 by Little Kid

[Free]

What's wrong with ♠A (♣ discard) and finessing ♣? If trumps are 4-1 we still make 50% of the time, if trumps are 3-2 I only lose if RHO has singleton ♣ and gets his ruff.

[Little Kid]

I'm pretty sure both the other lines are over 50% with the ♥s 4-1 with RHO. For one thing if LHO has 4♥s its cold anyway.

[gnasher]

When I did this problem I thought about it for a bit then decided I would going to ruff a ♠, draw some trumps, unblock A♦, AK♣ and throw RHO in with a club.

With a heart, you mean?

 

This was not the same as the proposed line, which is cashing one top ♣, throwing RHO in and finessing if necessary. My judgement is probably a little off but would anyone be able to find how big the difference between the lines is? It would be very much appreciated!

 

Cashing a second club gains when RHO (who has four hearts) has ♣xx or ♣xxxx. Retaining the club gains when he has ♣Qxx, ♣Qxxx, ♣Qxxxx.

 

Using Pavlicek's calculator with a vacant space ratio of 12:9, I got:

 

Qxxx-xx 21.9%

Qx-xxxx 5.1%

xxx-Qxx 17.0%

xx-Qxxx 10.2%

x-Qxxxx 2.3%

 

So Martens's line is a bit better.

 

Obviously, either line is better than a simple club finesse at trick 2.

 

Edited (again) to correct earlier misanalysis and false conclusion :)

Edited May 31, 2010 by gnasher

[Little Kid]

Yes, I meant throwing in with a ♥! Thanks very much!

[ceeb]

... would anyone be able to find how big the difference between the lines is? It would be very much appreciated!

Assuming no inferences from the lead or bidding, just calculating a priori lies of the cards --

 

All lines lose if there's a void trump.

 

Immediate ♣ finesse works if the ♣q is onside, or trumps break and no singleton ♣ onside. 78%

 

Strip two rounds of ♣ and endplay works

if trumps break 3-2, or

if 4-1 and long trumps has short clubs or the ♣Q drops. 83%

 

Strip only one round of ♣ and endplay works

if trumps break 3-2, or

if 4=1 as Little Kid points out, or

if 1=4 and ♣Q onside, or 0,1, or 5 small ♣ onside. 90%

[Free]

Yes, I meant throwing in with a ♥! Thanks very much!

Ah that makes more sense obviously :)

[pooltuna]

[hv=d=s&n=sat9752hdk873cj95&s=shakq98742dacakt2]133|200|6♥, lead K♠.[/hv]

This is one of the "easy" declarer play problems in Marten's Declarer Play Book: Virtual European Championship Part 1. The reason I'm posting it is not because of the declarer play problem itself but because I'm curious what people feel is the best line intuitively. I've asked some players and they pretty much all give the same line, not the one I had in mind. :)

 

When I did this problem I thought about it for a bit then decided I would going to ruff a ♠, draw some trumps, unblock A♦, AK♣ and throw RHO in with a club (EDIT: a ♥ throw in!). This was not the same as the proposed line, which is cashing one top ♣, throwing RHO in and finessing if necessary. My judgement is probably a little off but would anyone be able to find how big the difference between the lines is? It would be very much appreciated!

can't be much since it eliminates all the 5-1 ♣ breaks that would have lost the slam to the line that wins the A♠ and takes an immediate losing ♣ finesse with a ♣ return that gets ruffed with 3-2♥

[gnasher]

Strip two rounds of ♣ and endplay works

if trumps break 3-2, or

if 4-1 and long trumps has short clubs or the ♣Q drops. 83%

If LHO has four trumps, you don't cash two rounds of clubs - you just exit with a turmp and claim. Hence this should be

 

  if trumps break 3-2, or

  if 4=1, or

  if 1=4 and long trumps has short clubs or the ♣Q drops.

[OleBerg]

At a glance:

 

Low spade, three hearts (4-1 or I'm home), ♦A, ♣A, Endplay.

[ceeb]

Strip two rounds of ♣ and endplay works

if trumps break 3-2, or

if 4-1 and long trumps has short clubs or the ♣Q drops. 83%

If LHO has four trumps, you don't cash two rounds of clubs - you just exit with a turmp and claim. Hence this should be

 

  if trumps break 3-2, or

  if 4=1, or

  if 1=4 and long trumps has short clubs or the ♣Q drops.

Right. I read the OPs line too literally, and I posted without first seeing your post.

 

To summarize, your 2.5% differential is conditioned on 1=4 hearts, hence corresponds to an 0.3% overall success differential between the author's and the poster's lines of play.

[bluecalm]

Intuitively ?

 

Duck, ruff in hand. AKQ♥ if the split or 4 are with LHO I've already won. If 4 are with RHO I have additional chance of Q♣ being there too (or stiff ♣ or stiff♣ with LHO).