Simple but unusual application of empty space

[frank0]

[hv=pc=n&s=sq432h32da32c5432&n=sa765hkqjt9dk4ckq&d=n&v=n&b=5&a=1h2cppdp2sp3sp4sppp]266|200[/hv]

Modified from the hand I (mis)played in sectional. LHO leads a club to RHO's ♣A. RHO returns a club, which LHO shows high low(doubleton), you are in dummy now. What's next?

 

Answer:

You can only afford 1 spade loser, that means RHO has to have Kx or Kxx(x=7~J) in spade. In the former case you need to lead small ♠ at this trick(♠A in dummy to protect ♣ ruff), in the later case you need to play ♠A(remove the possibility of trump promotion on 3rd♣) first then a small♠ to Q. Because of the information in ♣

length the correct answer is a small♠ now, not the A.

 

It reminds me it's easy to forget a basic concept when it shows up in the unfamiliar format at table. :(

 

Anyone has similar experience?

[Antrax]

I don't understand this experience. You play a low ♠, RHO hops the K and plays a club. Now what? how do you avoid a second spade loser?

[iviehoff]

Doesn't even Mrs Guggenheim know that W is more likely to have one doubleton than two? Hardly need to have a deep understanding of empty space theory to realise that.

 

Antrax: frank's play analysis is correct - when W has 3 spades and you over-ruff a club with the A, you still have the SQ to take care of the two remaining evenly divided trumps.

[Vampyr]

I am always suspicious of vacant-spaces information provided by the opponents. I know it is valid information sometimes, but here? East looked at his hand before bidding.

[Antrax]

I wasn't implying his analysis is faulty, I said specifically that I don't understand. I thought that by vacant spaces, the K with RHO is expected to be with length?

What happens if LHO refuses to ruff?

[iviehoff]

Antrax, your last comment has woken me up to a problem with the analysis. I now realise that this is one of those occasions where Mrs Guggenheim is wrong, and I succeeded in giving Mrs Guggenheim's fallacious argument. Vampyr, I think that the 5/2 club break is a valid constraint for probability purposes, so we should model W with 11 vacant spaces and E with 8 vacant spaces. I realise that we should in general ignore "volunteered information", but in this case it is more than "volunteered information" in the sense that means (read Pavlicek's essay).

 

The fact that one requires the K to be E to make, means that it is wrong to be thinking of ratios 3/2 breaks in general according to the vacant spaces, because they do not evenly divide between those where E has the K and those where he doesn't. In breaks where W has 3 cards, the fact that one specifies that one of E's two spades is the K, these are less common than other breaks where E has 2 spades. So this is a factor that operates in the opposite direction to the vacant spaces argument, and in fact is sufficient entirely to wipe it out.

 

Using Richard Pavlicek's card combination analyser http://www.rpbridge.net/cgi-bin/xcc1.pl with 11/8 vacant spaces, I find these probabilities for W/E

 

xx/KJx 7.95%

Jx/Kxx 7.95%

total 15.90%

 

xxx/KJ 3.97%

Jxx/Kx 11.92%

total 15.89%

 

So actually when one requires the K to be with E, that fully cancels out the 11/8 vacant spaces effect, and it now becomes 50/50 to all intents and purposes, and at the 4th sig fig it is actually E who is favourite to have 2 cards accompanying rather than 1 card accompanying.

 

But actually we have some more information, that E made a simple overcall at the 2-level with a not-too-special 5-cd suit, and there are only 16 points between W/E. Surely E is favourite to have most of those HCPs. If I constrain the points division between the hands to 4/12, as an example, (so as not totally to exclude W having KJ), E now becomes much more of a favourite to have KJx/Kxx, as apposed to Kx/KJ (25.6% vs 21.1%).

 

And, Antrax, you are also right that with perfect defence, (assuming Frank's preferred line and 3 trumps with W) the contract goes off if LHO refuses to ruff and E has the HA, and assuming S won't have a master club on the 4th round. Declarer now can't draw trumps before attacking hearts, because if he did E would have a club to cash when he got in with the HA. If declarer refuses to draw trumps, or draws only one round, and then attacks hearts, E wins and plays another round of clubs. If declarer did draw one round of trumps, W can now ruff. If declarer drew no trumps, then W holds off again, N has to ruff with the A, and W comes to another trump later. There are also some other defence possibilities if they don't get that perfectly right, because declarer has communication problems.

 

So, actually, frank, you will be delighted to know you took the best line, but were just unlucky the cards were unhelpful.

Edited January 11, 2013 by iviehoff