[cherdano]

The essential holding in a play problem in the recent bridge world is the following (p. 47 July 2005 for those who have it):

---

You have no losers in the minors, sufficient communication, no ruff threatening, and you are playing in 4♠.

West leads a low heart, East winning with the Q. He continues with the A and K. From the carding and auction you know that West started with Jxxxx (5th) of hearts, and East with AKQ. You ruff and play...?

Arend

[FrancesHinden]

Well I haven't read the BW write up yet (I'm a few months behind) but my immediate response is that
a) we need trumps 3-2
when we play a spade up, West rises with any K to three and plays a heart and we'll have a second spade loser.

so we need to play one of East or West for Kx.
As hearts are 5-2, it's more likely West has Kx, so I cross to hand in a minor and play a spade up.

However, BW play hands are usually harder than this, so I've probably missed something.

[Winstonm]

I call TD: dummy has 6 cards while I hold 7.

[cherdano]

Winstonm, on Jul 9 2005, 07:31 PM, said:

I call TD: dummy has 6 cards while I hold 7.

This is just the holdings in the majors. Dummy has 7 cards in the minors, i have 6 (all winners).

[luke warm]

if this is right (after a heart ruff in dummy)

♠Q65

opposite

♠A742

i play for ♠K,x and lead a low spade from dummy, ducking.. now i hope that whoever wins either can't lead a heart or that, if it's lho and if he can lead a heart, rho has only the ♠K left

[FrancesHinden]

Let me think about this...
You are making when RHO has Kx, I was making when LHO has Kx which is slightly more likely.

You are also making when RHO has J10 doubleton if LHO doesn't overtake with the King. The non-overtake looks quite likely, but there's no easy way to measure the odds.

[cherdano]

FrancesHinden, on Jul 10 2005, 12:04 AM, said:

Let me think about this...
You are making when RHO has Kx, I was making when LHO has Kx which is slightly more likely.

You are also making when RHO has J10 doubleton if LHO doesn't overtake with the King. The non-overtake looks quite likely, but there's no easy way to measure the odds.

Now I am confused. If RHO has JT doubleton, Jimmy's line seems to never make. But he does make when RHO has JT9.

There is still another reasonable line.

Arend

[Fluffy]

Best percentage seems to cash ♠A and lead a low ♠ trying to find west with ♠Kxx, but vacant spaces might say something here.

[LH2650]

Since West is assumed to be long in hearts, East is assumed to be long in spades. On the bidding, West is assumed to have the spade King, so the most likely holding is Kx opposite Jxx. The point of the problem is that if you play Ace and a spade toward the Queen, West can win the King and play another heart for a high ruff. If you come to your hand in a side suit and lead a small spade, you are in a position to overruff with the Ace when West rises with the King and leads the 4th heart. The Queen then clears the suit.

[FrancesHinden]

If West has Kxx in spades, ace and another works.
If West has Kx in spades, a low spade towards the Queen works.
If West has xxx in spades, ace and duck works.

Given only the information that hearts are 5-3, I think the first two of these are exactly equally likely, and the third less so.

We may know something about the auction which gives an indication of minor suit lengths. For example, West has chosen to lead a Jxxxx suit which might not be very attractive if he had a minor suit singleton to lead instead. If he cannot have a minor suit singleton the chance of Kx is now higher than Kxx.

[han]

Given that west has five hearts and east three, Kx is more likely than either Kxx or xxx. Right?

[FrancesHinden]

Kx and Kxx are equally likely.

There are 4 Kx holdings and 6 Kxx holdings

West has 8 vacant spaces and East 11. A bit of arithmetic will show you that each Kxx holding is only 2/3 as likely as each Kx holding.

[FrancesHinden]

*******
Now I read the reply I see the error.
East has 10, not 11 VPs.
Idiot.

I've not edited the other post so you can all laugh at me.

Kx onside is about 16%, Kxx about 18%
So maybe BW is wrong (I looked it up last night) and A and another is better.

[cherdano]

I think you were consistent, after your earlier assumption that hearts split 5-2...
(In case someone wonders, there are 6*C(13,5) holdings with Kxx and 4*C(13,6) with Kx. Now C(13,6) is bigger than C(13,5), but only by a factor of 8/6, so the 1st number is bigger.)

Arend

C(n,p) = n!/(p!(n-p)!)

[LH2650]

FrancesHinden, on Jul 11 2005, 10:34 AM, said:

West has 8 vacant spaces and East 11.

According to the problem assumptions, West holds 5 hearts and the spade King, so he has 7 unknown cards, and East has 10. However, the basic conclusion that Kxx is more likely than Kx appears to be correct. I make the probabilities to be .397 and .353.

[Winstonm]

Is this a somewhat twisted version of restricted choice? The only holdings that matter for RHO are KJ, K10, K9, K8. With KJ10, K109, and K98 RHO has an option of which card to play. Does the fact that he plays one infer a lack of the other? The holdings of KJ9, KJ8, K108 do not matter, as I must assume the suit can be played correctly. Either Kx on the right or Kxx on my left. Assuming no false card, if I lead low from dummy and East plays the 10, this must be from either J10 or K10; if he plays the J, it must be from KJ. So I would venture to say that leading low from dummy and playing RHO for KJ(10) when he follows with either of those cards and playing LHO for Kxx when RHO follows with the 8 or 9 might possibly maximize the chances?

WinstonM