[inquiry]

1♣ - 1♥
2♥ - 2♠
3♣ - 4NT ?
5♠ - 6♥
Pass

5♠ = two key cards plus the ♥Q

Opening lead ♦7

---

Ok, this one can be argued a number of ways. I think the winning line is the best percentage chance based on the opening lead.

[quiddity]

Let's assume standard leads, and assume that West is not averse to leading from kings against suit slams. The lead could be from KJ7, KT7, K87, KJ87, KT87, or 8 possible 5-card holdings with the K. Or it could be from J87, T87, or a doubleton.

It looks like the best chance by far is to run the lead around to the Q. We even have the double-finesse in spades to fall back on.

[wclass___]

Why does opener treat ♥A as ♥Q?

[inquiry]

wclass___, on Feb 8 2010, 04:08 PM, said:

Why does opener treat ♥A as ♥Q?

Responder showed 4 card support for this pair, opener had six hearts. With 10 hearts assured between the two partners some partnerships will show the queen of trumps even when not holding it. That must have been the case here (this is a real world BBO hand, bidding and opening lead) not a "problem hand" constructed to make one point or another.

[wclass___]

Didn't opener show 4 card support?

If we assume that RHO has ♦K, playing him for less than 3 spades seems a better percentage play, else it is hard to assess.

[G_R__E_G]

I'm thinking that the 5♠ bid was actually showing 3 aces but it's really immaterial to the topic at hand so it doesn't really matter.

[FrancesHinden]

quiddity, on Feb 8 2010, 08:19 PM, said:

Let's assume standard leads, and assume that West is not averse to leading from kings against suit slams. The lead could be from KJ7, KT7, K87, KJ87, KT87, or 8 possible 5-card holdings with the K. Or it could be from J87, T87, or a doubleton.

It looks like the best chance by far is to run the lead around to the Q. We even have the double-finesse in spades to fall back on.

The auction certainly seems to suggest a diamond lead so I agree it's quite likely he would lead from the king if he had it (and single dummy we would have been pretty well off on a non-diamond lead as well).

How can we answer without knowing their leading style?

If they play "standard" 2nd & 4th then you are right, it is about 13:6 that the DK is onside which seems better than all other odds (although you have missed out the 6+ card holdings on lead which change the odds a bit).

If they play 3rd & 5th, the 7 is from
KJ7
KT7
K87
4x KJ7x
4x KT7x
4x K87x
4x KJ7xxx
4x KT7xxx
4x K87xxx

or from
J87
T87
4x J87x
4x 1087x
4x J87xxx
4x 1087xxx
4x 7x

or about 27:22 for the king onside

But with 7x on lead, that gives RHO KJ10xxxx in the suit and he passed over the 1C opening (admittedly at unknown vulnerability) which to me makes it more likely there is length onside. NV, a lot of people would overcall 2D on plenty of KJxxxx - type suits, particulatly if they had a bit of shape outside.

SO I agree with running the diamond lead.

It's not as if anything else is particularly attractive: you can play for the same hand to have a doubleton spade and the king of diamonds, but that is surely anti-percentage. Or you can play for someone to have 6 clubs and the spade guard, but that appears even more unlikely.

[inquiry]

Looking at the opening leaders hand, it looks like they lead 2nd/4th. 2nd from weak holding and 4th best from good holdings.

[quiddity]

So they lead second from 3 or 4 small?
I don't think it matters much. The best alternative (I think?) is to try to endplay someone with the king of diamonds and fewer than 3 spades. The chance of someone having 2 or fewer spades is 100 - P(3-3 spades) = 64%. The king of diamonds is slightly more likely to be with the short spade holder and there's also the chance of dropping QJ doubleton of spades. Can we estimate 38% for that line? 40%?

The spade double finesse alone is around 25%, so we need:
x = chance of west holding the diamond king
x + .25(1-x) > .4
x > .2

We need just a 20% chance of LHO holding the diamond king to make the diamond finesse plus spade double finesse the best line.

Every time I try a probability calculation I do something ridiculous. What did I mess up this time?

[inquiry]

First, let me begin by saying I think this hand is fatally flawed from the standpoint of a puzzle hand. Jdonn, FrancesHinden, and quiddity's (first post) have convinced me the right play is duck the opening lead to the queen, and if that loses, take the double spade hook. When I saw this hand I assumed west's lead would be clear "top of nothing" type of thing placing the king in EAST.... that is the problem with knowing all four hands...

Anyway, the king was with EAST, so the question became if you won the first trick what is a better percentage, playing EAST (specifically) for any doubleton (or shorter) spade or for the QJ of spades to be with EAST (any legnth). The a priori for EAST holding the QJ is 24%, the chance EAST holds two or less spades is higher (32%). However, once EAST shows up with 2 hearts to WEST's one during play, vacant space theory changes these odds. The chance for EAST having the QJ (any legnth) decreases, the chance that EAST has 0,1 or 2 spades goes up (If i calculated this correctly, QJ with east decreases to 21.7%, and no more than doubleton increases to 36.5%).

Since the diamond KING is a significant card, and since the line of play of winning the first diamond in dummy seems to play EAST for the diamond KING, his vacant space is actually two less than WEST's (12 to 10) dropping EAST's chance of QJ (any legnth) to less than 20% and increasing his shortness chances further (to something like 41.7%)

So the "winning play" was win diamond, pull trumps, ruff a club, cash two top spades, throw EAST in with a diamond Queen. While that wins, the right play was as pointed out by others unless you are CERTAIN the lead was away NOT away from the King.

This one has 7 votes and rates out at 2.5. We should just ignore this one I think.

---

[wclass___]

I still think it is hard to assess.

Sure LHO may have ♦K, but IMO it is hard to assess the exact probability, and i think it is much closer.

As a player on lead i would expect ♦A to be with the one who bid 4NT (unlike this case), so i can't hope that my king would be finessed anyway, because of the 4N bid that suggest ♦ cue(no cue this time). If i found ♦A in the dummy it would be unexpected for me.

If i have side queens and jacks i surely don't want to risk blowing a trick, because if i have points parter is likely to have less, so finding him with ♦Q is less probable.

And the ♦7 aspect. There are not many cards above 7 left, and JT shouldn't be together with the leader, so it reduce possible holdings for ♦K underlead. Also it can't really be from Jxx7. Maybe only J87. Passive lead feels much more probable to me (X7xx...)

[inquiry]

On a small plus side, play the line I gave above will work if Opener lead had the diamond King and two or fewer spades as well. Still, the true odds favor letting the diamond run unless you are very certain about the king location.