[inquiry]

Scoring: IMPS


2♣=2♦
3N=4♦
4♥=5N
6N=all pass
Opening lead ♦5.

T1. D5-T-3-2
T2. H2-Q-A-3
T3. DA-7-8-6
T4. HK-5-4-♣3

Diamond lead solved the risk of losing a diamond, the heart queen being singleton gives you 4 but not 5 hearts. The hand is now cold (double dummy) as there is a 100% line if East has the SPADE ACE and a 100% line if WEST has the SPADE ACE. So who has the ACE?

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First thought is VACANT SPACE. If my guess that WEST has the diamond JACK is correct, West has 6 vacant spaces (13-4H-3D) compared to EAST's 10 vacant spaces (13-1H-2D). So the odds strongly favor EAST having the spade ACE (10/16 versus 6/16). That seems odds are 62.5% chance spade ACE is with EAST.

Second thought, West lead from Jxx of diamonds. This is not a particular lead that stood out (in addition, East did not double 2D/4D for lead), so would restricted choice of some sort apply to the opening lead? That is without the spade ace, would WEST have been just as likely to lead a spade (or club)? How much, if any, would you consider the implications of a non-spade lead here? I would guess if WEST didn't have the spade ACE, he would be as likely to lead a spade as any of the other two non-heart suits. I guess, I might place the likelyhood or a spade lead without the ACE at 1/3, but we also know that WEST lacked club and diamond ACE, so if we treat them as equal suits, would this be 50% or so?

Straight up math (vacant space) suggest playing EAST for spade ACE, adding some value for restricted choice on opening lead decreases this advantage. Is it enough to sway you into playing WEST for the spade ACE? Let's assume that WEST would lead a spade 1/3 of the time when he lacked the ACE, does that reduce the chance EAST has the spade ACE from 62.5% of the time (62.5 - 1/3*62.5 = 41.7%)? What if you place the chance at 20% for a spade lead (62.5 - 1/5*62.5=50%).

Any other math considerations? If your opponents got to 6♥ they are going down one. If you play EAST for spade ACE and are wrong, you are down likely 4 or 5. If you play WEST for spade ace you are down two. Does the imp odds -- lose 7 to 9 imps if you guess EAST and are wrong, versus 3 imps if you guess WEST and are wrong factor in at all (assuming opponents are in 6♥).

As an aside, it is somewhat fun to see how to make this hand if you do decide to play WEST for the Spade ACE.

[quiddity]

inquiry, on Feb 11 2010, 01:42 PM, said:

I would guess if WEST didn't have the spade ACE, he would be as likely to lead a spade as any of the other two non-heart suits.

I don't completely agree with this; a queen is not the same as a jack in the eyes of a defender who is trying to find a passive lead (as we might expect from West, holding a possible heart stopper). Your holdings in spades and diamonds are also significantly different in terms of number of cards and quality of intermediates.

But I do think it reduces the chance that West has nothing in spades.

[nigel_k]

If I was West I would rather lead a spade from the queen or ten than a diamond from Jxx, and a club would be an option as well. So I would probably play West for it though it depends on West's tendencies and no doubt there are lots of people out there happily making 'passive' leads from Jxx against 6NT. I also think I might have done better to play off four diamonds forcing discards before the ♥K.

[jdonn]

West wouldn't lead a spade with the ace or the queen, and if east had both there is a reasonable chance he would have bid over 2♦ with his 10 cards in the black suits. In short I don't think the inference about the lead tips things that much, just a hair.

Another factor is if I play west for the ace and I'm wrong I'm down 2. If I play east for the ace and I'm wrong I could go down like 3 or 4. If I'm vul and I think it's so close I can't decide then that could be a tiebreaker, but ultimately I'm going with the math here and playing east for it.

[bid_em_up]

inquiry, on Feb 11 2010, 01:42 PM, said:

First thought is VACANT SPACE. If my guess that WEST has the diamond JACK is correct,

Why don't you cash the 3rd diamond and find out? I also think you need to take the club that East discarded into consideration as it occupied one of the "vacant" spots in the East hand. (At that point, you know he had 2D-1H-1C for 9, not 10).

Edit: Because you may need the 3rd diamond as entry back to hand. Never mind.

[ceeb]

Minor point -- don't cash the 2nd heart early. Instead, come down to

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with the lead in the dummy and West of course retaining ♥109x. If only 1 club remains, cashing the club, playing a spade and misguessing is down 1. If more clubs remain then misguessing East for the spade (play a spade to the K) is at worst down 2, misguessing West for it (cash the club and duck a spade) is down 1. So there is no need to consider down 3 etc.

If East was being playful with ♥Qx so be it. (But to make such a play East would have to hold the ♠AQ.)

[inquiry]

ceeb, on Feb 13 2010, 10:38 PM, said:

Minor point -- don't cash the 2nd heart early. Instead, come down to

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with the lead in the dummy and West of course retaining ♥109x. If only 1 club remains, cashing the club, playing a spade and misguessing is down 1. If more clubs remain then misguessing East for the spade (play a spade to the K) is at worst down 2, misguessing West for it (cash the club and duck a spade) is down 1. So there is no need to consider down 3 etc.

If East was being playful with ♥Qx so be it. (But to make such a play East would have to hold the ♠AQ.)

West has T9x of hearts and Ax of spades, EAST two clubs and Qxx of spades. You are down four if you play a spade and insert the king. If you cash the club King you are down anytime EAST does hold the ACE.

As an aside, you would have a hard time taking the score back if you go down when EAST did have Qx of hearts, or maybe a creative QT doubleton of hearts.

[ceeb]

inquiry, on Feb 13 2010, 10:56 PM, said:

ceeb, on Feb 13 2010, 10:38 PM, said:

Minor point -- don't cash the 2nd heart early. Instead, come down to

Dealer: ????? Vul: ???? Scoring: Unknown

♠ J ♥ J8x ♦   ♣ K ♠ K9x ♥ Kx ♦   ♣

with the lead in the dummy and West of course retaining ♥109x. If only 1 club remains, cashing the club, playing a spade and misguessing is down 1. If more clubs remain then misguessing East for the spade (play a spade to the K) is at worst down 2, misguessing West for it (cash the club and duck a spade) is down 1. So there is no need to consider down 3 etc.

West has T9x of hearts and Ax of spades, EAST two clubs and Qxx of spades. You are down four if you play a spade and insert the king.

The point about keeping track of the clubs is that you don't cash the last club unless it is safe to do so (or unless you have decided to play West for the ♠A). Given the defensive holding you mention and assuming the misguess of playing East for the ♠A the contract is down 1 if LHO has ♠A10 and down 2 if RHO has ♠Q10x. Not more.

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If you cash the club King you are down anytime EAST does hold the ACE.

That is why you don't cash the club king (unless there is only one club left) when you decide to play E for the ♠A.

Quote

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If East was being playful with ♥Qx so be it. (But to make such a play East would have to hold the ♠AQ.)

As an aside, you would have a hard time taking the score back if you go down when EAST did have Qx of hearts, or maybe a creative QT doubleton of hearts.

At the point of the matrix above you judge which heart holding to believe, having a lot of clues from the discards.