best play in 6D

[kgr]

[hv=n=saxxxhtxdktxxcajx&s=sxhaj9dajxxxxcktx]133|200|1D-(1S)-2S-Pass

5D-(Pass)-6D-All Pass[/hv]

You reach 6D after LHO overcalled 1S.

LHO starts a S that you take with ♠A and you ruf a ♠.

You now play ♦A and RHO surprises you by discarding a ♥.

You play a ♦ to the ♦T (RHO discarding a ♥) and ruff another ♠.

You play ♦ to ♦K (RHO discarding a ♣)

You finesse ♥ loosing to LHO ♥Q and he returns a ♠ that you ruff in hand (RHO discarding a ♥).

[hv=n=saxxxhtxdktxxcajx&s=sxhaj9dajxxxxcktx]133|200|1D-(1S)-2S-Pass

5D-(Pass)-6D-All Pass[/hv]

LHO started with: 5=[1-4]=3=[1-4] RHO: 3=[4-7]=0=[3-6]

Assume that I made up the discards of RHO and that they don't tell you anything and that LHO already showed enough in ♠ and ♥ for his overcall

What is best play from here and what are the probabilities of both lines:

1) Play ♥A and ruff a ♥. You will now have a good count to play the ♣'s for the best probability.

2) Play ♣K, ♣A, the ♦ discarding a ♣ from hand and finesse ♥ if ♣J is not high

 

Thanks,

Koen

(hope this makes sense)

[eyhung]

This is an interesting end-position with some theoretically plausible alternative lines you didn't mention, but the bidding and early play indicates something odd is going on. RHO has 3-card support for his partner's overcall and a void in the enemy suit, yet passed? Even if they are at unfavorable vulnerability, it's hard to see many good opponents passing there if they have any high cards. So assuming competent opponents, and that LHO's spades are at least KQxxx, I'd probably play LHO for the HK, going against restricted choice, and play HA and ruff a heart. If:

 

1) hearts are surprisingly 1-7 or 2-6 with RHO holding the HK, then I am playing LHO for the CQ -- I think even the worst RHO would have bid with both missing highcards, 3 card support, a 6+-card unbid major, and a void.

 

2) hearts are 3-5 with LHO holding the HK, then I am playing RHO for the CQ (5:2 odds in favor, and if LHO had KQJxx KQx Qxx Qx he might have overcalled 1NT).

 

3) hearts are 3-5 with RHO holding the HK, then the HK falls underneath my ace (RHO has played 4 hearts already) and I claim.

 

3) hearts are 4-4, claim (club to ace and finesse RHO will guarantee the contract.)

[kgr]

Thanks for the answer Eugene. Probably right that not raising spades (or doubling 2S) indicates that LHO will have the ♥K.

 

But I'm also interested in the probabilities for best play without taking into account the info you got from the bidding and without taking into account the psycholgies of the plays.

(I wonder how difficult that question is).

 

Thanks,

Koen

PS: ....I was also wondering if restricted choice applies for the ♥ suit. For beginners like me that always have to rethink this:

Before you play the ♥'s, the double finesse gains 75% of the time one trick (RHO having ♥K and/or ♥Q). After you have lost the 1st finesse the probability that LHO has the other ♥ honour is 50%, but that is divided by 2 because of restriceted choice to 25%. So still 75% to gain a trick with the double finesse. If LHO always plays the Q from KQ then the probability is 50% after loosing the 1st finesse to the Q, and 100% after loosing the 1st finesse to the K.

[Fluffy]

The simplified probability of split honnors after you lose first double finese is 67% not 75%.

 

You have already dissmissed the case where RHO has ♥KQ, so yo uno longer have the 75% avaible.

 

LHO has half the chances of having King when he has both. this means that from the 4 original cases, there are only 2 left, and one of them is half as likelly as the other. so 1/3 vs 2/3.

[eyhung]

But I'm also interested in the probabilities for best play without taking into account the info you got from the bidding and without taking into account the psycholgies of the plays.

(I wonder how difficult that question is).

Probabilities can be very easy if you ignore information, but that gives you a false number. If you really want to become a good bridge player, you must assign conditional probabilities based on previous information. For example, my estimate was that if East held the HK and 6+ hearts, he had a near 0% probability of holding the CQ -- although the mathematics would say that he had a significant, non-zero chance.

 

Anyway, if you want the misleading math, use http://www.automaton.gr/tt/en/OddsTbl.htm for odds given vacant spaces:

 

Line 1 depends on how you play after each heart break. I already said that I do not think East can have the CQ if he holds a 6+ heart suit with the king, but pure math would ignore that. The odds of each heart break in isolation with 5 empty spaces to 10 are roughly:

 

1-7 : 9%

2-6 : 34%

3-5 : 40%

4-4 : 17%

 

If you always play the long club hand for the queen, then my back-of-the-envelope calculation is :

 

9% * 4/7 (hearts are 1-7, clubs are 4-3, and heart king cannot be singleton) +

6/8 * 34% * 4/7 (hearts are 2-6, clubs are 3-4) + 2/8 * 34% (doubleton HK) +

40% * 5/7 (hearts are 3-5, clubs are 2-5) +

17% * 7/7 (hearts are 4-4, clubs are 1-6, and we always find the CQ)

 

(4.5%) + (14% + 8.5%) + (28%) + (17%) = 73%.

 

 

 

Line 2 is strictly P(doubleton CQ or restricted choice finesse) = 2/7 * P(2-5 or 5-2 break given the 8-3 ratio) + 67% - P(both) = 11% + 67% - (67%)(11%) = 11% + 67% - 8% = 70%.

 

So surprisingly, the pure math slightly supports line 1. I hadn't expected that because a restricted choice finesse is usually quite strong (2/3).

 

At the table I would know none of the probabilities based on vacant spaces -- I would just follow the reasoning I outlined in my first reply. Even if I had all the odds memorized, I wouldn't do it because the numbers I get from the calculation are misleading. Garbage in, garbage out.

[kgr]

Thanks a lot for the answers Eugene!

[kenrexford]

In the end position, if you play the A-K in spades and the Queen does not fall, you end up with ♠-- ♥x ♦x ♣J on dummy and ♠-- ♥AJ ♣10 in hand.

 

If you now play the diamond x, RHO is squeezed if he has the club Queen and heart King, remote as that may be, and on the play of a small heart you see the King and claim. So, we assume that RHO does not have both.

 

If LHO has both, we squeeze him into baring his heart King and can simply drop it by playing small to the Ace, not finessing.

 

The squeeze line fails when the honors are split and the heart King is protected.

 

So, playing the two top clubs and then finessing wins over the drop when RHO has the protected heart King but not the club Queen. Playing two top clubs and then playing the heart Ace wins over the finesse whenever LHO has both the club Queen and the heart King or whenever he started with K-Q tight in hearts.

 

A heart pitch at any time by LHO makes the latter impossible, though.