[Flem72]

AQTxxx
Qxx
x
Axx


Kxx
x
AKJTxxxx
x

Contract is 6S; they take their H and lead a C. FWIW, they have bid and raised C, but to me this is purely a play problem and it is strictly a %s thing as to how good is the slam?

My feeling is that it is well over 50%, but I have trouble lining up the S & D probabilities. I can see that it is down if S are 4-0; it makes if S are 2-2 so long as lefty doesn't hold 4 D; it is making if S are 3-1 and J drops stiff so long as lefty doesn't hold 4 D; and it is making if S & D are each 3-1 so long as one opp holds both long S and long D. This last one is the problem

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Regards and Happy Trails,

Scott Needham
Boulder, Colorado, USA

[ArtK78]

Way over 50%.

2-2 spades is roughly 40% by itself. When spades are 2-2, the diamonds will be 4-0 in LHO's hand is roughly 4.5% of the time, or 1.8% of all hands, so the chances that spades are 2-2 and diamonds are not 4-0 in LHO's hand is roughly 38.2%, which is a clear make. If spades are 3-1 (roughly 50% of the time) the diamond Q will be singleton about 12.4% of the time, and the diamonds will be 2-2 about 40% of the time. So, 52.4% of the remaining 50%, or 26.2%, will be easy makes. That brings you up to 64.4%.

Spades 3-1 and diamonds 3-1 with the ♦Q not being singleton will also result in a make whenever the long spades and the long diamonds are in the same hand. The diamonds will split 3-1 with the Q being part of the 3 about 37% of the time. Of that, the 3 card trump holding will be with the 3 card diamond holding about 40% of the time. Overall, the long trump and the long diamonds will be together about 14.7% of the time. Since the spades will be 3-1 about 50% of the time, this adds about 7.35% to your chances of making the hand.

The ♠J being singleton is only relevant when the diamonds do not break and the spades are 3-1, as you intend to pull two rounds of trump with the A and Q before testing diamonds. You intend to cash one diamond and ruff the second round in dummy, succeeding whenever diamonds are 2-2, there is a singleton ♦Q or when diamonds are 3-1 (no ♦Q singleton) and trumps are 3-1 with the long trump and short diamonds in the same hand. It turns out that 3-1 spades with the ♠J singleton and 3-1 diamonds (ignoring the Q) with the long spades and short diamonds together occurs about 7% of the time when spades are 3-1, or about 3.5% of the time overall.

There are also some chances when diamonds are 4-0 as long as you don't get an opening ruff.

You are not necessarily down if spades are 4-0. If RHO has Jxxx of spades, you can pick it up and then run the diamonds if the ♦Q is doubleton or less.

All told, the chances of your making this slam seem to be pretty good.

Now, if the defense had started off with two rounds of hearts, your chances would be much worse.

[Flem72]

ArtK78, on 2012-June-21, 14:11, said:

Way over 50%.

TY.

[dake50]

Instead of summing %-success cases, try %-failing.
Seems that failing cases is a much easier calculation.

[FrancesHinden]

ArtK78, on 2012-June-21, 14:11, said:

Way over 50%.
......
Now, if the defense had started off with two rounds of hearts, your chances would be much worse.

And if the 3181 is in dummy, it's astonishing that they didn't. In fact, if they don't tap dummy at trick 2 the slam is huge because I reckon it means spades are almost certainly 2-2 and they can't see the point.
It's a better slam before the opening lead if they have bid and raised clubs, because it increases the chance of a club lead.