Hook or drop?

[Phil]

Here's an interesting 3N I played:

 

[hv=pc=n&s=sjt93haq52d6ct854&n=sk2h6dakt942cakq2&d=n&v=0&b=1&a=1d1hdp2hp2np3cp3nppp]266|200[/hv]

 

Maybe you should have tried harder for 5♣ or 6♣, but its too late for that now.

 

LHO leads the ♥T and RHO encourages. You can choose to win this now or on the next trick, but you won't see the ♥9.

 

 

If you play two high diamonds, both follow but the Q or J do not appear.

 

[Hanoi5]

I'll take my chances with a third diamond round

[Phil]

Show your work :)

[Finch]

How interested am I in overtricks?

There's some reason to think that I should duck two rounds of hearts, but I don't know what to discard from dummy on the third (or indeed on the second), so I'll duck one and then discard a diamond on the second heart. There are some signs that hearts are 6-2 if the 9 wasn't played on my left on the second round.

 

I'm not sure it's right to play diamonds at all. If LHO has either spade honour and hearts are indeed 6-2 I can make by playing on spades. I also make by if clubs are 3-2 and hearts are 3-5 if RHO has the ace of spades (I run the SJ which holds, then cash the AK of clubs).

 

If RHO does have the AQ of spades then I'm off anyway if I have two diamond losers as they can cash 5 tricks.

 

A first round diamond finesse feels worse than a spade a trick 2. What I'm not sure about is whether it's right to cash the AK of diamonds then play the SK from dummy if no diamond honour falls, or so start by running the SJ.

The first round diamond finesse is going to go off every time RHO has Hx of diamonds (or singleton honour) and the SA.

[Phil]

How interested am I in overtricks?

There's some reason to think that I should duck two rounds of hearts, but I don't know what to discard from dummy on the third (or indeed on the second), so I'll duck one and then discard a diamond on the second heart. There are some signs that hearts are 6-2 if the 9 wasn't played on my left on the second round.

 

I'm not sure it's right to play diamonds at all. If LHO has either spade honour and hearts are indeed 6-2 I can make by playing on spades. I also make by if clubs are 3-2 and hearts are 3-5 if RHO has the ace of spades (I run the SJ which holds, then cash the AK of clubs).

 

If RHO does have the AQ of spades then I'm off anyway if I have two diamond losers as they can cash 5 tricks.

 

A first round diamond finesse feels worse than a spade a trick 2. What I'm not sure about is whether it's right to cash the AK of diamonds then play the SK from dummy if no diamond honour falls, or so start by running the SJ.

The first round diamond finesse is going to go off every time RHO has Hx of diamonds (or singleton honour) and the SA.

 

You aren't interested in overtricks, however it should be clear that LHO is not leading from Tx, since RHO can safely overtake with most KJ9-6th's, so I'd put LHO on any ♥T9x that couldn't raise, or ♥T9, T8 or T7 doubleton.

 

I hadn't considered the spade play early, but its banking on hearts being 6-2 which is far from clear, as well as clubs being 3-2. Granted, there is a subset of hands where LHO could have three hearts and enough junk to muster up a raise to 2♥. LHO actually led the ♥T from T83 (I should have mentioned that RHO is a strong player and LHO is relatively random), so a little noise might be factored into the calculations.

 

If you duck the 1st heart, LHO's next play should almost give away his holding however. RHO does have an easy overtake when LHO continues the 9, even from KJ8xx, but even so I agree spades is the best option here, at least against reliable opponents. However, if you are going after spades, after you judge hearts are 6-2 its clear to try 2 rounds of clubs first. If they don't split you need diamonds. If they split, you can simply play the ♠K from dummy and they cannot stop 9 unless RHO has ♠AQ as you say.

 

Should we still try two high diamonds prior to the spade play (or club)? If a diamond honor drops, you can claim, and if one doesn't, you can still fall back on spades. The pitfall is when one hand has ♦QJxx (x), since we've set up a 5th trick trick for the defense and they have an entry if we misguess spades.

 

The reason I originally posted this hand was a straightforward calculation between the spade finesse and diamond dropping, which is initially what I thought this hand was all about. Diamonds a priori are more likely to be 4-2 than 3-3, however, once the opponents each follow with small diamonds, we can take out all of the 6-0's, the 5-1's as well as the 4-2's with Qx and Jx, but also the QJx's. The original ratio of 4-2 to 3-3 now becomes a slight favorite over finding the ♠Q in LHO, since there are 12 combos left, but a particular 3-3 is more common than a particular 4-2.