[pescetom]

MP
Nobody vulnerable

---

Decent opponents playing standard carding.


What is your plan as North to make 4♠ after a ♣Q lead?

[Douglas43]

Duck the first club. Win assumed second club. SQ and A. If trumps are 3-2 play HAK and (if no Jack dropping in two rounds) the Queen. This should make on hearts 3-3 or 4-2 when the same hand has four hearts and three spades. By playing the Q early, you can ruff a club high back to hand.

If trumps are 4-1 it's asking a lot for an opponent to be 1-2 in the majors and stay silent, so I'd draw trumps and hope the hearts break.

[AL78]

Duck the first trick, win the second assuming a club continuation (I can't tell whether ducking or winning immediately makes any difference). Play a spade to the ace and run the ♦9. If it is covered by the jack, cover with the queen, and assuming it loses, next time I'm in lead a diamond to the ten and hope the outstanding honor is onside (West might have led a top diamond holding AK). If the diamond nine loses to the A or K offside, next time I am in I can lead another diamond to the QT and set up a diamond winner. If neither of those come to pass, draw trumps and cash the top hearts hoping the jack falls. Have to be careful to keep the spade queen in dummy to provide an entry to the diamond winner if I manage to set one up.

[mikeh]

I’m not able to calculate the odds, at least not without far more time and/or pen and paper, and I always try to ‘solve’ these play problems within the time I’d be able to take at the table.

It being mps makes that challenging: at imps in a long match one can usually afford to play important hands slowly and catch upon the easier ones

I’d be reluctant to play on diamonds. Sure, it could well work and, as I say, I haven’t crunched the numbers. I’d be concerned that I’m going to be in trouble if diamonds sit badly and anyone but especially east has 4 trump. Say I duck the lead, win the next club, assuming they continue the suit, cross in spades, lead the diamond 9. East pops and plays a club. I have to ruff. Say I play another diamond…to the 10. West wins. If he has KJxxx or the more likely AJxxx (given that east popping is more suggestive of Kx than Ax) he should win the king, not the jack. Now he plays another diamond…a decent opponent by this time knows almost precisely what’s going on.

There are various other risks with playing on diamonds.

If I duck the club, the odds are they continue, but that’s not a sure thing…maybe opening leader can usefully play on diamonds. But let’s assume clubs are continued


Firstly, while it’s normal to duck from Axx, it’s not clearly correct here (though that’s not the same as saying it’s wrong)…again, if diamonds are splitting badly and trump are 4-1, they may be able to hurt us with a diamond switch.

Also, simply knowing that the opps are ‘decent’ is less than I might know at the table.

Some opps, even some experts, love to give count. Against them I’d consider winning the club and playing a heart to the Queen, as if I’m taking a finesse. Frequent count givers may tell me how hearts are breaking.

Then I draw two rounds of trump, ending in dummy. If trump are 3-2, I play on hearts, succeeding with 3-3 or Jx or Jxxx holding the third spade.

If trump are 4-1, and east has 4, I play a heart to my 9 unless I believe they gave honest count in hearts and that hearts are 3-3.

If west has 4 trump, I need to hope hearts come home.

[Douglas43]

Thanks Mikeh for an interesting improvement. That point about different 4-1 trump breaks and their effects on the odds is interesting. I didn't think about the vacant spaces issue, which is probably an indication of the gap between a decent player and a real expert.

Here are some simple probabilities for the basic line (with no allowance for vacant spaces or the absence of opposition bidding which could indicate against extreme distribution):
Works where Spades 3-2 (68%) or 4-1 (28%) and Hearts 3-3 (36%) or 4-2 with Jack dropping (16%) or singleton Jack (3%). That's 96% x 55% = 52.8%

[LBengtsson]

I have just made a quick calculation - hope no mistakes - using this useful bridge tool.

http://www.automaton.../en/OddsTbl.htm Thank you Theodore

I have entered all 1,2,3,4,5 combination of ♥ cards using mikeh's analysis with out the 6-0 as that will probably result in a ♠ ruff. I can not combine all the 3-2, 4-1 ♠ distributions into the analysis but looking at ♥ suit in isolation the results are as follows.

Dropping ♥J in 1,2 or 3 rounds = 54.1%

Dropping ♥J in 1,2 or 3 rounds (with West showing ♥J on trick 3) or finessing West for ♥J on trick 3 = 56.9%

I do not like the idea of playing on the ♦ suit to try to make a winner to discard a ♥ loser as lack of entries, trumps need to be drawn, and possibility of a ♠ ruff.

I like mikeh's play to closed hand of ♥Q early in play: the defense might be off their station and give away clues, though a good defenser might see around that asking why is not declarer drawing trumps, setting up other side suit ♦?

Edit: I always get beaten to the post, lol! Thank you Douglas43 for your probability analysis also.

[Douglas43]

Douglas43, on 2022-June-24, 03:17, said:

Thanks Mikeh for an interesting improvement. That point about different 4-1 trump breaks and their effects on the odds is interesting. I didn't think about the vacant spaces issue, which is probably an indication of the gap between a decent player and a real expert.

Here are some simple probabilities for the basic line (with no allowance for vacant spaces or the absence of opposition bidding which could indicate against extreme distribution):
Works where Spades 3-2 (68%) or 4-1 (28%) and Hearts 3-3 (36%) or 4-2 with Jack dropping (16%) or singleton Jack (3%). That's 96% x 55% = 52.8%

Sorry, I should have added: There is the additional chance that one player has Jxxx in Hearts, and the third trump in a 3-2 split. Here the third heart honour stands up and the fourth heart can be ruffed, then we ruff back to hand (high) and draw the last trump.
That works on half of the situations where Spades 3-2 (68%) and hearts 4-2 with Jack not dropping (32%), less a reduction for vacant spaces. That's 21.7% less the reduction for vacant spaces.

Overall about a 70% chance of success.

[pescetom]

Thanks to all who answered.

I found this a difficult plan at the table, not just because I was brought up in the school of "at least be fast".
The odds were far from clear (albeit close) on the various lines.
I actually decided not to duck, just as I decided not to risk the diamonds, for much the same reasons as mikeh suggests although with a fuzzier logic ("this looks like one of those situations where diamonds and spades might well be in the wrong places and then the post mortem is going to be a mess").
It turned out that W had ♠T97 ♥754 ♦KJ74 ♣K98 and so all lines lead to Rome, with almost all of us making the contract.