[kfay]

Had a difference of opinion with two good declarers about the following hand, but I may have overlooked a simple point.

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West led the ♥10 (AJ10 or 109) and the ♥K holds.

[Mbodell]

I would run the ♣J since I want to set up clubs and put west in. The other choice seems to be low to the ♣8. I guess both fail opposite H=H97 with proper defense (unless declarer ducks the 9 which will fail on H7=H9 layouts) and low to the 8 can fail opposite K7=Q9 but not sure it would in practice (unless you duck the 9), low to the 8 might win opposite a lazy 7 from H=H97.

[mikeh]

I'd often know at the table whether RHO had an even or odd number of hearts, and that would influence my thinking and maybe my play.

if he showed an even number, I would be more inclined to consider A and a club.

If hearts are 4-4, it probably doesn't matter what I do since clubs are unlikely to be 1=3 (he'd have either a 5 card suit to lead or a more passive lead than AJ10x. However, at least in theory he is more likely to hold either stiff honour than he is to hold the stiff 9, and my concern is to avoid 2 club losers more than it is to avoid rho winning the defensive club trick when they hold only one stopper.

I'd have to be worried that an even break is 6=2 rather than 4=4 but some LHO's would need little more than AJ10xxx to come in nv.

I'd be worried about the lead as well: AJ10x or AJ109 are not clear leads when one is 4=4=4=1 or 3=4=5=1

Otoh, if I felt that hearts were 5=3 or decided 6=2 was too risky a proposition, then I have to choose an avoidance play in clubs and the choices seem to be advancing the J or leading to the 8.

I don't like low to the 8 because it loses to H9 on my right. Q9 I might survive since many LHOs won't know to pitch the K under my Ace, tho it is clearly right to do so imo. Advancing the J, otoh, prevails on all 2-2 splits other than 97 = KQ, on which nothing works.

The main problem with the hypothetical H = H97 is that after the stiff H wins, they may well exit a low heart (or the 10) and now you have to guess the clubs: were they 2-2 all along or does RHO now hold H9?

So even the lie that appears to gain on low to the 8 may not gain at all.

Ok: I run the club J unless I think hearts are 4-4. If I think they are 4-4, I play the club A, still surviving against weak or lazy players with Kx on my left even if I have misread hearts. If I think they can beat me in hearts, with RHO leading next, I run the club J.

[kfay]

Mbodell, on 2013-February-14, 13:51, said:

I would run the ♣J since I want to set up clubs and put west in. The other choice seems to be low to the ♣8. I guess both fail opposite H=H97 with proper defense (unless declarer ducks the 9 which will fail on H7=H9 layouts) and low to the 8 can fail opposite K7=Q9 but not sure it would in practice (unless you duck the 9), low to the 8 might win opposite a lazy 7 from H=H97.

In the actual hand declarer played low to the 8 and did duck when RHO put in the 9 from H97 (possibly because after the 9 shows up this is the only winning option). As did the other declarer with whom I disagreed.

I argued that a priori H9 is more likely than H97 (OK... not that much more likely). But in hindsight, if we're worried about 5=3 hearts then it seems to push the odds in favor of playing as declarer actually did.

So who was right? I know there are probably many other things I haven't considered.

[ArtK78]

If clubs were the only consideration (assume hearts are 4-4), then I would play A and another club.

But I suspect that on an unrevealing auction such as the one here LHO might not lead a heart from AJTx. If LHO had 5 hearts, however, the lead of a heart honor is far more attractive. Perhaps RHO's play at trick one will help me to determine if the hearts are 4-4 or not, but I suspect that LHO has 5 hearts.

Given that I am going to play LHO for 5 hearts, I think that a low club to the 8 on the first round is the right play. Assuming that the 8 loses to an honor and LHO clears the heart suit, I will play RHO for H97. Of the layouts of the club suit which give us a chance at success, this line only loses to HH doubleton in LHO's hand.

So, the choices really boil down to this: If heart are 5-3 or 6-2 with length in LHO, low club to the 8 seems best; if hearts are 4-4, then A and another club seems best. As I believe that LHO has 5 hearts, I will play a low club to the 8.

EDIT: I note that it has been mentioned that with H97 RHO would put in the 9 to force declarer to either try to run the trick to a singleton honor or play the ace and hope for a 2-2 split with LHO winning the second round of the suit. Should RHO play the 9 (which, among those options where declarer has a chance to succeed, could be from H97 or H9 or 97) it is 100% for declarer to duck. In the case of H97 LHO will be forced to win his singleton honor. In the case of H9 declarer has no winning play, as LHO will unblock under the A. And in the case of 97 declarer has to play LHO for HH doubleton to succeed. In any event, ducking the first round of clubs leaves declarer no worse off.

[nige1]

kfay writes "Had a difference of opinion with two good declarers about the following hand, but I may have overlooked a simple point. West led the ♥10 (AJ10 or 109) and the ♥K holds.



I guess to run ♣J, hoping for a 2-2 break with honours split or RHO with a singleton honour.

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[PhilKing]

FWIW I doubt there is much correlation between being a good declarer and solving this kind of problem correctly (unless the key is discounting the chance of a decent West holding AJTx).

[Alik1974]

We don't want RHO to obtain the lead.
If ♣ are 2-2, the best play is ♣J intending to finesse.
If ♣ are 1-3, the best play is low ♣ ducked all around, then run ♣J on the next round.

Some have suggested ♣A and another club, but I think this play can be improved by crossing to a ♠ and playing a low ♣. East is the danger hand and may choose to play the doubleton King for a ♥ through, but he will be deprived of his entry.

[lesh]

kfay, on 2013-February-14, 15:19, said:

In the actual hand declarer played low to the 8 and did duck when RHO put in the 9 from H97 (possibly because after the 9 shows up this is the only winning option). As did the other declarer with whom I disagreed.

I argued that a priori H9 is more likely than H97 (OK... not that much more likely). But in hindsight, if we're worried about 5=3 hearts then it seems to push the odds in favor of playing as declarer actually did.

So who was right? I know there are probably many other things I haven't considered.

The odds for 3-1 are 49 and for 2-2 are 40. On top of that if LHO has a length in ♥ then the odds for LHO to have a length in ♣ start to increase. Therefore, small to the 8 or ducking the 9 turns to be not bad after all compared to running the J♣

[kfay]

lesh, on 2013-February-21, 11:12, said:

The odds for 3-1 are 49 and for 2-2 are 40. On top of that if LHO has a length in ♥ then the odds for LHO to have a length in ♣ start to increase. Therefore, small to the 8 or ducking the 9 turns to be not bad after all compared to running the J♣

Your odds aren't correct because we're not just talking about 1-3 and 2-2, but specific 1-3s and 2-2s.

Regarding LHO's heart length, I did discuss that.

[Mbodell]

lesh, on 2013-February-21, 11:12, said:

The odds for 3-1 are 49 and for 2-2 are 40. On top of that if LHO has a length in ♥ then the odds for LHO to have a length in ♣ start to increase. Therefore, small to the 8 or ducking the 9 turns to be not bad after all compared to running the J♣

3-1 and 1-3 together are ~49 a priori. Not 1=3 which is what matters. And specific 2=2 are slightly more likely than specific 3=1 (there are 6 2=2 combinations, each 40/6 = 6.67%, there are 8 3-1 possibilities, each 49/8 = 6.17%). There are 2 H9 hands, so 13.3% compared to 2 H97 hands which is 12.3%. So the H9 is about 1% more likely a priori. If LHO has 5+ hearts, that will shift the percentages slightly, but we don't really know the heart split so it is hard to calculate (plus if LHO always leads longest suit then some of the inference about hearts is tainted, b/c LHO is likely shorter than RHO in spades [and diamonds] as well. The heart length doesn't carry full vacant space values).

[PhilKing]

Assuming defenders play correctly, and ignoring break even winning combos (West holding K9, Q9, K97 and Q97), the situation is simple.

Running the jack gains when West has K7 and Q7. Low gains when West has stiff K or Q. The tie breaker is KQ doubleton with West, where running the jack wins. The rest is just noise.