[Stephen Tu]

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3C = club shortness.

Matchpoints
West leads a small diamond, which turns out to be a stiff. East plays Q,K,Ace. On the 2nd diamond west pitches a club. On the third diamond, west ruffs and leads a club.


Thoughts?

[mikeh]

Spoiler

I suspect west knows what he’s doing…the typical club player wouldn’t think of ruffing his partner’s trick.

If you have 5=3=4=1, nothing matters, from his pov. If you have 5=4=3=1, then he has to make you guess. Most club players don’t do this, so good on him.

Is it more likely that hearts are 3-2 or that the club hook works?

Absent this defence, we’d try hearts first.

There is no inference about either suit from this defence…a good defender would definitely do this with 2 or 3 hearts and/or the club king….so long as he has either 4 hearts or the club king his only goal is to prevent you from combining chances…hoping you misguess now.

3-2 is 68.5% but only a priori. The diamond break seriously reduces that figure. At the same time, the diamond break increases the chances of the club hook since as of trick 2, west had 11 spaces and east only 6.

I think it’s pretty much a coin toss…I’m going to feel badly no matter which way I go should I go wrong. But I think I’d feel just a tiny bit worse if I finesse, lose, and find that hearts behaved…west would have ‘got me’.

I don’t let those sorts of things affect me unless I really can’t think of any other reason to choose one way or the other. I’ve looked silly before, and will again, by going with what I felt were the odds even when counter intuitive. But I really can’t work out why one play should be better than the other. West rates, imo, to hold 4 hearts but he also rates to hold the club king…

Ok…I pop the Ace…

Ask me tomorrow and I’ll hook😀

Btw, would he find this defence if we played a less informative J2N? 3C showing any minimum seems superior…north asks about shape if interested, which he wouldn’t be here.

Last point: I draw no inference from east’s silence…he is red v white. Having the club king or a stiff heart wouldn’t likely be enough to make him bid even though good players usually stretch to interfere over J2N.

[nullve]

Spoiler

The fact that

* West didn't pitch hearts as if trying to get a heart ruff
* East didn't play the AKQ of diamonds in a different order to suggest a heart shift

strongly suggests that East has 1-2 hearts.

The fact that West

* risked ruffing the third diamond (potentially solving Declarer's problem in trumps with Jxxxx opposite AKTx)
* didn't preempt, which he might have done with 1417 or 1318 shape

strongly suggests that East has 0-1 spades.

So East appears to have at least four clubs, and I think we can rule out that East didn't overcall with ♦AKQ+♣K because of semi-balanced shape and (say) a lack of playing tricks.

I guess the reason he didn't overcall is that in his opinion he lacked the points to do it. (It's a very bad reason, but I can't think of a better one.)

So I'll play him for

♠x ♥x ♦AKQxxx ♣xxxxx,

in which case I need to take the club finesse, rather than

♠x ♥xx ♦AKQxxx ♣Kxxx.

[shyams]

I used the "Suit Break Calculator" on RPBridge website. According to the output to my query, the hearts are splitting 3<->2 39.7% of the time, 2<->3 19.9% of the time, any 4-1 33.4% of the time. The 6.3% incremental probability is enough to not try a finesse in clubs.

I am rising with the Club Ace and playing for a 3-2 split.

[pescetom]

shyams, on 2023-May-18, 08:14, said:

I used the "Suit Break Calculator" on RPBridge website.

Did the opponents complain?

[eagles123]

Really cool problem. My gut feel is to finesse, but it's a difficult situation for sure.

[smerriman]

shyams, on 2023-May-18, 08:14, said:

I used the "Suit Break Calculator" on RPBridge website. According to the output to my query, the hearts are splitting 3<->2 39.7% of the time, 2<->3 19.9% of the time, any 4-1 33.4% of the time. The 6.3% incremental probability is enough to not try a finesse in clubs.

I am rising with the Club Ace and playing for a 3-2 split.

I may have misunderstood since I don't know what you mean by 6.3% incremental probability, but based on those numbers a 3-2 split is 59.6% (plus another 1.4% for West having a stiff J/T), while the same 12 to 7 vacant places numbers gives the club being onside as 63.1%. Ignoring carding / defensive strategy entirely, doesn't this favour the finesse?

But nullve makes a good point that West would have thrown hearts with 2 or less, which I think makes a 4-1 heart break even more likely.

[shyams]

I used a (hopefully more appropriate) calculator from RPBridge website (link here)

Conditions: (1) West has 12 & East has 7 vacant spaces; (2) West has 3 or 4 heart cards. There are 4,185 combinations where West holds 4 hearts vs. 6,370 combinations where West holds 3.

If I rise with ♣A, my contract is safe 60.3% of the time (i.e. all combinations where West holds 3 hearts). If I finesse, the ♣K will be onside 57.7% of the time (that's 6,090 combinations across 4-1 and 3-2 heart splits).

I hope this time my calculations are more robust and more accurate. What I am discovering is that yes, it is still better odds to disbelieve West and go up with the Ace.

[shyams]

As a postscript: I excluded some holdings in the heart suit in my post above:
* With a heart void, West would not ruff trick 3
* With a singleton or doubleton, West would discard his hearts to obtain a ruff at trick 4 (again, no ruff at trick 3)
* If West held a 5-card heart suit, East would have underled at trick 3 compelling West to ruff and get a heart back for a ruff.
Even if East overlooked it, West may have found it easier to lead a heart at trick 4.

I am also excluding sleepy plays by West (e.g. forgot to throw a ♥ at trick 2 from ♥xx, woke up at trick 3 & conjured up a potential escape hatch.

[Stephen Tu]

shyams, on 2023-May-18, 21:49, said:

I used a (hopefully more appropriate) calculator from RPBridge website (link here)

Conditions: (1) West has 12 & East has 7 vacant spaces; (2) West has 3 or 4 heart cards. There are 4,185 combinations where West holds 4 hearts vs. 6,370 combinations where West holds 3.

Not quite sure how you are calculating this.Aren't there 10 * 14c9 = 20020 combos where West is 3-1 in the reds, and 5 * 14c8 = 15015 combos where West is 4-1 in the reds?
By my calcs:hearts 4-1, ck onside, 8580 out of the 15015 combos of x=4=1=x deals, need to hook (others down regardless).
hearts 3-2, CK offside, 7150 out of the 20020 combos of x=3=1=x deals, need to go up CA (others anything works).

So hook is favored. I think this holds as long as West finds the 2 pitches of hearts from 2-1 in the reds at least half the time.

In real life, my opponents were proverbial LOLs with not a lot of awareness, and gave me no such difficulties. East led low on the third diamond to force West to ruff, which might be clever, but with this opponent maybe more likely just random. West, despite looking at HJxxx and the CK, led a heart (??!) and avoided immediate disaster when partner held stiff T, but of course I had no problems after that. But I was wondering what the right play was against better defense, I didn't know how much the odds of 3-2 heart break were swung by the 6-1 break not having studied it before, now I know it's swung only a little by a 5-2 break but quite a bit when 6-1.

I think I am convinced that finesse club is best against good opps on the proposed defense. Other questions worth thinking about:
- What should East's strategy be? Should he underlead 3rd round holding CK, to force partner to ruff but then also maybe dissuading declarer from finesse? Or should he lead high honors and trust expert partner to ruff good trick to lead the club? Should he only underlead 3rd round *not* holding CK trying to convince declarer not to hook?

- What's the strategy if the diamond split were 2-5 rather than 1-6? The pure math swings strongly now to playing for 3-2 hearts, but also, isn't it easier to be awake to ruff and lead C from 4 hearts and CK, than to be aware to ruff and lead C from like HTxx and CJxxxxx?

[mikeh]

Stephen Tu, on 2023-May-18, 22:48, said:

Not quite sure how you are calculating this.Aren't there 10 * 14c9 = 20020 combos where West is 3-1 in the reds, and 5 * 14c8 = 15015 combos where West is 4-1 in the reds?
By my calcs:hearts 4-1, ck onside, 8580 out of the 15015 combos of x=4=1=x deals, need to hook (others down regardless).
hearts 3-2, CK offside, 7150 out of the 20020 combos of x=3=1=x deals, need to go up CA (others anything works).

So hook is favored. I think this holds as long as West finds the 2 pitches from heart pitches from 2-1 in the reds at least half the time.

In real life, my opponents were proverbial LOLs with not a lot of awareness, and gave me no such difficulties. East led low on the third diamond to force West to ruff, which might be clever, but with this opponent maybe more likely just random. West, despite looking at HJxxx and the CK, led a heart (??!) and avoided immediate disaster when partner held stiff T, but of course I had no problems after that. But I was wondering what the right play was against better defense, I didn't know how much the odds of 3-2 heart break were swung by the 6-1 break not having studied it before, now I know it's swung only a little by a 5-2 break but quite a bit when 6-1.

I think I am convinced that finesse club is best against good opps on the proposed defense. Other questions worth thinking about:
- What should East's strategy be? Should he underlead 3rd round holding CK, to force partner to ruff but then also maybe dissuading declarer from finesse? Or should he lead high honors and trust expert partner to ruff good trick to lead the club? Should he only underlead 3rd round *not* holding CK trying to convince declarer not to hook?

- What's the strategy if the diamond split were 2-5 rather than 1-6? The pure math swings strongly now to playing for 3-2 hearts, but also, isn't it easier to be awake to ruff and lead C from 4 hearts and CK, than to be aware to ruff and lead C from like HTxx and CJxxxxx?

Your penultimate point gets into the realm of game theory, about which I know little. But certainly, east should force partner to ruff some of the time pretty much whatever he has, unless he has a spade void (and even then there are hands where it’s right).

If he has the club king, no matter how many hearts he has, he wants partner to ruff and lead a club. But this also means that he should force partner to ruff and lead a club when he has a stiff heart, since he knows declarer is either 5431 or 6331, and in the latter case, nothing matters.

So while west ruffing the queen suggests he’s a good player, playing the queen suggests that east isn’t as strong.

How one ought to factor these ideas into the guess is beyond me. I’m not convinced that pure math is ‘the’ only approach…one needs to factor in one’s views of the opps. When the odds are, as I see them, very close on a pure math basis, I think psychology may be enough to sway one either way.

Edit: I think the notion of west being 2-1 in the reds is a red herring. If he has 2 hearts, even a weak player will pitch hearts.

[shyams]

I used the output from the link provided in my previous post. I also listed the conditions.

Okay the calculator works for two suits and the absence of an option to include the third unknown suit (♠) split will affect the calcs.

[Stephen Tu]

shyams, on 2023-May-18, 23:12, said:

I used the output from the link provided in my previous post. I also listed the conditions.

Okay the calculator works for two suits and the absence of an option to include the third unknown suit (♠) split will affect the calcs.

I think you misinterpreted the output of the calculator. The combos from one line to the next are not all of equal frequency and can't just be totaled, you have to look/use the percent column.
For example, 4-1 hearts, 7-3 clubs there are 600 combos of these particular suits, but you have to look at the percentage column, it makes up 4.76 percent of hands.
But 4-1 hearts, 6-4 clubs is 1050 combos making up 12.5% of hands.

The latter combos are each worth more, because the first is multiplied by just the 4 ways to deal a singleton spade out of the 4 remaining, while the 2nd is multiplied by 6 ways to deal 2 spades.
1050/600 * 6/4 = 2.63
12.5% / 4.76% = 2.63
So my advice would be if you want to use that calculator to total based on the percentage column, not the combos column.

[Cyberyeti]

nullve, on 2023-May-18, 07:21, said:

Spoiler

The fact that

* West didn't pitch hearts as if trying to get a heart ruff
* East didn't play the AKQ of diamonds in a different order to suggest a heart shift

strongly suggests that East has 1-2 hearts.

The fact that West

* risked ruffing the third diamond (potentially solving Declarer's problem in trumps with Jxxxx opposite AKTx)
* didn't preempt, which he might have done with 1417 or 1318 shape

strongly suggests that East has 0-1 spades.

So East appears to have at least four clubs, and I think we can rule out that East didn't overcall with ♦AKQ+♣K because of semi-balanced shape and (say) a lack of playing tricks.

I guess the reason he didn't overcall is that in his opinion he lacked the points to do it. (It's a very bad reason, but I can't think of a better one.)

So I'll play him for

♠x ♥x ♦AKQxxx ♣xxxxx,

in which case I need to take the club finesse, rather than

♠x ♥xx ♦AKQxxx ♣Kxxx.

I think I agree with your conclusion but don't like some of the analysis. If W holds say xx, J10xx, x, KJxxxx unless S opens Jxxxx, AKQx, xxx, x which some do but many don't, he has the ♠Q and there is no guess to resolve by ruffing with the doubleton.

[gszes]

I am going to play the club Q. I realize the ODDS FAVOR PLAYING FOR THE HEART SUIT TO BREAK 32. What I am unsure about is if the odds are what I should be looking at here. LHO would have NO KNOWN REASON (if they do not possess the club K) to assume a club is going to be of benefit to the defense since declarer has a known singleton in clubs UNLESS: LHO has both 4 hearts and the club K. The club switch is mandatory to break up a squeeze against lho. If we rise with the ace the squeeze is gone because the club Q is no longer a threat. It is a TON easier to find this defense when looking at the club K and 4 hearts.
For those that think it is automatic to ruff the 3rd diamond and return a club to give declarer a GUESS: How does lho know for sure declarer does not have a 4th diamond and it is necessary for lho to ruff the 4th round to keep declarer from pitching a potential heart loser?. IMVHO the defense at the table should ONLY be perpetrated when it can have a positive outcome vs a theoretical positive outcome i.e. LHO can see breaking up a potential squeeze but they cannot verify declarer has only 3 diamonds.