Simple Percentage question

[inquiry]

[hv=pc=n&s=sakq32hkdak32c732&n=st98haqt2d54cak54&d=n&v=0&b=1&a=1cp1sp2sp3dp3hp4dp4hp4np5hp5np6cp6dp6hp7sppp]266|200|Imps, I am not going to try to explain the bidding. The question is, what is the percentage play after the heart NINE is lead to you king, East plays the ♥6?

 

Assume for the percentage question that spades are splitting, 3-2 but for choosing your line in the poll, feel free to go with the first or second round spade finesse if you like.

 

II want to know what you think about ruffing third round diamond versus combined ♥J drop some kind of squeeze if that doesn't happen (compound, simple, double, etc). [/hv]

[awm]

The diamond-ruffing line seems to be over 75%, working any time diamonds are 4-3 or if diamonds are 5-2 with the short diamonds not holding the spade jack.

 

Given the lead, it really looks like RHO has the ♥J (leading from a jack vs. slam not so desirable, the nine seems to deny an honor, etc). This reduces some of the squeeze options (i.e. no positional round-suit squeeze chance against west). It seems like in the end position you'll have ♥T and ♦5 and ♣5 in dummy, and ♦AK3 in hand. This works any time LHO started with four clubs (he must guard clubs, RHO guards hearts, no one can guard diams) or if RHO started with five diamonds (he's squeezed in the reds), or if the heart jack just falls third. However, each of these three events is substantially less than 50%, and I doubt the combination of them beats the diamond ruff.

[Fluffy]

cash ♠A and ruff third round of diamonds in dummy looks very straightforward, maybe this is one of those positions where there is always a squeeze whatever the distribution is, but I think it will be a blind one.

[ceeb]

The diamond-ruffing line seems to be over 75%, working any time diamonds are 4-3 or if diamonds are 5-2 with the short diamonds not holding the spade jack.

I agree (we're conditioning on the assumption that all followed low to two rounds of trumps). In fact maybe 79% if you figure LHO would lead a diamond from QJ10(...), which increases the chances that they are breaking.

 

Given the lead, it really looks like RHO has the ♥J (leading from a jack vs. slam not so desirable, the nine seems to deny an honor, etc).

Presumably the bidding was explained as showing ♥Q and ♣K in the dummy, and perhaps defender can deduce from the 7♠ bid that declarer has the fitting ♥K. But still, yes a heart lead from ♥J98 seems a little risky (plus some players just habitually play "honest" cards even though on lead against a slam is a good time to stop being predictable). But then so does ♥98x seem risky. What if declarer has ♥K10? Maybe there is an inference that LHO has heart length for this slightly surprising lead (why not a trump? Surely the bidding tells that either ♠Jxx or ♠xx is safe to lead from.)

 

This reduces some of the squeeze options (i.e. no positional round-suit squeeze chance against west). It seems like in the end position you'll have ♥T and ♦5 and ♣5 in dummy, and ♦AK3 in hand. This works any time LHO started with four clubs (he must guard clubs, RHO guards hearts, no one can guard diams) or if RHO started with five diamonds (he's squeezed in the reds), or if the heart jack just falls third. However, each of these three events is substantially less than 50%, and I doubt the combination of them beats the diamond ruff.

Accepting your assumptions I agree that the combination chance (drop ♥J or squeeze) amounts to well less -- 67% or so depending on detailed assumptions.

 

On the other hand, if you allow LHO to have the ♥J, the squeezes get enough better that the case is much closer. I get 78% ot 74% favoring the ruff. As a "percentage" question perhaps this or the previous is the answer.

 

However, depending on ones assessment of RHOs thought processes on lead, the probability of the ♥J dropping could be very high and that might change things.

[inquiry]

[hv=pc=n&s=sakq32hkdak32c732&w=sj64h987543d97cq9&n=st98haqt2d54cak54&e=s75hj6dqjt86cjt86]399|300|This is the hand. It was kind of funny, everyone in Notrump took 13 tricks (the heart JACK, as you see falls in two rounds), everyone in spades took 12 tricks (west gets to ruff third diamond with his ♠JACK),

 

One might try to justify some alterative lines other than going for an immediate diamond ruff. My thoughts upon seeing the results was that:

 

South has to start with one spade, incase there was a singleton jack. When both follow, lead a club to ACE and cash a heart. The likelyhood of a 7-1 heart split or 6-0 club split being low enough to more or less ignore. Good things would happen on the second heart, and you could claim. If the ♥Jack does not fall, then the question becomes should you risk a third round of hearts, (I think the answer is no) or go ahead and play a second round of trumps and then ruff a diamond, then play to ruff a heart to get back to your hand to pull the last trump. (risk of a third round heart ruff behind you -- which is a big negative to this line, which might outweigh the slight advantage of cashing a heart first).

 

Note: Even a minor suit squeeze works on this hand, as well as drop the ♥ jack. So I was wonder what the trade-off was for trying a second heart before going for the diamond ruff. Transportation is also a little iffy if you are going to try cash some hearts first, so you might not even want to play one round of spades before cashing the second heart.

[/hv]

[ceeb]

Testing hearts with a trump outstanding does seem like a results-influenced line. It's not 100% wrong but justifying it does seem post hoc.

 

Assuming one draws no particular distributional inference from the lead:

 

Testing the ♥ gains compared to just ruffing a ♦ when an opponent -- presumably RHO -- has ♥Jx and someone has 3 trumps and short ♦. I make that about half a percent.

 

A singleton heart on the other hand is 1+% on either side the majority of that percent or two the ♦ ruff line would work. So even if you figure you can often recover when RHO ruffs the second heart, you are down when LHO led a singleton so the total chance of loss must be over 1%.

 

If on the other hand you figure LHO wouldn't lead a singleton then you begin to seriously analyze what LHO would lead from, and if you conclude as I suggested before that the answer is length then maybe the squeeze is best anyway.

[Free]

Testing ♥s is safer than ruffing a ♦, since you only have 5 ♥s while you have 6 ♦s.

[Fluffy]

yes but it is a lot less rewarding :).

 

I though yesterday that it was likelly that LHO was leading from long hearts without a jack, in fact doubleton is very unlikelly IMO, it might be singleton though, but anyway Ben's alternative line seems very strong contender. But if it just gains 1-2% it will be better to just keep your energies for next boards :)

[Free]

After testing the ♥s you can still try to ruff your ♦ and combine the chances. It's less risky but also less rewarding indeed, so it's more a question if it's worth the trouble.

[nige1]

[hv=pc=n&s=sakq32hkdak32c732&w=sj64h987543d97cq9&n=st98haqt2d54cak54&e=s75hj6dqjt86cjt86]399|300|This is the hand. It was kind of funny, everyone in Notrump took 13 tricks (the heart JACK, as you see falls in two rounds), everyone in spades took 12 tricks (west gets to ruff third diamond with his ♠JACK),

One might try to justify some alterative lines other than going for an immediate diamond ruff. My thoughts upon seeing the results was that:

South has to start with one spade, incase there was a singleton jack. When both follow, lead a club to ACE and cash a heart. The likelyhood of a 7-1 heart split or 6-0 club split being low enough to more or less ignore. Good things would happen on the second heart, and you could claim. If the ♥Jack does not fall, then the question becomes should you risk a third round of hearts, (I think the answer is no) or go ahead and play a second round of trumps and then ruff a diamond, then play to ruff a heart to get back to your hand to pull the last trump. (risk of a third round heart ruff behind you -- which is a big negative to this line, which might outweigh the slight advantage of cashing a heart first).

Note: Even a minor suit squeeze works on this hand, as well as drop the ♥ jack. So I was wonder what the trade-off was for trying a second heart before going for the diamond ruff. Transportation is also a little iffy if you are going to try cash some hearts first, so you might not even want to play oneround of spades before cashing the second heart.

[/hv]

Interesting % question inquiry! But "Simple"? :). Although, the initial poll didn't provide that option, a simple soul like me would just pull one round of trumps and ruff a ♦. As inquiry points out, pulling two rounds of trumps is more fraught, especially if you want to test ♥ before committing to the ♦ ruff, because then the only way back to hand is ruffing a 3rd ♥. Testing hearts risks an adverse round-suit ruff, so I don't think it's worth it. The compound-squeeze depends on LHO holding ♥Jxxx and a lot of Rainer quality card reading. The more straight-forward double squeeze seems to rely on one opponent having sole control of ♣.

[inquiry]

Testing hearts with a trump outstanding does seem like a results-influenced line. It's not 100% wrong but justifying it does seem post hoc.

 

Strange you would suggest that the alterative line I brought up was "results-influenced". In fact, I don't know which line is the highest percentage. If I knew, I would not post the hand. I was hoping someone could work out that playing for the immediate diamond ruff (after two trumps, of course) is x% better and here is why, or trying to cash one more heart then play to ruff a diamond, is better, and here is why. Or try to cash three hearts, or whatever.

 

The math gets complicated because of the re-entry stuff. Even after discussing the hand above, it is not clear what is best. Fluffy is thinking it is a few % better to try to cash one heart, but he provides no calculations. I tried to work out the math, before posting and gave up. I might re-try. I often re-analyze hands, and usually come up with the "correct play" (note, not necessarily the winning play on a given hand) to my satisfaction. This one was an exception, as I got lost in trying analyze the splits of the sides (hearts and clubs) if someone had 3 spades to the JACK (3/5 of 3-2 splits) and a doubleton diamond.

 

I'm still curious of how to approach the odds of the two lines.

[nige1]

Rubbish deleted :( bed-time :)

[ceeb]

Strange you would suggest that the alterative line I brought up was "results-influenced". In fact, I don't know which line is the highest percentage.

I stand behind my calculation and comments (i.e. stated assumptions). To recap, the most obvious and straightforward computation says you should not cash ♥s. Of course the vast majority of the time it neither helps nor hurts, but the obvious "hurt" greatly exceeds the obvious "help".

 

However, I could stipulate and plausibly argue for assumptions under which cashing the ♥ tends to gain rather than lose compared to ruffing a ♦, and given that the full layout shows it is the winning play, it is tempting talk oneself into such assumptions. That's what I mean by results-influenced.

If I knew, I would not post the hand. I was hoping someone could work out that playing for the immediate diamond ruff (after two trumps, of course) is x% better and here is why, or trying to cash one more heart then play to ruff a diamond, is better, and here is why. Or try to cash three hearts, or whatever.

I calculated and calculated, but tried to explain that all the calculations rest on imponderables.

 

To calculate a hand like this manually strikes me as horrendously tedious. For a start the probabilities of various diamond breaks vary a lot according to what you assume about the heart break.

 

The math gets complicated because of the re-entry stuff.[/Quote]That's a bit of a complication (but of course with a computer not necessarily difficult -- I just need the patience to enumerate the situations I want to bother about) and I confess I didn't take it into account but I don't think that matters as it would work against cashing the ♥s, yes?

 

Fluffy is thinking it is a few % better to try to cash one heart, but he provides no calculations.[/Quote]I read Fluffy's comment not as an assertion about probabilities but merely as expressing disinterest in a percent or two even if.

[gnasher]

Disregarding inferences from the lead, it's easy enough to compare these three lines:

(1) Ruff a diamond

(2) Cash a second heart, then ruff a dimaond

(3) Cash two more hearts, then ruff a diamond

 

 

(2) gains over (1) when:

- ♥J is doubleton (17.1 * 1/4) and diamonds are 5-2 (30.5), which is 1.3%

 

(1) gains over (2) when:

- Hearts are 7-1 (2.86) and diamonds are 4-3 (62.2), which is 1.8%

- Some further percentage of the time, caused by the communication problems in (2)

 

So (1) is better than (2)

 

 

(3) gains over (1) when:

- ♥J is doubleton (17.1 * 1/4) and diamonds are 5-2 (30.5), which is 1.3%

- ♥J is trebleton (47.1 * 3/8) and diamonds are 5-2 (30.5), which is 5.4%

 

(1) gains over (3) when:

- Hearts are 7-1 (2.86) and diamonds are 4-3 (62.2), which is 1.8%

- Hearts are 6-2 (17.1) and diamonds are 4-3 (62.2), which is 10.6%

- Some further percentage of the time, caused by the communication problems in (3)

 

So (1) is better than (3)

[PhantomSac]

You guys are good at math. I know gnasher did not state what line he thinks is actually right (since he said disregarding lead inferences)...but it's pretty freaking obvious that cashing 2 hearts is right on the H9 lead. Do we really think they're leading stiff 9 or 9x against a grand?

 

The biggest concern is that they have led the 9 from J98xxx(x) imo, but still when you see the H9 surely your first thought is 987xxx or 987xx or 987x which it would be against most people (with the first 2 being more likely since leading from a long suit with no honor is quite attractive). I would say MOST opponents would lead the H9 from 9 to nothing and length a large percentage of the time they chose to lead the suit, and they would often choose to lead the suit. MOST opponents would probably lead low most of the time from J98xxx, and would lead the suit less often. Not to mention that 987xx(x) is more commonly dealt to an opponent than J98xxx imo because I am totally excluding a lead from J98xx which seems crazy.

 

Obviously the auction might make a difference also with how often they'll lead a heart from various holdings, if south showed a stiff a heart lead is always attractive, if north showed length then a heart lead becomes less attractive from the jack (unless you have 6 probably).

 

Another thing is that with 6-2 hearts spades being 4-1 becomes more common, since we're working on the assumption that spades are 3-2 that makes it less likely. Again all roads are pointing to 987xx to me VERY often assuming spades are actually 3-2. It is possible that they lead a heart from the jack far more often with a stiff spade, or Jxxx of spades, but both of these are irrelevant to us since we're going to go down then anyways.

 

People always say stuff like "well vs a grand they will always falsecard their lead" or do something tricky otherwise, but im strong opinion you should take them at face value ESPECIALLY when it comes to their opening lead, or first signal to partner's lead. Trick 1 is where we get our most accurate (least falsecarded) info and it is silly to me to take no inference, or to say it's resulting to make stipulations which make cashing the AQ of hearts correct which are obvious to me (LHO is not leading from shortness, and is unlikely to have the HJ).

 

Furthermore, if LHO has led from J98xxx of hearts, and spades are 3-2, I am not automatically down after the HQ gets ruffed, , which seems to have been ignored by some of the math done so far. For instance, If LHO is 2632 a minor suit squeeze will work (overruff, pull the trump, ruff a diamond, ruff a heart to my hand, play the spades).

[ceeb]

If your experienced judgment supports my suggestion that the lead means heart length then I'm reassured. But all that seems freaking obvious from that is that we shouldn't ruff any diamonds. That being the case there's no point in risking any accident in the heart suit. Why not just pull trumps -- if the ♥J is short it will still drop.

 

And as Nigel said there is a guaranteed compound squeeze. I think it's an exceptionally easy one to read, as it seems we can run all five trumps discarding a diamond from dummy. If LHO retains a ♥ and a minor suit guard in the 7-card ending he will have only a single card remaining in the other minor. Cross in ♣, cash ♥A, then decide: If LHO guards ♦, cash ♣ to squeeze LHO then ♥ to squeeze RHO. If LHO guards ♣, cash the ♥ discarding ♣ and then the ♦s.

[PhantomSac]

If your experienced judgment supports my suggestion that the lead means heart length then I'm reassured. But all that seems freaking obvious from that is that we shouldn't ruff any diamonds

 

LOL - nice try!

 

As I said multiple times if you bothered to read what I wrote... if the HJ doesn't drop then I think RHO has it -- 987x seems the most likely. EG:

 

but still when you see the H9 surely your first thought is 987xxx or 987xx or 987x

because I am totally excluding a lead from J98xx which seems crazy.

 

I think the HJ will drop very often but if it is a question of whether LHO has J98xx or 987x I go with the latter. So I think RHO will guard hearts in the event that the HJ does not drop, in which case ruffing a diamond is correct.

 

But hey at least now we're discussing a bridge hand and not a math problem!

 

IMO people are almost always trying to make a passive lead vs a grand that doesn't blow a trick, unless there is some special purpose (knocking out a dummy entry, or giving partner a ruff being the most common 2). IMO people also are not actively falsecarding their lead at trick 1 very often. Yes I could see this being the case if LHO had J98xxx (might give partner a ruff, and the falsecard is less likely to matter), but J98xx seems suicidal. Again we need an auction and what level our opponents are at to fully make inferences like this, but with none of that given I will work on those assumptions.

 

But that is why bridge is so interesting, you or some other good player might work on a different set of asusmptions, or weight them differently. I do not think it is "results-induced" to just play to take their lead at face value though, and if you do then it is overwhelmingly better to try and cash 3 hearts. I doubt anyone at any level is leading from 9x or stiff 9 against 7S though, and it would be hard to convince me otherwise!

[ceeb]

True, I did not take your comment about 987x as you apparently intended. Sorry about that -- possibly neither of us read the other carefully. You are literally correct that no one explicitly computed the chance of recovering after RHO ruffs a ♥, but I did mention it. I also argued as you did against a short suit lead, but I took the inference further. Can you comment why you don't buy the theory that LHO would prefer an apparently safe trump lead rather than risk a heart from 987x into a possible ♥K10 say?

[PhantomSac]

Maybe he has Jx of trumps or Jxx and doesn't believe us ;) I am always curious how people led in the days before keycard, did they ever lead a trump?

 

Anyways, you COULD argue that a trump is safer than a heart from any holding if he believes us, except with Jxxx or a stiff, in which case we should hook the spade if we're going to the extreme.

 

IMO even if a heart lead seems bad from 987x it is worse or at least perceived as worse by most people from J98xx and those would be the holdings we're comparing if 3 rounds of hearts lived and the jack didn't drop. At that point it's not really a question of "would they lead a heart from 987x instead of a trump" it's "would they lead a heart from 987x instead of J98xx." Even if someone were equally likely to lead from those holdings, I think they would always lead the 9 from the first one and often would lead a different one from the second holding, which gives it a restricted-choice like element also.

 

I suppose if we thought all of the following are true:

 

1) West would prefer a heart from 5 or 6 small over a "safe" trump

2) West would not often lead the 9 of hearts from the jack, if he did it would only be from J98xxx(x)

3) West would prefer to lead a "safe trump" from 4 small or worse, or J98xx or worse

 

Then we could argue for cashing 3 hearts, and if the jack does NOT drop, finessing the spade (based on assumption number 3). This is way too deep to me though, largely because I think many people would prefer 987x to Jx of trumps, and possibly to Jxx. It depends on the player though and how much they trusted our auction to have the trump queen (did we have a keycard auction), if we showed the AKQ of trumps then not leading from Jx might be irrational/novice like (or it might not if they were hoping to overruff something, or hoping that we did something strange in trumps because of the failure to lead a trump...). If someone is of the mindset that any trump lead is safe when trumps are 3-2, they might always lead a trump from 2 or 3, so I don't see why assumptions 1 and 3 would both be true to more than a very small subset of people.

 

Sorry if my post seemed inflammatory btw, I was just trying to generate some discussion about what assumptions we should make, since as we can see depending on our assumptions it might be right to hook a spade, or ruff a diamond, or cash 3 hearts, or play for a compound squeeze etc, that's what makes it an interesting hand to me and that is what bridge is all about. As far as I can tell Jeff Meckstroth is not very good at bridge-math but he is arguably the best card player because he makes the right inferences and weights them correctly so often.

 

My view is that the H9 is so often 5 small or 6 small that we should start by testing that out since it will be true an enormous amount of time. After that fails I fall back on ruffing a diamond because I don't feel confident enough about any other inference (like the opp would always have chosen a spade from Jx or Jxx rather than a heart from 987x) to hook a spade. As such I can cash a spade first to test for stiff jack of spades before doing the hearts (although another interesting point about this suit in this situation in general, if there were no entry problems and you chose to hook a spade, it might well be correct to cash one first anyways in case of stiff jack on your left. This is not a good play in theory since they can cover the second one if they have J7xx preventing you from taking a ruff in dummy, but they probably don't know this and it's very natural to duck...). I also feel like 987x is more likely than J98xx from the lead, even if both would be poor choices in my opinion generally speaking, since one of them probably exists. All of this leads me to cash 1 spade, cash 3 hearts, and then try to ruff a diamond.

 

At that point we have the question: should we cash a second spade before ruffing a diamond? This gains when LHO is 2425 with Jx of spades, as well as 3451 with no spade jack. But this means LHO had a desirable club holding to lead from in the first scenario, unless RHO had stiff jack (in which case we would see the jack drop when we had crossed to dummy). In the second case it would mean LHO didn't lead a trump from 3 small and chose a heart instead which also seems quite unlikely. The main gain seems to be when LHO does have J98xx and something like 2524 with Jx of spades. Is this holding worth the risk that LHO led from 98x and diamonds were 4-3? I don't know, I might try to read the position when I got there (for example if RHO played the CJ is relevant, or if LHO had 987 third of hearts it would be more attractive than 9xx, so which 2 hearts LHO followed with would be important...of course LHO could manipulate me in this way but most people are not thinking about stuff like that etc etc).

[ceeb]

I like that message a lot, especially the part articulating why "safe" trump leads are really not.