[mikeh]

Justin, I like your analysis, but I am not 100% convinced because of what follows:

Firstly, I do not believe that the probabilties are exactly balanced when it comes to the location of the ♦A: this is critical because the main power of the AK trump line flows from RHO holding the Qx trump and the ♦A (I know, it is not the only lie where the play works).

There is a tenuous but non-trivial inference that the ♦A is on your left. LHO led a non-honour ♥ (if I read the problem correctly). There was nothing in the auction to suggest a ♥ rather than a ♦ and so, if his reds were equal, he might well lead a ♦. The fact that he led a ♥ gives rise to a slight inference that he has a holding in ♦ that was unattractive: and the A (or the irrelevant AQ) is such a holding.

How to quantify that, and how that flows through your equations is too much for me to try to assess right now. I was trying to figure this impact when thinking about the choice of trump Ak or one high trump then hook, and it was coming very close to break even... too close for me to intuit which line was superior.

Secondly, (and I may have missed something here), you assume that when LHO holds Qxx, you will strip the round suits and exit a trump, and ALWAYS go right when LHO leads a low ♦. Indeed, you have (I think) postulated that you will play low and thus win when LHO holds the ♦Q. Surely LHO is not only slightly favoured to hold the ♦A (in which case your line loses for sure: you had an easy 12 tricks by hooking) but when you guess wrong, you are a full trick behind the trump finesse line?

I think the combination of these two factors makes the trump finesse line very slightly superior, but I am balancing this analysis with reading some particularly technical caselaw, so I may well have missed something

[inquiry]

Mike,

Another way to look at this is you can play either opponent for Qxx. We have to agree that the odds of that is the same. (If WEST has Qxx hook him, if EAST has Qxx run the elimination).

So hooking the spade wins if WEST has Qxx, playing AK wins roughly half the time when EAST has Qxx (not counting what every vacant space (3S versus 2S) and hint from opening lead.

So, playing AK wins when Qx is offside (13.65%) and gains a trick roughly 1/2 the time when Qxx is offside (20.35/2=10.17) or 23.82. Playing the hook wins when WEST is Qxx (20.35%).

So at this simplistic view, AK gains a trick works 23.82 (when it matters) versus the hook which gains 20.35 (when it matters). I am not sure what vacant space says, but I estimate that if RHO has 3S to West 2 Spades, the chance EAST holds the ACE is decreased by about 9 to 10% so the 23.82 drops by 2% to 21.82% (not correcting for rounding). The psychological restricted choice decision to the opening lead has not been factored in, but I already weight the ace being with the opening leader when the Qxx is offside. This is why I guess the odds were close, but AK is about 1% better than the hook.

Note this does not factor in the recovery of the lost trick when Qxx is onside. As you point out then you have to guess which diamond honor WEST has, and in this case with either Q of A, it will be a guess, but the correct quess is to play WEST for the queen I guess, so you can gain the trick you lost when you played AK....

All in all, Justins analysis looks right to me, and suggest my 1% is probably an underestimate. I think becausue of the recapture of extra trick on the throw in when the heart hook would have worked (although when you can guess right, you will do so only half the time).

[whereagles]

Well, a good player will reject the percentage play if the vibes at table tell him it won't work. Not that Meckstroth is the sort of person who'd give the show away

[Halo]

I liked AK here. Slightly surprised it proves a BAM winner on spade contracts at both tables - did we actually prove that?

We are not claiming we calculated this at the table are we?

[sathyab]

Jlall, on Dec 15 2006, 05:20 PM, said:

Obviously you cant calculate everything precisely, but you can see if you look deeply at it that you are going to frequently make 11 tricks by playing AK when you otherwise would have made 10, but you decrease chances of making 12. It also looks (to me) like you are gaining more  than you are losing by playing the AK of spades. That is how I thought about it at the table.

In the 1.5 or two minutes that you have available to play to trick 1, you were able to figure out that playing the AK of spades increases your chances of making 11 tricks but reduces the chances of making 12 tricks ? Really ?

It's far from clear even with all your analysis why or how much one line is superior to the other. Numbers like 47% for one line and 44% for the other don't pop up at the table for most of us and even if they did that could hardly be the basis for doing some unorthodox like rejecting a routine finesse in trumps.

It'd be nice if we had play records available so we could at least see how the good players, of whom there'd be so many in a BAM event, played it even if we wouldn't know why they did what they did.

[Stephen Tu]

Well, I don't think one can do the long form of computation like Justin did in a normal amount of time, but I think one can estimate that, roughly,
(doubleton Q off + 0.5 (tripleton Q off)) > (0.75 (tripleton Q on))
if one is going to make no major assumptions about the diamond honors because
of the lead. (This is inaccurate because of vacant spaces, but one doesn't have time to calculate to the last percent without Rain Man abilities)

Basically AK wins if you drop the Q or can gain by endplaying RHO. It loses to the hook with tripleton onside + no endplay recovering trick (LHO Q of d alone, which makes you break even). I haven't thought too much about the 4-1 cases.
(I think in Justin's calc he didn't break out the case where LHO has SQxx + DAQ, so his numbers are likely off)

Comparing vs. 3nt is difficult, who knows whether diamond or heart is the natural lead ...

[whereagles]

Why all this fuss? Clearly ♠AK is a good line, as is finessing twice.

[sathyab]

Jlall, on Dec 15 2006, 06:22 PM, said:

[
You don't need to come up with exact percentages to figure out whether one line is better than another. You don't even need to come up with any percentages. You can just come up with cases where one line wins against another vs one line losing against another and figure out which is more likely most of hte time. I don't understand how this can not be the basis for making a certain play, making the play most likely to win should be the basis of ALL plays. All I can do is rofl at calling this a routine finesse, just because a finesse is available does not make it routine. Saying you can't fail  to take that line because of "numbers" is really funny too.

Quote

It'd be nice if we had play records available so we could at least see how the good players, of whom there'd be so many in a BAM event, played it even if we wouldn't know why they did what they did.

Results:

Obviously I am not a good player but I will tell you what happened. I played AK of spades and later played LHO for the DQ in order to try and tie the board if they hooked at the other table. 10 tricks. At the other table they opened a strong club and got intervention from a bad hand on their right showing the reds so obviously they finessed the spade. Fredrik Nystrom played identically to me. Marty Fleisher took 2 finesses. My partner said he agreed with my line.

Even if you can figure out which line of play offers a better chance for 11 tricks and which one for 12 tricks, to reject the line that offers 12 tricks in favor the 11 trick lineyou must have a strong reason. So far I haven't seen any compelling argument that says the 11 trick line was more likely than the 12 trick line.

Sorry if you thought I was implying that you were not a good player, I certainly didn't intend to. No matter how good a player one is, the Fall Nationals is a veritable collection of who-is-who in the world of bridge. When my partner and I found ourselves sixteenth in the qualifying list for the Blue Ribbon Pairs finals, I was telling a director from the Bay Area that our names were the only ones that I couldn't recognize in that illustrious list It was in that vein that I used the phrase "good players". My apologies again if it came across differently.

[Stephen Tu]

Quote

Even if you can figure out which line of play offers a better chance for 11 tricks and which one for 12 tricks, to reject the line that offers 12 tricks in favor the 11 trick lineyou must have a strong reason. So far I haven't seen any compelling argument that says the 11 trick line was more likely than the 12 trick line.

It's not efficient at all to think in terms of total # of tricks taken. If comparing just two lines just count cases where one takes "more" tricks, don't worry about how many total you are taking.

AK line takes more tricks when the Q is doubleton offside. This is 12 vs. 11 or 11 vs. 10 depending where the DA is.

AK line also takes more tricks when the Q is trebleton offside + DA offside. This is 11 vs. 10.

finesse line takes more tricks when Q is trebleton onside, & LHO doesn't have the DQ only. Some of these are 12 vs. 11, some 12 vs. 10, some 11 vs. 10. But # of tricks the other line beats you by doesn't matter in BAM assuming same contract.

Just count total percentages of winning/losing cases, waste of time to calculate exactly when it's 12 vs. 11 or 11 vs. 10 or 12 vs. 10.

If you count just these cases, one gets an advantage of ~8% or so for the AK line. Now, perhaps there are some 4-1 split cases I am overlooking, & perhaps there are lead inferences about the DA, but don't know if enough to cancel this out.

[Halo]

The AK line does not always gain against Qx offside since the hearts are eliminated.

However, calculating correctly (my version of properly!) and taking account of changing odds there is an irreducible 1% or slightly more advantage to cashing AK - madeup of less than half the cases where East has doubleton or trebleton Q of spades, versus 75% or so of the cases where West has Qxx.

[Stephen Tu]

Quote

The AK line does not always gain against Qx offside since the hearts are eliminated.

It will gain on almost all of these; RHO will have club exit cards most of the time. If you play clubs to increase the endplay possibilities here you run into alternate risk of club ruffs. How do you get "less than half" of the offside doubleton Q possibility winning?

The main thing my calcs omitted was a few percent when spades 4-1 onside, & defense can tap dummy in diamonds or run diamonds after trumps drawn. Still prob 5% edge for SAK.

[Halo]

Expressed myself badly.

I started by thinking that the finesse was best if both sides played in spades and AK if 3NT was in the frame. I was wrong. Even if we could eliminate clubs and hearts before finessing, it would actually still be better (by a small amount) to just cash AK of spades.