[dburn]

Requiring three tricks from:

♣AQ98

♣5432

and with enough entries, side stoppers and so forth to play however you wish, you lead the deuce - six; eight; ten. When later you lead the three, West plays the seven. Should you:

[a] play the nine
[b] play the queen
[c] play the ace
[d] use some randomizing device to decide among possibilities - none is superior to both of the others.

[pooltuna]

It seems strange to me but a) looks correct as restricted choice acts in an abnormal manner. By that I mean that holding KJ, KT, or JT a sharp RHO could have won the first trick with either card in any of those holdings thereby increasing the probability of LHO hold KJ76, KT76, or JT76. If this is wrong I am sure someone will step right up and say "Pooltuna has been eating the algae bloom again and is hallucinating."

[AlexJonson]

I'd play the Ace whatever he won with on the first round.

[kenberg]

I believe this to be difficult. Here is why:


Suppose first that lho will play his two spots in arbitrary order and that he will play them whether or not he has a higher card. As always, treat the ten and the jack in rho's hand as equals, call them tacks. We analyze:

lho has followed with the two spots, we can infer that he was dealt the two spots and we cannot infer anything else. rho has played a tack. He would play a tack, one or the other, when he held one or both (or let us assume so). He can hold a stiff tack in two ways, a doubleton Jack-Ten in one way, and a King-Tack in two ways. If he holds King-Jack-Ten nothing can be done so forget that. Playing the Q only succeeds against Jack-Ten tight so that's out. Playing the Ace succeeds against two holdings (Yes we saw the Ten, but the idea is to develop a strategy for what we will do when the 8 is taken by a Tack and Lho plays a second spot on the next round). Playing low also succeeds against two holdings. On empty spaces, I guess the ace is slightly superior.


But: Suppose lho reads the position. On the second round, having started with J76, should he play the spot? If he plays the J, will not declarer reason "surely the other spot is on my right, so it must that my only hope is to take the finesse". Or suppose rho reads the position and, holding KT, takes the first trick with the King. Would not declarer now play lho for both Tacks and plan to lead twice to the AQ9? It's tough for rho to do this I think, but maybe not so tough for lho to play his Tack on the second round.

And this plays havoc with the analysis.

[cherdano]

Probably David Burn is too young to have been here when this came up the last time:
http://www.bridgebas...it-combination/

[kayin801]

pooltuna, on 2011-February-13, 15:50, said:

It seems strange to me but a) looks correct as restricted choice acts in an abnormal manner. By that I mean that holding KJ, KT, or JT a sharp RHO could have won the first trick with either card in any of those holdings thereby increasing the probability of LHO hold KJ76, KT76, or JT76. If this is wrong I am sure someone will step right up and say "Pooltuna has been eating the algae bloom again and is hallucinating."

Re-edit: I think RHO can randomize from KT but not from KJ, since they don't know who has the T when they hold KJ and when declarer holds the T they can afford to cash a top honor in dummy to clarify the situation. Declarer wouldn't play to the 8 with the J in his hand if RHO had KT, so they know what's going on at that point.

[aguahombre]

I am jealous of all you people who have maids.

[lamford]

I agree the right line is low to nine, then low to the eight. If the jack appears on your left you should play the queen. The same layout:

3.24.1 North AQ98 South 7654
3T L-9,L-8 L-A,L-9 L-Q
% 54.83% 52.57% 45.78%
2T L-9 L-A L-Q
% 92.39% 92.39% 92.39%
Max tricks L-9, L-8
Average tricks 2.472173913

are my figures. I expect the tabbing will be poor. All lines are the same for 2 tricks, of course, and the best line is also the best at MPs (all other things being equal).

[AlexJonson]

The tabbing is a bit poor.

Calculation at the table looks demanding.

[whereagles]

Excuse me, but isn't this a normal book play, i.e. low to the 8 then low to the queen?

If you wanna invent something funny I guess you can say "RHO won the T so odds are doesn't have the jack. Thus LHO should have Jxx or KJxx. Since the later is less likely, I'll just go up with the ace and fetch RHO's now singleton K."

[kenberg]

Look at the thread Cherdano supplies. I think the short version is that any analysis should at least consider whether lho, holding Jxx, will play the Jack on the second round. There are some that will, some that won't, and some you just can't tell. And it matters. Fred refers to the play of the Jack as a "mandatory falsecard", concealing the second spot and sharply reducing the chance of declarer dropping the king (since the J is also played from KJx, when the finesse is right). If so, then the play of the low spot on the second round denies an original holding of Jxx.

Now the falsecard will be not all that mandatory IF declarer can be trusted to always play the Q on the second round anyway. Let's assume lho can be trusted not to falsecard. Declarer will reason: If the T was stiff, I must now play the 8, but that is against the odds. So I will assume that the Ten is not stiff. I have seen the two spots so, under my assumption, my rho has the Ten and, if I have any hope, exactly one other honor. Applying Restricted Choice to the JT combo, he is more likely be far to hold the K the remaining of the JT. Therefore play the ace.

I think that is the argument. If not, read Fred's post on the other thread. At any rate, the false card of the J does appear to be mandatory and therefore the non-play fo the Jack, against someone aware of this, rules out a holding of J76.


Added: Of course such a conclusion now makes the play of the 8 significantly less against the odds than it would be if lho is blissfully unaware of the falsecarding argument. I did say above that I think this is difficult. Possibly we still need to consider that rho from KT might have played the ten.. In the games I play in, this would be a misclick, not a brilliancy.

[dburn]

I have looked at the earlier thread, in which low to the eight then low to the ace was (as far as I can see) not considered in mikeh's analysis. It might have been, because it loses only to stiff jack, stiff 10 and J10 doubleton with East whereas low to the eight then low to the nine loses to KJ, K10 and J10 doubleton with East. Since a specific singleton is less likely than a specific doubleton, the former line is superior to the latter if West will always, or often, "forget" to play his honour on the second round from an original holding of J76 or 1076.

Fred's analysis of AQ9 facing five low concluded correctly that West should always (or sufficiently often) play his honour from those holdings on the second round, and as far as I can see the same is true in the original problem. In both cases, of course, low to the nine then low to the queen is hopeless - though whenever my opponents do it, I always have J10 doubleton offside. How about yours?

[lamford]

dburn, on 2011-February-14, 17:52, said:

I have looked at the earlier thread, in which low to the eight then low to the ace was (as far as I can see) not considered in mikeh's analysis. It might have been, because it loses only to stiff jack, stiff 10 and J10 doubleton with East whereas low to the eight then low to the nine loses to KJ, K10 and J10 doubleton with East. Since a specific singleton is less likely than a specific doubleton, the former line is superior to the latter if West will always, or often, "forget" to play his honour on the second round from an original holding of J76 or 1076.

Fred's analysis of AQ9 facing five low concluded correctly that West should always (or sufficiently often) play his honour from those holdings on the second round, and as far as I can see the same is true in the original problem. In both cases, of course, low to the nine then low to the queen is hopeless - though whenever my opponents do it, I always have J10 doubleton offside. How about yours?

In fact West only has to find the false-card of the remaining honour as often as the difference between the specific singleton and the specific doubleton. So even Eddie the Eagle from our club (who largely plays cards at random) will play the honour often enough to make covering his card correct.

[dburn]

Just wondering - are there players against whom failure to falsecard would constitute a Grosvenor Gambit?

[cherdano]

dburn, on 2011-February-14, 17:52, said:

I have looked at the earlier thread, in which low to the eight then low to the ace was (as far as I can see) not considered in mikeh's analysis. It might have been, because it loses only to stiff jack, stiff 10 and J10 doubleton with East whereas low to the eight then low to the nine loses to KJ, K10 and J10 doubleton with East. Since a specific singleton is less likely than a specific doubleton, the former line is superior to the latter if West will always, or often, "forget" to play his honour on the second round from an original holding of J76 or 1076.

If LHO is a client, then RHO has to falsecard with KJ and KT some of the time. (I thought that had been covered in the old thread, too, but I am too lazy to look it up now.)

[dburn]

cherdano, on 2011-February-14, 22:03, said:

If LHO is a client, then RHO has to falsecard with KJ and KT some of the time. (I thought that had been covered in the old thread, too, but I am too lazy to look it up now.)

An interesting point that had not occurred to me has been made above by kayin801: RHO can (and maybe should, if he is a better player than his partner) falsecard with K10 but not with KJ (because he doesn't know where the ten is). Cases where seemingly equal cards are not in fact equal are of interest only to nerds, but...