What card do you play?

[Free]

[hv=d=n&v=e&n=sk8654hdaj43cak43&s=s2hqt3dkt8cqjt652]133|200|Scoring: IMP[/hv]

Opponents silent, you end up in 3NT by South. You get a lead of ♥5 (4th) to the K, and RHO returns a ♥. What do you play? Does it matter what ♥ RHO plays? Is it a gamble or do you have a good reasoning to play the way you do?

 

Auction was (playing 2/1GF):

1♠ - 1NT (forcing)

2♣ - 3♣

3♦ - 3NT

[Apollo81]

I would play the ♥10 if RHO was me because I usually play the ♥A from AK if I can recognize this position. Most people are unimaginitive and play an auto-K from AK.

 

IMO the best play is the ♥Q because even if you play the ♥10 and are right, you still need the ♠A onside to make if LHO switches.

[skjaeran]

You don't give the auction, so I can't tell if there's just one unbid suit.

 

It looks like the lead is from a five- or sixbagger (although what ♥ east returns at trick two isn't clear). From the look of things, we'd have received a ♥ from any holding. Thus there's not much to decuce from the lead itself. West would have lead the ♥5 both from Axx5x and Jxx5x.

 

Seen the ♥ suit in isolation, the ten is the correct card. But even if that's right, west might switch to a ♠ after winning the ace. Then I'd need the ♠A onside as well.

 

So it's best to go up with the queen all in all.

[bid_em_up]

Why are we in 3N instead of 6C, or at least 5C?

 

Oh well, we can discuss that later.....

 

I'll play the 10♥. I expect to go down a bunch.

[kenrexford]

If you assume the necessary assumption that RHO has two honors, he either has AK, AJ, or KJ a priori. Two thirds of the time it is with the Jack. So, it seems like a simple restricted choice problem -- finesse the 10. I don't see anything compelling any thought but this.

[Free]

If you assume the necessary assumption that RHO has two honors, he either has AK, AJ, or KJ a priori. Two thirds of the time it is with the Jack. So, it seems like a simple restricted choice problem -- finesse the 10. I don't see anything compelling any thought but this.

I think there's a flaw in this analyse: RHO played the K, so AJ is not a possibility anymore which makes this a 50-50 situation. RHO having AKJ is irrelevant, same as Kx.

[kenrexford]

If you assume the necessary assumption that RHO has two honors, he either has AK, AJ, or KJ a priori.  Two thirds of the time it is with the Jack.  So, it seems like a simple restricted choice problem -- finesse the 10.  I don't see anything compelling any thought but this.

I think there's a flaw in this analyse: RHO played the K, so AJ is not a possibility anymore which makes this a 50-50 situation. RHO having AKJ is irrelevant, same as Kx.

OK, so we are getting back to the a priori versus a posteriori issue with restricted choice. Ugh.

 

Imagine that we get to play this hand three trimes in a row. All three trimes, the game will make if I guess heart right. Thus, all three times, RHO has two honors.

 

On Board #1, he has AKxxx.

On Board #2, he has AJxxx.

On board #3, he has KJxxx.

 

If we stick in the Queen, we make game on Board #1 but go down on boards #2 and #3. If we stick in the 10, we make on boards #2 and #3 but go down on board #1. Hence, we make game twice as often if we stick in the 10.

 

The play of the King by RHO only tells us that the board number is #2 or #3. That might help us in placing the score on the recap sheet, but not so much with the play of the hand.

 

If we wait on each of the three hands to see what honor RHO plays (Ace or KIng) before deciding, this accomplishes nothing. This is because of the backwards way of looking at the problem, which works for some people but seems unnecessarily confusing to me. That is, if he played the King, we know the deal is #1 or #3. So, we decide that it is probably #3 because, on #1, RHO might have decided to play the Ace instead but is forced, on #3, to play the King.

 

That analysis works somewhat in explaining weird versions of restricted choice, such as safety leads suggesting that an alternative was not safe. But, the "play it three times" analysis works better for me.

[Finch]

What was South's 3NT bid? What was North's pass of South's 3NT bid? Do you not get a game bonus for bidding and making 5m any more? (never mind a slam bonus for 6m).

 

Anyway, as Apollo points out, it's not just a matter of the heart suit, as they might well be able to cash 3 rounds of spades against you.

[jdonn]

If you assume the necessary assumption that RHO has two honors, he either has AK, AJ, or KJ a priori.  Two thirds of the time it is with the Jack.  So, it seems like a simple restricted choice problem -- finesse the 10.  I don't see anything compelling any thought but this.

I think there's a flaw in this analyse: RHO played the K, so AJ is not a possibility anymore which makes this a 50-50 situation. RHO having AKJ is irrelevant, same as Kx.

No, restricted choice is a difficult concept the first time someone hears it since your statement seems so obvious, yet is untrue. Think of it this way.

 

of the times RHO has two honors, he has

AK = 1/3

AJ = 1/3

KJ = 1/3

 

From AJ he will play the A at trick 1. From KJ he will play the K. From AK he will play the A half the time and the K half the time. So now the table looks like this

AK, plays A = 1/6

AK, plays K = 1/6

AJ, plays A = 1/3

KJ, plays K = 1/3

 

So of the 50% that he plays the king, that encompasses the 1/6 he had AK and 1/3 he had KJ. Meaning it's twice as likely he had KJ. That's why, taking the suit in a vacuum, the 10 is correct.

 

Of course others have pointed out it may be incorrect on the actual hand since if the Q wins you have made, but if the T works may still go down. That's why it is a good problem.

[kenrexford]

So, the idea is to fly the Queen because, in that 1/3 of the time that the Queen is right, you grab nine tricks and go. Makes sense, except...

 

What happens on the two times that the 10 forces a high honor? Sometimes the opponents will send back another heart. Sometimes they may try a diamond, When they do neither, they may switch to spades, and roughly 50% of the time I am safe anyway. If RHO has AQ tight, I cannot guess wrong.

 

But, if the Queen works, will RHO have the heart A-K and the spade Ace?

 

The a priori's are:

 

AJxxx without the spade Ace

AJxxx with the spade Ace (and not AQ tight)

KJxxx without the spade Ace

AJxxx with the spade Ace (and not AQ tight)

AKxxx without the spade Ace

AKxxx with the spade Ace.

 

If I play the 10, I am down on the last two quickly. I make on roughly two of the remaining four. If I play the Queen, I am down immediately on all of the first four, but I make on the last two.

 

However, the "roughly" means that A-Q tight protects me on the 10 play. I am also protected on the chance of the defense not finding the spade switch. I am also protected by weak restricted choice principles (LHO did not lead a spade, meaning that he is slightly more likely to have the Ace and not to have QJ10x).

 

I am also protected in playing the 10 by the reality that, on one of the two situations where the Q works, RHO holds AK of hearts, the spade Ace, and probably a spade honor (Ace or Jack). He also has roughly one-half of a diamond Queen. With all of that, sometimes he will overcall 2♥, immediately or later. Sometimes he will have AKxx in hearts, four diamonds, and three clubs, or just both reds, and will be able to make a takeout of 1♠ or 2♣.

 

Sure, this is not solely a heart play, but the spade issue does not seem to change the odds tilt, just narrow the margin.

[bid_em_up]

So of the 50% that he plays the king, that encompasses the 1/6 he had AK and 1/3 he had KJ. Meaning it's twice as likely he had KJ. That's why, taking the suit in a vacuum, the 10 is correct.

 

So, it seems like a simple restricted choice problem -- finesse the 10.  I don't see anything compelling any thought but this.

 

So you both agree the 10 is the "correct" technical play. It really doesn't matter how you reached this conclusion as long as you got there.

 

But as someone stated elsewhere, its fun to watch. LOL!!

 

Now there are other ways of approaching this:

 

1) I play the Queen, it wins and I roll home regardless of the location of the spade Ace.

2) I play the Queen, it loses to the Ace, and I go down immediately.

3) I make the correct technical play of the 10, and it loses to AJxxx behind me. Oh well, I was never making.

4) I make the correct technical play of the 10 and it loses to the A. I still make if LHO blindly returns a heart, or if the spade A is onside or if RHO has A doubleton♠.

 

Given that LHO is still a heavy favorite to hold the heart Ace, I'll still take my chances on the heart 10 and either they don't switch to spades, they do but the Ace is onside, or RHO has Ax.

 

I still expect to go down, but I think this has to be the correct long-term play.

[Halo]

The plays appear technically equivalent because of the spade suit, but that implies the ten is better since opponents may not play perfectly.

 

Without the spade suit it has been understood for a long time that the ten is best for restricted choice reasons.

[jdonn]

So, the idea is to fly the Queen because, in that 1/3 of the time that the Queen is right, you grab nine tricks and go.  Makes sense, except...

 

What happens on the two times that the 10 forces a high honor?  Sometimes the opponents will send back another heart.  Sometimes they may try a diamond,  When they do neither, they may switch to spades, and roughly 50% of the time I am safe anyway.  If RHO has AQ tight, I cannot guess wrong.

 

But, if the Queen works, will RHO have the heart A-K and the spade Ace?

 

The a priori's are:

 

AJxxx without the spade Ace

AJxxx with the spade Ace (and not AQ tight)

KJxxx without the spade Ace

AJxxx with the spade Ace (and not AQ tight)

AKxxx without the spade Ace

AKxxx with the spade Ace.

 

If I play the 10, I am down on the last two quickly.  I make on roughly two of the remaining four.  If I play the Queen, I am down immediately on all of the first four, but I make on the last two.

 

However, the "roughly" means that A-Q tight protects me on the 10 play.  I am also protected on the chance of the defense not finding the spade switch.  I am also protected by weak restricted choice principles (LHO did not lead a spade, meaning that he is slightly more likely to have the Ace and not to have QJ10x). 

 

I am also protected in playing the 10 by the reality that, on one of the two situations where the Q works, RHO holds AK of hearts, the spade Ace, and probably a spade honor (Ace or Jack).  He also has roughly one-half of a diamond Queen.  With all of that, sometimes he will overcall 2♥, immediately or later.  Sometimes he will have AKxx in hearts, four diamonds, and three clubs, or just both reds, and will be able to make a takeout of 1♠ or 2♣.

 

Sure, this is not solely a heart play, but the spade issue does not seem to change the odds tilt, just narrow the margin.

I can't believe I'm saying it...

 

I agree 100%! (maybe just 90% with the reasoning but 100% with the conclusion.) Maybe you should just post about defense and not bidding from now on :P

[Mosene]

Can we re-examine the restricted choice question for a moment - particularly the part about a priori and posteriori. We now know that RHO started with either AK or KJ (at least the hands we care about). In the first case, 1/2 the time RHO plays the A and 1/2 the time RHO plays the King (or at the very least - does not play the King every time). In the second case RHO always plays the King. This is what tells me the 10 is right. Why should we throw out the information we have and only look at a priori odds?

 

BTW, I am only looking to understand the issue, not asserting that what I say is correct.

[Guest Jlall]

jdonn and ken are saying the exact same thing, you can look at it either way, but it's restricted choice.

 

As far as the opps being able to cash 3 spades and LHO finding it, good luck. If the ace is onside I'm fine, and LHO will not figure out to shift to a sapde, sorry. I will play the ten and congratulate LHO if he shifts to spades.

[Guest Jlall]

Can we re-examine the restricted choice question for a moment - particularly the part about a priori and posteriori.  We now know that RHO started with either AK or KJ (at least the hands we care about).  In the first case, 1/2 the time RHO plays the A and 1/2 the time RHO plays the King (or at the very least - does not play the King every time).  In the second case RHO always plays the King.  This is what tells me the 10 is right.  Why should we throw out the information we have and only look at a priori odds?

 

BTW, I am only looking to understand the issue, not asserting that what I say is correct.

Yes you can think of it like that, or you can think of it a priori. They are the exact same thing. Most people have an easier time with whole numbers so a 2:1 ratio is easier than a 1:0.5 ratio, but of course its the same ratio.

[Finch]

Here's one reason to play the 10: not every defender (particular one selected at random) will think to play a low heart back having started with the AK. Most of my local club would cash the other high honour.

 

Here's another reason to play the 10: I believe that the majority of defenders looking at AK planning to win and return a low one tend to win with the Ace; as usually the 'normal' card from AK is the King and they think they are being deceptive.

 

But while we're at it, here's a reason to play the Q quickly: LHO might duck it! 3NT was an insane, but LHO might believe you actually held a heart stop. From his point of view the heart layout could be:

 

[hv=n=s&w=sa9652&e=sk1074&s=sqj83]399|300|[/hv]

 

and his partner has the ace of spades, or perhaps the queen of clubs, or the DK as an entry; if he plays the ace and clears the suit declarer can duck the third round and shut out the suit.

[jdonn]

Here's one reason to play the 10: not every defender (particular one selected at random) will think to play a low heart back having started with the AK. Most of my local club would cash the other high honour.

 

Here's another reason to play the 10: I believe that the majority of defenders looking at AK planning to win and return a low one tend to win with the Ace; as usually the 'normal' card from AK is the King and they think they are being deceptive.

 

But while we're at it, here's a reason to play the Q quickly: LHO might duck it! 3NT was an insane, but LHO might believe you actually held a heart stop. From his point of view the heart layout could be:

 

[space] A9652 K1074 QJ83

 

and his partner has the ace of spades, or perhaps the queen of clubs, or the DK as an entry; if he plays the ace and clears the suit declarer can duck the third round and shut out the suit.

That argument about the queen doesn't matter since it applies to both cards. After all if you play the ten it can be

 

[hv=n=s&w=sa9652&e=skj74&s=sqt83]399|300|[/hv]

[kenrexford]

As a matter of clarification of restricted choice, I thought about this for a while and now realize that there is one situation plausible where the a posteriori analysis is critical.

 

Suppose, for instance, that a person could have QJx or Qxx or xxx, but not Jxx. This would be strange, but plausible. [A plausible example might be an opening bid that is known to be particularly light, where we expect all values to be working. Qxx or QJx are "working" values, but Jxx is not so enticing. The xxx holding is "working" in the sense of no wasted values in this suit and, accordingly, maybe working values elsewhere. This would seem to be a relatively weak inference, but an inference nonetheless.]

 

If this weird situation occurred, then a deceptive defender, if somehow forced to play an honor when he had it, should play the Queen all of the time, if he also realizes that he must have Qxx, QJx, or xxx, but not Jxx. However, if that person does not realize constraints that happen to exist, or if he is not being deceptive, or if he is lazy, then the play of the Queen suggests Qxx and not QJx. A priori the odds are 50-50, but the flexibility of the QJx situation affects the a posteriori circumstance of the play of the Queen.

 

You would have to see a particularly rare situation for that to occur, it seems, but the analysis from the a posteriori perspective may be useful if it comes up.

[cherdano]

That argument about the queen doesn't matter since it applies to both cards. After all if you play the ten it can be

 

[space] A9652 KJ74 QT83

I suppose you meant[hv=n=s&w=saj752&e=sk964&s=sqt83]399|300|[/hv] (In your layout the T was the winning play anyway.)

[kenrexford]

I thought of another example of the a posteriori being necessary.

 

Suppose you get what appears to be a passive club lead. Suppose a passive diamond lead is also possible. Suppose, however, that your club holding is solid (AKQJ combined, notrump contract).

 

A priori, you opponent could have held nothing in clubs or diamonds, or nothing in clubs but something in diamonds. He could not have something in clubs but nothing in diamonds. Thus, there are only two options.

 

However, only in the case of two nothings would he have flexibility.

 

If the eliminated option (nothing in diamonds but something in clubs) were available, then restricted choice suggests that the opponent lead from his only weakness, as 2/3 of the time he has strength in the other suit.

 

When that a priori analysis is not valid, because one of the 2/3 options is eliminated, a posteriori analysis still supports the restricted choice analysis, because the "both weak" option was flexible.

 

There could even be a one-suit or one-card restricted choice problem. If only one suit might provide a source for a passive lead, the failure to lead that suit might be because of force of it being dangerous or of a random decision to not make that passive lead. For instance, what if a person had the option of either a passive club lead or an aggressive diamond lead? If a passive diamond lead was possible, then the opponent might, in a sense, be capable of either attack. If, however, a passive diamond lead was not possible, then the person may have been boxed into an aggressive slub lead. The flexibility of the latter suggests, by restricted choice, that the passive diamond lead was not an option.

[jdonn]

That argument about the queen doesn't matter since it applies to both cards. After all if you play the ten it can be

 

<!-- ONESUIT begin --><table border=1> <tr> <td> <table> <tr> <th> </th> <th> <table> <tr> <td>  </td> </tr> </table> </th> <th> </th> </tr> <tr> <th> <table> <tr> <td> A9652 </td> </tr> </table> </th> <th> </th> <th> <table> <tr> <td> KJ74 </td> </tr> </table> </th> </tr> <tr> <th> </th> <th> <table> <tr> <td> QT83 </td> </tr> </table> </th> <th> </th> </tr> </table> </td> <td>  </td> </tr> </table><!-- ONESUIT end -->

I suppose you meant[hv=n=s&w=saj752&e=sk964&s=sqt83]399|300|[/hv] (In your layout the T was the winning play anyway.)

Good point that is a much more accurate example. The point being that west might mistakenly duck no matter which card you play, since it's right on another layout.

[Halo]

In my world this LHO ducking just isn't happening when East has five - is East returning an ambiguous card? No.

[Finch]

My example didn't work - but there may be a layout where LHO might duck when you play the Q and not the 10. I've ducked by mistake myself in a slightly different position when the suit was running all along... it's not always easy to work these things out. The trick as declarer is to play confidently!

 

This isn't quite the right layout for it, because the pips don't work, but the standard successful swindle is a layout such as this one:

 

[hv=n=s9x&w=sk108x&e=saj73&s=sq42]399|300|[/hv]

 

West leads the low pip to East's ace and declarer's 4, and East returns the 3 to South's Queen... if South started with QJ74 and East with A32 then West should duck this, but if South has Q42 then ducking looks very silly. (this isn't a 'swindle' as such because South's only legit chance is to play the queen)

 

Going off topic a bit here, but I think the principle is valid.

[HeartA]

Why are we in 3N instead of 6C, or at least 5C?

That's exactly the question I want to ask.

 

Now, I play 10.