[dickiegera]

If you play A and then small to Q North plays 9
and South plays 7&J.

Do play Q or duck?

No bidding by N/S
West opened 1NT and stayman got to a 4 HEART contract

Hearts are Trump

---

[ahydra]

Ostensibly it's 50-50 as there's nothing to go on. North could have either 109 or K9, and you can't do anything against South's KJ10x, nor North's K109.

You could apply restricted choice. If North started with 109 he might have played the ten some of the time. Also South starting with KJ7 might have taken the trick with the king (depending on your view of South's skill, what he thinks the layout is, etc). So you could argue North is slightly more likely to have started with K9 and hence you duck.

ahydra

[MrAce]

If you cashed A and played small to Q, seeing S play 7 and J while N played 9 the cases are'

KJT7 - 9 (this case it does not matter what you play, you lose 2)

KJ7 -T9 (this case you need to play Q to win, it is about 3.39%)

JT7 - K9 (this case you need to duck, it is about 3.39 %)

J7 - KT9 (it does not matter what you play)

So if it was me, I would duck despite the odds are ducking and playing the Q are same due to the common habits of players and what they do particularly with KJ7 holding.

[rmnka447]

I'm rising with the Q. In the 2 cases that matter, KJ7 and J107, LHO will virtually always play J from KJ7, but may choose to vary what is played (J or 10) on the second round of the suit from J107. So it seems like a restricted choice situation.

[smerriman]

rmnka447, on 2017-May-30, 19:19, said:

I'm rising with the Q. In the 2 cases that matter, KJ7 and J107, LHO will virtually always play J from KJ7, but may choose to vary what is played (J or 10) on the second round of the suit from J107. So it seems like a restricted choice situation.

That was my initial thought. However, if South has KJ7, then North has chosen to play 9 from T9, and could have played the T equally often. Doesn't that cancel things out and make it a completely even split again?

[Tramticket]

smerriman, on 2017-May-30, 20:38, said:

That was my initial thought. However, if South has KJ7, then North has chosen to play 9 from T9, and could have played the T equally often. Doesn't that cancel things out and make it a completely even split again?

Timo's point was that a South player will often rise with the king on the second round.

Interesting suit combination. I found it counter-intuitive and thought that playing the queen "must" be right until I did the calculation.

[NickRW]

Re the restricted choice aspect of this, surely they cancel one another out. One player could have started with T9, the other could have started with JT7. So it is strictly a 50/50 bet. Your real choice comes from your assessment of whether South would have risen (or not) at trick two from KJ7

[msjennifer]

I shall follow the restricted choice principle ( may not work always).Hence I shall follow with a small one hoping to see the King appear.

[Tramticket]

msjennifer, on 2017-May-31, 07:21, said:

I shall follow the restricted choice principle ( may not work always).Hence I shall follow with a small one hoping to see the King appear.

Restricted Choice considerations balance out - it's worth re-reading smerriman's comment.

But South's failure to play the king may well be significant. Put yourself in South's seat holding KJ7 with dummy on your right and holding A842. After a small card to the ace and a heart back. The options are:
- Partner has the queen - you know that you are making two heart tricks regardless - whether you play king or jack.
- Declarer has the queen and partner started with a singleton 9 - you will make one heart trick regardless - whether you play king or jack.
- Declarer has the queen and partner started with a doubleton 9X - you will make one heart trick regardless - whether you play king or jack.
- Declarer has the queen and partner started with a doubleton T9 - you can put declarer to a guess by playing the jack.

It is only in this latter case that there is a reason to play the jack. But there may be a good bridge reason to win the trick and direct the defence. Even a good defender might easily play the king on the second round.

Given that declarer might play the king, holding KJX, it must be better for declarer to play for south to have held JTX - duck the second round and hope that north is forced to play the ace.

[johnu]

Tramticket, on 2017-May-31, 09:14, said:

But there may be a good bridge reason to win the trick and direct the defence. Even a good defender might easily play the king on the second round.

Good point. There's a math solution when given just 2 hands and no bidding. There may be a different bridge solution when you have the bidding (or lack of), the other suits, and the play up to that point.

[MrAce]

Good discussion, I am glad that some of you mentioned that the R.C does not apply only to LHO as oppose to what rmnka447 thinks.

[cherdano]

MrAce, on 2017-May-31, 13:12, said:

Good discussion, ...

Good discussion, but still incomplete!
Let's say the early play is clear enough, and the opponents are good enough, to never play the K from K?x in the second round.

What would you do if LHO played the T instead of the J?

• RHO has to play the 9 from J9 - he doesn't know partner has the T, and doesn't want to give away the guess when partner has Kxx.
  
• LHO has to play the 7 and T from KT7.
  
• RHO has to play the 9 from K9.
  
• LHO has a choice between T and J from JT7.

So restricted choice says you should go up with Q.
So, if LHO realizes that, he should play the T from from JT7.

Ok, back to our situation. Since LHO is more likely to play the T from JT7, it becomes more likely that the J is from KJ7. So we should go up with the Q.

But if RHO realizes that, he should protect partner's holding by playing the T from T9!

You can keep going around in circles. I think the only non-exploitable strategy is for LHO to play
JT7, J97, T97, and RHO to play JT, J9, T9.

But then the situation we are given doesn't happen! So if LHO is the kind of person who reads BBF and has studies such suit combinations, you should play him for KJ7. But if RHO is, play her for K9.

(But what if RHO knows that you know that she is that kind of person, and that partner isn't??)

[miamijd]

In F2F, it seems like it ought to depend on LHO's playing level. The key case is when LHO has KJx. If LHO is anything less than expert, he'll either rise with the King or else give the situation away by hitching. If he plays the J smoothly, he's more likely to have JTx.

On the other hand, if LHO is an expert player, he'll play the Jack in normal tempo. Now you have a pure guess.

With computer bridge, it's not quite as easy, because you can't get a good read of tempo a lot of the time.

Cheers,
mike

[GrahamJson]

It seems very odd to me that there is so much debate over what seems to be a very straightforward situation. The outstanding cards are all equals, except for the 7, and given the bidding both oppo know exactly what the situation is so can play their cards at random. Hence little can be read into the sequence in which they are played. Given that the a priori odds favour going up with the queen I see nothing to change my mind.

Would the same discussion come up if it were AQxx opposite xxxx? Surely everyone would take the finesse or play Ace then small to the queen, depending on the play of the hand as a whole. Would anyone play Ace then small from both hands unless there was clear evidence of Kx over the queen.

[miamijd]

GrahamJson, on 2017-June-01, 10:39, said:

It seems very odd to me that there is so much debate over what seems to be a very straightforward situation. The outstanding cards are all equals, except for the 7, and given the bidding both oppo know exactly what the situation is so can play their cards at random. Hence little can be read into the sequence in which they are played. Given that the a priori odds favour going up with the queen I see nothing to change my mind.

Would the same discussion come up if it were AQxx opposite xxxx? Surely everyone would take the finesse or play Ace then small to the queen, depending on the play of the hand as a whole. Would anyone play Ace then small from both hands unless there was clear evidence of Kx over the queen.

Why would the a priori odds favor going up with the Queen? There are only two holdings for LHO that matter -- KJ7 and JT7, and both are equally likely.

[cherdano]

If you write stuff like this...

GrahamJson, on 2017-June-01, 10:39, said:

It seems very odd to me that there is so much debate over what seems to be a very straightforward situation.

...it looks better if you don't get twothings wrong in the same paragraph:

Quote

The outstanding cards are all equals, except for the 7, and given the bidding both oppo know exactly what the situation is so can play their cards at random. Hence little can be read into the sequence in which they are played. Given that the a priori odds favour going up with the queen I see nothing to change my mind.

Meanwhile:

Quote

Would the same discussion come up if it were AQxx opposite xxxx? Surely everyone would take the finesse or play Ace then small to the queen, depending on the play of the hand as a whole. Would anyone play Ace then small from both hands unless there was clear evidence of Kx over the queen.

Nope, noone would discuss AQxx opposite xxxx. But you should think about AQ9x opposite xxxx!

[nullve]

GrahamJson, on 2017-June-01, 10:39, said:

Would the same discussion come up if it were AQxx opposite xxxx? Surely everyone would take the finesse or play Ace then small to the queen, depending on the play of the hand as a whole.

Leading low from AQxx in dummy puts pressure on RHO if he has Kx.

[GrahamJson]

The situation we are catering four is when west has three cards and east two. In that case the odds are three to two that the king is with west. Nothing has happened to change those odds as east and west can play their cards in any order without potential loss, and they would know that.

Suppose it were coins, with one head and four tails. You have three coins on your left and one on the right. The odds are three to two that the head is on your left. You then take two coins away from the left and one from the right, with the proviso that all are tails. The odds are still that the head is on your left.

[MrAce]

GrahamJson, on 2017-June-02, 08:25, said:

The situation we are catering four is when west has three cards and east two. In that case the odds are three to two that the king is with west. Nothing has happened to change those odds as east and west can play their cards in any order without potential loss, and they would know that.

Suppose it were coins, with one head and four tails. You have three coins on your left and one on the right. The odds are three to two that the head is on your left. You then take two coins away from the left and one from the right, with the proviso that all are tails. The odds are still that the head is on your left.

Which forgets the most important part where we already saw the 2 of 3 hearts W holds.

[GrahamJson]

That makes no difference.

Take another situation. Suppose it was AQxxx opposite xxxxx. The odds are 2/1 in favour of the finesse. Does this change when you lead up to the AQ and see the card that LHO plays? The king could be the unknown card on your left or the unknown card on your right, but it is not even money.

Going back to the original hand. The initial odds favour the king on your left, assuming that the suit is 3-2. Suppose when you play the suit you don't see what cards are played by E and W, other than they don't include the king. The odds don't change, in the same way as with the coins. Why should knowing which card is the J, or 9, or 10 make any difference?