[pclayton]

---

You need three tricks from this suit. You cash the Ace and the 10 drops from LHO.

There isn't much known here, but RHO can't have 5.

Does the presence of the 10 indicate a restricted choice position?

[helene_t]

Was tempted to vote for option 3 but really, LHO can only have T9 or he is falsecarding. Without the information that RHO can't have 5 it would be a RC situation of course.

[blackshoe]

LHO clearly has a doubleton (unless he is falsecarding). Might be T9 or Tx. Not sure why it can't be QT.

[david_c]

I voted yes, though I may be missing something. It seems that LHO has nothing to gain from falsecarding. So the only relevant holdings are indeed QT and T9, and PRC says the first is more likely.

[helene_t]

Oh yes of course, he can have T9 or QT. From T9 he might have played the 9 so he is 67% likely to have QT. So it is a RC situation, I think.

[Echognome]

Well I guess the issue is not whether he has QT or T9 (playing the K next works in both cases), but whether he could have Tx and falsecarded. Now if you play the K next (rather than small towards the J), you will only make 2 tricks.

[BillHiggin]

Echognome, on Sep 7 2008, 12:15 PM, said:

Well I guess the issue is not whether he has QT or T9 (playing the K next works in both cases), but whether he could have Tx and falsecarded. Now if you play the K next (rather than small towards the J), you will only make 2 tricks.

I think you have three options
Cash K - wins against either non-falsecard
Small to 7 - wins against falsecard and Q 10
Small to J - wins against falsecard and 10 9

I cannot estimate the odds of the falsecard
10 9 should be half as likely as Q 10 (he had a choice from the former)

Any play wins against all 3-3 splits as well as the grosvenor 10 from Q 10 x x (no 9)

[kfay]

I think the fact that LHO could have falsecarded from 10x (9x) make this case non-RC.

If they aren't capable of falsecarding, then it is restricted choice and you should drop the Q or squeeze RHO

[pclayton]

(stupid comment deleted)

[Cascade]

david_c, on Sep 8 2008, 03:57 AM, said:

I voted yes, though I may be missing something. It seems that LHO has nothing to gain from falsecarding. So the only relevant holdings are indeed QT and T9, and PRC says the first is more likely.

If he has 109x then false carding gives you a losing option of playing small to the 8 on the second round when the standard safety play of small to the jack would win.

[cherdano]

Cascade, on Sep 7 2008, 06:20 PM, said:

david_c, on Sep 8 2008, 03:57 AM, said:

I voted yes, though I may be missing something. It seems that LHO has nothing to gain from falsecarding. So the only relevant holdings are indeed QT and T9, and PRC says the first is more likely.

If he has 109x then false carding gives you a losing option of playing small to the 8 on the second round when the standard safety play of small to the jack would win.

Or he could falsecard from Tx, hoping you cash another honor next (which would win against QT and T9).

[TimG]

Cascade, on Sep 7 2008, 07:20 PM, said:

david_c, on Sep 8 2008, 03:57 AM, said:

I voted yes, though I may be missing something. It seems that LHO has nothing to gain from falsecarding. So the only relevant holdings are indeed QT and T9, and PRC says the first is more likely.

If he has 109x then false carding gives you a losing option of playing small to the 8 on the second round when the standard safety play of small to the jack would win.

But, on the 3rd round declarer will have no choice but to play the other high honor form dummy, right? So, still one loser in the suit (since the suit is 33).

[Cascade]

TimG, on Sep 8 2008, 02:07 PM, said:

Cascade, on Sep 7 2008, 07:20 PM, said:

david_c, on Sep 8 2008, 03:57 AM, said:

I voted yes, though I may be missing something. It seems that LHO has nothing to gain from falsecarding. So the only relevant holdings are indeed QT and T9, and PRC says the first is more likely.

If he has 109x then false carding gives you a losing option of playing small to the 8 on the second round when the standard safety play of small to the jack would win.

But, on the 3rd round declarer will have no choice but to play the other high honor form dummy, right? So, still one loser in the suit (since the suit is 33).

of course you are right

[fred]

"Restricted choice" typically applies whenever a defender plays a card that is an equal to at least one other card that is missing.

By this I mean that the play of the card in question has an impact on the likelyhood of the defender in question being dealt a card (or cards) that is equal to the card that was actually played.

Whether or not this has an impact on how declarer should play a hand or suit had the card in question not appeared, is an entirely different matter (which obviously depends on the hand or suit in question).

With this particular combination, West's play of the 10 increases the odds that East was dealt the 9.

Fred Gitelman
Bridge Base Inc.
www.bridgebase.com

[dburn]

I have been frying what are left of my brains for the last hour or so on this combination. On such occasions, it's a relief to learn that Suitplay doesn't know how to play it either.

The reason it doesn't is that in many likely positions, the defenders should chuck the ten and the nine around like confetti in order to disguise possession of the six. The state of the art is that we know how to play AK73 facing J82 for three tricks, but we do not know how to play AK74 facing J82 for three tricks.

Given the state of the art, you are well advised to follow Fred's dictum that a man who plays the ten is unlikely to hold the nine. Whether or not he holds the six is left as an exercise for the reader...

[nige1]

Tim Rees highlights a similar intriguing combination:
K103 [] A842
You play small to the 10, losing to an honour. You cash the K next, then what?

• If West has played the 9, it looks like restricted choice applies to East's play of an honour, in which case you should play for the drop of the other honour.
  
• If West has played the other honour on the second round, then restricted choice doesn't apply to East (he didn't have a choice), but it does to West (he had H9 left, which are equivalent). Therefore, you should finesse on the 3rd round.

West can also work this out, however. In which case, he should always play an honour with H9 on the 2nd round, to get you to finesse. (Is this an extension of playing a card you are known to hold?) If you know West's doing that, then when he plays an honour, you're on a guess. As H9x is a prioiri a tiny bit more likely than Hx, you will play for the drop. Conversely, if West plays the 9 on the 2nd round, you should finesse on the 3rd.

As this is the exact opposite of the original plan, there seems to be a paradox.

Is this restricted choice, game theory, or something else? Please give your views on the right way to play the suit if West drops a) the 9; the other honour. Also, what is West's optimum strategy holding H9x?

[dburn]

West in your diagram has the king, ten and three. How then was he able to play the nine?

Assuming that the actual position is:

---

and assuming that South plays to the ten, losing to West's honour, then cashes the king, he should next finesse the eight whether East plays the nine or the other honour under the king. If East has played the nine on the first round and a low card on the second, declarer should still finesse the eight on the third round.

The defenders cannot do anything to circumvent this strategy by declarer, which will win three tricks a little over 60% of the time.

[nige1]

dburn, on Sep 23 2008, 08:50 AM, said:

A842 K103

West in your diagram has the king, ten and three. How then was he able to play the nine? Assuming that the actual position is:

Sorry yes.

dburn, on Sep 23 2008, 08:50 AM, said:

and assuming that South plays to the ten, losing to West's honour, then cashes the king, he should next finesse the eight whether East plays the nine or the other honour under the king. If East has played the nine on the first round and a low card on the second, declarer should still finesse the eight on the third round. The defenders cannot do anything to circumvent this strategy by declarer, which will win three tricks a little over 60% of the time.

Thank you, David.