Can you suspect false carding from the following situation?

You are playing this hand at 3NT having arrived there after you bid 1NT and North 3NT, East and West having passed throughout. Only you are vulnerable. (The hand is linked for reference; but you'd only actually get to see your hand and dummy as below, plus individual cards as they are played). Dummy is North, the lead (by West) is the 5 of hearts 6, T, won by J in hand.

``````AK9
63
AT94
J985

QT8
KJ7
QJ82
AK3
``````

You have two chances for your ninth trick; a diamond finesse is 50-50. You also have an extra chance (8% by my calculation) if East has Qx of clubs, since you can drop the Q, then finesse against Tx remaining in West.

Since clubs is a "key" suit, I begin by inventorying the opponents' combined holding: QT7642. I start by playing the A, and expect the two lowest cards, 4 and 2 to drop (which in fact is the case). Say one opponent drops the 6 instead; I would then expect his partner to have the 4.

I lead the K, and sure enough, East drops the Q. But here's the tricky part; West drops the 7, meaning that the 6 and T are outstanding. Put another way, they can't both be playing their lowest card and at least one of them must be falsecarding!

Should I now suspect "chicanery," and go back to my 50-50 diamond finesse because my a priori 8% chance of a successful drop is now too low? (The actual South player tried a finesse which lost to East's ten.)

But perhaps South could now capitalize on the 3-3 break (36% a priori) by putting up his Jack, since the queen has been sacrificed. I can understand why East falsecarded, but why would West do so? Because if he hadn't I would have taken the club finesse, thinking that West had four cards and the queen was an honest drop from East. But faced with evidence of chicanery, I would suspect that E-W were trying to hide the fact that the diamond finesse would work.

• @PieterGeerkens: I changed the first two sentences so that the bidding and vulnerability information matches the link. Reminder noted. Jan 3 '16 at 2:40
• If the diamond hook loses you'll still make the hand when hearts are 4-4. That makes cashing a second club questionable, since you could be setting up the defenders' fifth winner. Jan 3 '16 at 3:44
• @AdamWildavsky: After trick 1 there is only a 11*10 / 20*19 = 11/38 chance that Hearts are split 4-4. (ie that both unplaced Hearts are with East, with 9 and 11 cards unknown in West and East respectively.) Combined with the Diamond finesse that gives roughly a 64.5% chance to make the contract. Testing the Club Q first gives a 50% + 1/3 * 48% = 66% chance to make on a straight doubleton Q, plus the additional chance here of an expert defender attempting a subterfuge that fails on an endplay. Jan 3 '16 at 15:45

Dear Frank has omitted one additional possibility - there is a throw-in working against West when (a) it is actually possible to make the contract and (b) West holds T762 of Clubs. Once the Club Q falls on trick three this play should be visible to Declarer.

Cash three Spade tricks ending in Dummy to leave this for Declarer

``````S: -
H: 3
D: AT94
C: 5

S: -
H: K7
D: QJ82
C: -
``````

and the possible West holding to be these:

``````S: -     or  J     or  J    or  J
H: AQ8       AQ8       AQ8      AQ
D: Kx        KX        K        Kx
C: 6         -         6        6
``````

In all cases West has at most three cashing tricks, and no exit - just lead the last Club to West, pitching a diamond from hand, and wait for your last 2 tricks.

Update #2 - Play details:

Spades should be cashed in the order K; then Q; then A to maintain control if Spades break worse then 4-2. Then the Diamond Q should be pitched from hand on the 4th round of Clubs to unblock; there is no need for more than 2 Diamond tricks and we desire to win both in Dummy.

Update #3 - Odds of both lines of play:

After trick 1 there is only a 11*10 / 20*19 = 11/38 chance that Hearts are split 4-4 (ie that both unplaced Hearts are with East, with 9 and 11 cards unknown in West and East respectively). Combined with the Diamond finesse that gives roughly a 64.5% chance to make the contract.

Testing the Club Q first gives a 50% + 1/3 * 48% = 66% chance to make on a straight doubleton Q, plus the additional chance, as here, of an expert defender attempting a subterfuge that fails on an endplay.

Update:

Note that an expert West holding the Diamond K, and thus knowing that his partner has at most three HCP, will almost always false card in Clubs so that (a) a false card by his partner in the suit is believable; and (b) if East cannot false card in Clubs then Declarer won't know whom to believe because the signals are inconsistent. It is a mandatory play at that level, and cannot hurt because his partner (a) already knows what to return if he gets in and (b) has nothing to be fooled about.

The guideline here is that when the defensive values are split decidedly unevenly between the two hands, the weaker hand false cards only out of necessity while the stronger hand will false card frequently. This can sometimes assist Declarer in placing cards, but works to Defenders' advantage more frequently.

• Note that after 3 rounds of Spades by Declarer any Spade remaining in West's hand cannot be an entry to East, as it is the 13th card of the suit. Jan 2 '16 at 20:05
• Thanks for your help/guidance in improving my question. I'll grant you that this sequence "works to defenders' advantage more frequently." But the price seems awfully high, because declarer would benefit more from one 36% chance (3-3 split with Jack high because the Queen was dumped) than with four 8% chances (exactly Qx with East). And the first is what was created to produce the illusion of the second. Not to mention the other possibility you brought up. Jan 3 '16 at 15:21
• @TomAu: I cannot follow what you are arguing. This hand has to be IMPS play because in matchpoints you test the diamonds first in order to set up a squeeze or throw-in for extras in Clubs and Hearts. Jan 3 '16 at 15:57
• Coming from me, a question would be IMPS or rubber, because I am not familiar with Matchpoints. It's been 40 years since I've played that version of bridge. Jan 3 '16 at 19:29
• @TomAu: Accurate defense is simply not possible without both communication, based on agreed signalling methods for attitude, count, and suit preference, and faith that partner's signals can be trusted absolutely whenever a decision actually needs to be made on the signal. That latter point is at the core of when and how to false card as a defender: Never lie to a partner who will have to make a decision based on your lie. This has the advantage of simultaneously showing mixed-signals to Declarer at occasional times when he is looking to make a critical decision. Jan 3 '16 at 20:31

Good defenders do not simply play the lowest card from their hands when following suit; they signal for partner. Intermediate players sometimes signal when they should not. Here, West was presumably signaling count -- initially playing their lowest card (showing that it was played from an odd number), then playing their highest (showing that it was played from an even number). This is consistent with the situation that West started with 762. Count signals are frequently played to declarer's leads.

If E played the Q from QT4, this was a very good play (assuming that they did not hold the DK as well) because it gives declarer a chance to go wrong. If West signaled count faithfully, they would have ruined partner's play. I would cash the CJ and try diamonds if clubs didn't start 3-3, congratulating West for deceptive signaling if they started with T762 and no DK.

• Throw in of West is on if West has 4 Clubs - just lead the last Club around to him after cashing three Spades, pitching a diamond from hand. Jan 2 '16 at 19:36
• @PieterGeerkens That's a good point.
– ruds
Jan 2 '16 at 23:45