[jillybean]

You are in 4♠

---

How do you play this, any lead from South LHO plays 7♠. Is this a restricted choice decision with just ♠Kxx missing?

[hatchett]

No restrictive choice, plain finesse is best.

[awm]

Well there's the simple analysis and the complicated analysis. They both get the same answer.

Simple Analysis: The odds of the finesse working are 50%. The odds of the king being singleton are 25% (there are 8 positions of the three outstanding spades, of which two involve stiff king). Of course if we eliminate singleton king onside and void onside, the odds become 1/2 and 1/6 respectively. We should finesse.

Complicated Analysis: After the play of the ♠7, there are four possible spade holdings for LHO. These are ♠7, ♠K7, ♠K72, ♠72. In the first and second case LHO would always play the seven but in the third and fourth case he would choose randomly between the spots (but never play the king). So restricted choice applies, making the third and fourth positions half as likely (since LHO might've played the deuce). Therefore the odds are ♠7, ♠K7 each 1/3 of the time and ♠K72, ♠72 each 1/6 of the time. So taking the finesse works (1/3 + 1/6 = 1/2) half the time. Putting up the ace and hoping for the drop works 1/6 of the time. We should finesse.

So how come the simpler analysis is available? Basically the reasoning is that which spot LHO played should not effect the odds of LHO holding the king, assuming LHO plays spots randomly when holding both the 7 and 2. So the only relevent information is that LHO does not have singleton king or void, and that's all you have to restrict on.

[pclayton]

In Grands, the opening lead is a strong inference too.

If we have 9 cards missing the Queen, there's good reason to hook the opening leader for the Q on a non-trump lead in a grand.

10 cards missing the King? Actually the opposite is true, I think. West never leads the spot from Kx (unless West is certain dummy has the A, then leading the spot can be a nice swindle).

But W is just as likely to lead a trump from 72, making dropping the K a 50/50 proposition (versus leading from K72). This is subject to the caveat above .

[gwnn]

"Bad defenders" always play 2 from 72 so actually finessing vs bad defenders has an even higher chance. If west's play had been the 2, the odds in "bad defender land" would have shifted in favor of dropping the singleton K.

[jillybean]

The leads was 6♦ to my 8♦

I led 10♠ and ducked, hoping 7 was from K7
As it turned out 7♠ was a stiff

[inquiry]

jillybean2, on Dec 20 2006, 02:03 PM, said:

The leads was 6♦ to my 8♦

I led 10♠ and ducked, hoping 7 was from K7
As it turned out 7♠ was a stiff

If the seven was "stiff" then nothing would help. You had one spade to lose...

So here is the situations AFTER the seven is played...


!. 7    K2 -- nothing you do matters, lose 1♠
2. 72   K -> winning play is the ACE drop the KING
3. K7   2 -> winning play is to hook
4. K72   void --> winning play is to hook

If you LHO would never play 7 from 72, that might affect the odds. If he is an honest citizen who would never do that, the chance of dropping the singleton king is zero. Unfortunately, too many players will play 7 from 72 about half the time (not the optional percentage, but you get the idea).

Technically when the 7 is played, some hands are removed for the mix. West with void in spades for example, or singleton King or singleton 2. In fact, only four hand patterns exist...West holds

7
72
K7
K72

The chances for 7, 72, K7 are all the same at this point, 26%. The chance for K72 is somewhat less (22%). Since you can remove singleton 7 from the mix (u must lose one trick), you end up with three possible holding.

72
K7
K72

Once again the odds of the first two are the same (just over 35%) so play for 72 or K7 is the same chance. But you can also play for WEST to be K72 (nearly 30% of the chances where your play makes a difference). 30+35 is > 35, so the precentage play is (clearly) to finessee. This is almos twice as likely to work after the the 7 appears (when it makes a difference) than to play for the drop.

NOTE:::

If WEST would ALWAYS play the two when he held it, WEST will have

7, or
K7

That is it. Not K72 (no 2), not 72 (no 2). In this case, the finessee is 100% when the 7 appears. Either EAST has K2 doubleton and nothing you do works (you lose a trick), or WEST has K7 doubleton and the hook wins.

[jillybean]

Another one...

AQ985 opposite
J743 for no losers

[inquiry]

jillybean2, on Dec 20 2006, 02:32 PM, said:

Another one...

AQ985 opposite
J743 for no losers

You need to get lucky. Two lines suggest themselves.

Small to the queen. This wins when West Has any of the following holdings

K (obvious)
Kx (play ACE next)
KT (play ACE next)
Kxx (hook again, since TEN falls singleton)

According to odds table at http://www.automaton.../en/OddsTbl.htm these holdings occur 32.782% of the time.

The second line is double hook in spades. This can be by leading the JACK or playing small to the 9. Small to the 9 is not a very good chance (winds 24% of the time) losing to singleton or doubleton JACK offside, winning only versus

KT
KTx
KTxx

Leading the JACK does better, it loses to Singleton King onside, but other than that, it works anytime leading to the Queen does, plus it picks up KTx and KTxx with LHO, winning on these LHO hands, this "appears" to be much better (43.783$)

Kx
KT
KTx
KTxx

But there is a hidden danger here. When WEST has Kx of clubs, if you play the JACK lead line and WEST covers, you have to guess correct on the next round of spades and not re-hook. And there are two Kx combination (K2 or K3). IF you are committed to hooking the second time, you will lose to Tx doubleton offside (since you can not see into their hands). Kx occurs 13,6% of the time, so playing the second hook decreases from 43.8 to 30.2%, and if you are not "committed" to the second hook when the jack is covered, you lose picking up KTx and KTxx (17% of the time).

So the "percentage" play for 5 tricks is low to the queen (not the jack, so you can handle singleton King with LHO).

[jillybean]

Thanks, I did lead low to the Q and lost when lho held K10x

[inquiry]

jillybean2, on Dec 20 2006, 03:30 PM, said:

Thanks, I did lead low to the Q and lost when lho held K10x

This is a place where you might take a shot at matchpoints.

As I noted above, the percentage play is low to the Queen, then the ACE. But is is only 2% better than leading the JACK (32 versus 30%). If the entire field leads low to the queen, and you need a board, leading the JACK would give you a reasonable shot at a pickup (top 30%, bottom 32%, essentially average the other times).

Late in a MATCHPOINT event, needing a board, going against the odds here is not a terrible idea.