Board 1
Neither side vulnerable
| ♠ K Q 2 ♥ J 7 ♦ A J 10 7 5 ♣ K Q 5 |
RHO opens with one spade. I overcall with one notrump. Partner bids two clubs, Stayman. I rebid two diamonds and partner invites game with two notrump. With 16 HCP and a good five-card suit, I have an obvious acceptance. I bid three notrump, and West leads the spade ten.
| NORTH Robot ♠ 8 7 6 ♥ A K 9 ♦ 8 2 ♣ J 9 7 6 2 |
||
| SOUTH Phillip ♠ K Q 2 ♥ J 7 ♦ A J 10 7 5 ♣ K Q 5 |
| West | North | East | South |
| Robot | Robot | Robot | Phillip |
| Pass | 1 ♠ | 1 NT | |
| Pass | 2 ♣ | Pass | 2 ♦ |
| Pass | 2 NT | Pass | 3 NT |
| (All pass) |
If clubs come home, I have nine tricks. Can I do better? If East has all the high cards (the queen-ten of hearts and the king-queen of diamonds), I can triple squeeze him. After I cash my black-suit tricks, I'll be down to
| NORTH Robot ♠ -- ♥ A K 9 ♦ 8 2 ♣ -- |
||
| SOUTH Phillip ♠ -- ♥ J 7 ♦ A J 10 ♣ -- |
To keep three hearts and the king-queen of diamonds, East must throw all his good spades away. I can then duck a diamond to take a tenth trick. I have no reason to believe East has all the high cards, but I'll keep this ending in mind as a possibility.
I play a low spade from dummy, and East encourages with the five. East can be pretty sure I have the spade king, but he may be less sure about the queen. So I win with king, the card I'm known to hold.
I lead the king of clubs--three--deuce--ace. East cashes the spade ace, and West drops the nine. East continues with the spade four, and West discards the heart deuce. This is probably from a five-card heart suit.
Here is the current position:
| NORTH Robot ♠ -- ♥ A K 9 ♦ 8 2 ♣ J 9 7 6 |
||
| SOUTH Phillip ♠ -- ♥ J 7 ♦ A J 10 7 5 ♣ Q 5 |
West is out of spades. So I can develop a diamond trick if he has a diamond honor and I can arrange to lose a diamond to him. I can cash the club queen, lead a club to dummy, and play a diamond. No, I can't. East simply puts up his diamond honor, forcing me to take the ace, and I have no way back to my hand after I drive the other honor.
If I'm going to develop a diamond trick, I have to do so while I still have a club entry to my hand: Heart to dummy immediately. Diamond. East rises with his honor. I win with the ace and play the diamond jack. That works if the diamond honors are split. But if East has both honors, I go down. It's not all that unlikely East has both diamond honors. In fact, there is a slight inference that he does. Clearing the spades suggests he has an entry. So I like playing for the triple squeeze better.
Maybe I can improve my chances for the squeeze, though. Suppose I lead the heart jack. If West has the queen, he will probably cover. Now all I need for the squeeze to work is for East to have both diamond honors and the heart ten. If West doesn't cover the jack, no harm done. I'll go up with the ace and play East for everything.
I lead the heart jack. West covers. Great! I take the ace, and East plays the four.
Let's take stock now. How likely is the squeeze to work? If East is balanced, he needs at least the diamond king to come up to 12 HCP. Both diamond honors would bring him up to 14. Either is possible, so the squeeze isn't necessarily working even if East has the heart ten. But I now have another option. I can simply finesse West for the heart ten. I'll run the clubs first, then decide which line to take.
I lead a club to the queen. East plays the ten; West, the eight. Now a club back to dummy. West discards the diamond six. If I'm right about his holding five hearts, that gives West 2-5-4-2 and East 5-3-2-3. The doubleton diamond does not bode well for East's having both diamond honors. There are four ways for him to hold Kx but only one way to hold KQ. The diamond queen is four to one to be on my left.
I cash the nine of clubs, and East pitches the heart five. A good player might be stiffing his heart ten here. But I don't think my robot opponent would do that. I suspect the heart ten is onside. I pitch the five of diamonds. West pitches the heart six.
On dummy's last club, East pitches the four of diamonds. West, the nine of diamonds. If I've read the deal correctly, we are down to this position:
| NORTH Robot ♠ -- ♥ K 9 ♦ 8 2 ♣ -- |
||
| WEST Robot ♠ -- ♥ 10 x ♦ Q x ♣ -- |
EAST Robot ♠ J x ♥ x ♦ K ♣ -- |
|
| SOUTH Phillip ♠ -- ♥ 7 ♦ A J 10 ♣ -- |
I lead a diamond. East plays the king. I take the ace and lead a heart to the nine. It holds. Making four.
| NORTH Robot ♠ 8 7 6 ♥ A K 9 ♦ 8 2 ♣ J 9 7 6 2 |
||
| WEST Robot ♠ 10 9 ♥ Q 10 6 3 2 ♦ Q 9 6 3 ♣ 8 3 |
EAST Robot ♠ A J 5 4 3 ♥ 8 5 4 ♦ K 4 ♣ A 10 4 |
|
| SOUTH Phillip ♠ K Q 2 ♥ J 7 ♦ A J 10 7 5 ♣ K Q 5 |
Plus 430 is worth 86%. I thought it would be better, but quite a few players made four, which surprises me. It takes a bit of foresight to make four, and the field doesn't often have foresight.
It turns out at most tables, East, after taking the club ace, cashed the spade ace then shifted to the king of diamonds, making it easy to make four. Why was the defense so soft at the other tables?
Most other declarers won trick one with the spade queen. It shouldn't matter. Either way declarer knows I have the remaining honor after he cashes the ace, since West would unblock from honor-ten-nine. But robots don't draws inferences from the play. So my East must have thought his partner had the queen left. At the other tables, East thought it unlikely his partner had the king left, since that meant South had overcalled one notrump with queen doubleton of spades. Looking at no entries, they gave up on spades and shifted to the diamond king.
As declarer, I almost always try to play the card that is most apt to keep the defense in the dark. But that's lazy of me. Sometimes you don't want to keep the defense in the dark. Here, I would welcome any shift, so I should be advertising my spade strength, not trying to hide it. Winning with the spade queen at trick one is the correct play. By playing routinely, I made the deal harder for myself than it should have been.
Your suggested defense of playing the Queen should only work against the robots, right? Against a good human player, playing the Queen, instead of the card you are known to hold, should make the defense wonder why you are going out of your way to show your spade strength. They should conclude you welcome a shift and therefore keep playing spades when getting in with the club ace.
ReplyDeleteSo is this situation (holding KQx in the suit led) a case where declarer should employ a mixed strategy and randomly play the King or Queen, so the defense cannot make an inference?
I was hoping to avoid this discussion. Yes, a human expert who has sufficient respect for your game might be suspicious when you play the queen. So at the highest level, a mixed strategy might be best. But simply randomizing wouldn't be the right mixed strategy. You would need to take into account (A) the relative likelihood of your holding K alone vs KQ and (B) the likelihood, when you hold KQ that it's right to continue the suit anyway. If you know those odds, you can calculate the proper mixed strategy. But as a practical matter, I don't think that's necessary. An opponent good enough to ask himself why you're playing the queen and giving your hand away will probably be inclined to think you simply made you careless play. Personally, I try to make enough mistakes so that my opponent can't blithely assume I haven't just made another one.
DeleteActually, after thinking about this more carefully, I take back what I said. A mixed strategy is not correct. East's best defense is always to continue the suit whichever card South plays. Given that, there is no reason for declarer NOT to play the Q from KQ if he wants a shift, just in case East doesn't adopt his optimal strategy. Try constructing a payoff matrix and checking this for yourself.
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