Board 8
Neither side vulnerable
♠ A 7 6 2 ♥ A 10 ♦ A J 7 2 ♣ J 7 4 |
LHO opens with one club, partner passes, and RHO bids one heart. I prefer to have at least nine cards in my suits for a two-suited take-out double. But it's now or never. If I pass, I'm probably out of the auction for good. And what fun is that? I double.
LHO redoubles to show three-card heart support, and partner bids one spade. This bid does not necessarily show four spades. Partner must bid one spade any time he doesn't want to hear me bid two diamonds if he passes. So he could easily have only three spades.
RHO bids two hearts. I now know they have an eight-card heart fit, and so does partner. If two hearts is passed around to him, he should compete to two spades on almost any hand with four spades. Since I have no game interest and no fifth spade, there is no reason for me to bid two spades in front of him.
No reason opposite a reliable partner, that is. The robots are not always Law-abiding citizens, so there is a serious danger we will defend two hearts if I pass. I bid two spades. Even if partner has only three, maybe this won't be too bad. Or maybe we'll push them up a level.
LHO passes, and partner bids three diamonds. I was trying to push the opponents up a level, partner. Not us. Presumably partner is making a game try. Or maybe he's getting even with me for bidding his hand for him. Anyway, I'm below minimum for my auction, so I sign off in three spades. Everyone passes, and RHO leads the three of diamonds.
NORTH Phillip ♠ A 7 6 2 ♥ A 10 ♦ A J 7 2 ♣ J 7 4 |
||
SOUTH Robot ♠ Q J 9 3 ♥ K 7 4 ♦ Q 9 6 5 ♣ 10 8 |
West | North | East | South |
Robot | Phillip | Robot | Robot |
1 ♣ | Pass | ||
1 ♥ | Double | Redouble | 1 ♠ |
2 ♥ | 2 ♠ | Pass | 3 ♦ |
Pass | 3 ♠ | (All pass) |
West chose to lead our second suit in preference to his partner's suit or the suit they bid and raised. So this is probably a singleton. The robots open one diamond with four-four in the minors, so the only way this can be a singleton is if East is 1-3-4-5. But how can that be? With four trumps, West wouldn't be going for ruffs. He would be leading one of their suits to start a tap. I've changed my mind. I suspect West is leading from length, trying to give his partner a ruff rather than going after one himself. In any event, I don't think he would lead from the diamond king. Maybe he has four small and the king is singleton offside.
I hop with the ace of diamonds. East plays the eight. No stiff king. The fact that East played the eight, however, is convenient. It means if I'm wrong about the diamond suit and West did lead from king-ten fourth, I haven't saddled myself with two diamonds losers. I can lead the queen to drive his king, then lead low to the seven, finessing against his ten.
I don't think that's the case, however. I suspect West led from three small, hoping his partner had a singleton and that the defense has a trump entry. Catching his partner with king doubleton as he did may be just as good. If I take a trump finesse and it loses, East can cash the king and put his partner in with a club for a ruff.
I'm off three top tricks in the minors. I can afford to lose a spade trick so long as I don't lose a diamond ruff as well. Should I play ace and a spade in an attempt to stop the ruff? If East has king third of spades, that does no good. He still gets his ruff. Ace and a spade stops the ruff only if East has king doubleton. If West has king doubleton, ace and a spade lets East get a ruff he wasn't entitled to.
Which layout is more likely? If East has king doubleton of spades, he holds six clubs. If West has king doubleton of spades, East holds five clubs. The latter is more likely. In addition, choosing to go after a diamond ruff in the first place is a more attractive defense if West holds a potential trump entry. So the diamond lead itself suggests West has the spade king. It looks right to finesse the spade.
I lead the ten of hearts from dummy. East covers with the jack. I play the king, and West follows with the deuce. I lead the spade queen, and West covers with the king. I win in dummy with the ace and play a low spade. East follows with the ten, so I have no further problems. I win, draw the last trump, and drive the diamond king. The defense cashes two clubs and I claim.
Making four. I guess I should have accepted partner's game try.
NORTH Phillip ♠ A 7 6 2 ♥ A 10 ♦ A J 7 2 ♣ J 7 4 |
||
WEST Robot ♠ K 8 5 ♥ Q 9 5 3 2 ♦ 10 4 3 ♣ Q 3 |
EAST Robot ♠ 10 4 ♥ J 8 6 ♦ K 8 ♣ A K 9 6 5 2 |
|
SOUTH Robot ♠ Q J 9 3 ♥ K 7 4 ♦ Q 9 6 5 ♣ 10 8 |
The right play in the spade suit is trickier if queen-jack-nine are in dummy where the defense can see it. Suppose this is the layout and our goal is to take four tricks:
NORTH ♠ Q J 9 3 |
||
SOUTH ♠ A 7 6 2 |
The only four-one break where we can take four tricks is if East has the stiff king. We aren't going to play for that, so let's ignore four-one breaks.
There are seven cases where our play matters. East can hold king-ten (1 case), king-small (3 cases), or king-third (3 cases). We have four possible strategies. If we lead the queen and it holds, we can continue with a low card or we can continue with the jack. If the queen is covered and we win the ace, we can hook the nine on the way back or rise with jack, playing to drop the ten. Our four strategies are the four combinations of these decisions, which we will call Low-Hook, Low-Rise, Jack-Hook, and Jack-Rise.
What strategies does East have? He must cover the queen with king-ten, and he must duck with king-third. If he doesn't, we have no losing options. So his only choice is whether to cover or play low when he holds king-small.
First, we'll figure out our best strategy the long way. Then we'll discuss a shortcut that leads to the same conclusion.
Since we don't know what East will do with king-small, we'll consider each of his strategies separately. The table below shows the number of cases where each of our strategies succeeds if East covers.
Low- Hook |
Low- Rise |
Jack- Hook |
Jack- Rise |
|
---|---|---|---|---|
K 10 | 0 | 1 | 0 | 1 |
K x | 3 | 0 | 3 | 0 |
K x x | 0 | 0 | 3 | 3 |
Total | 3 | 1 | 6 | 4 |
As we can see, if East covers with king-small, our best strategy is Jack-Hook, that is, continue with the jack if East doesn't cover and finesse the nine on the way back if he does. This wins six times out of seven.
The next table shows the number of cases where each strategy succeeds if East ducks with king-small.
Low- Hook |
Low- Rise |
Jack- Hook |
Jack- Rise |
|
---|---|---|---|---|
K 10 | 0 | 1 | 0 | 1 |
K x | 3 | 3 | 0 | 0 |
K x x | 0 | 0 | 3 | 3 |
Total | 3 | 4 | 3 | 4 |
If East ducks, the winning strategy is to rise with the jack if East covers (no surprise, since he covers only when holding king-ten). It's a toss-up what to do if he ducks.
Overall, our best strategy is Jack-Rise: If the queen holds, lead the jack. If it's covered, take the ace and lead to the jack. This guarantees four wins out of seven. Since East has available a strategy that holds us to four wins out of seven perforce, we can't do better than that. Jack-Rise ensures that we do as well as we are entitled to.
What's the best strategy for East? If South plays correctly, what East does with king-small makes no difference. His play matters only if South adopts one of the inferior strategies. Since East doesn't know which inferior strategy South will adopt, he can hedge his bet by adopting a mixed strategy. If the covers with king-small one sixth of the time, the payoff matrix is as follows:
Low- Hook |
Low- Rise |
Jack- Hook |
Jack- Rise |
|
---|---|---|---|---|
K 10 | 0 | 1 | 0 | 1 |
K x | 3 | 2.5 | .5 | 0 |
K x x | 0 | 0 | 3 | 3 |
Total | 3 | 3.5 | 3.5 | 4 |
Covering one sixth of the time ensures a South who misplays can't do better than three and a half wins out of seven whichever mistake he makes.
I promised you a shortcut. Since this theme occurs in a variety of suit combinations, a shortcut is useful. Here is a quicker way to come up with the best strategy:
There are seven cases we are concerned with. There is no strategy that is guaranteed to pick up both king-small and king-third. So the best we can possibly do is to pick up four cases: one of the major combinations plus king-ten. If we pick up king-ten, then we can't guarantee picking up king-small. So we give up on king-small. We resign ourselves to losing a trick to king-small no matter how East defends. We don’t play mind games and try to guess what East will do. We simply play to ensure we never lose a trick when East has king-third or king-ten. That way, we always win in four cases out of seven.
We stipulated earlier that our goal was to take four tricks. What if our goal is to take maximum tricks? We would like to take four tricks as often as possible, but not at the risk of losing two unnecessarily. So we can no longer ignore four-one breaks. Specifically, we must worry about king-ten fourth offside. If we lead the queen and it holds, then we continue with the jack and East shows out, we won’t be happy.
Let’s add that layout to our list. Now we have ten cases to consider: King-ten onside (1 case), king-small onside (3 cases), king-third onside (3 cases), and king-ten fourth offside (3 cases). For the first three scenarios, a "win" consists of taking all four tricks. For the fourth scenario, a "win" consists of losing only one trick. We could add a row to our tables above, but let's use our shortcut instead.
Our goal is to find a strategy that wins in two of the three major cases. If it happens to win for king-ten doubleton, great. If not, six wins out of ten is the best we can do.
We know that no strategy wins for both king-small and king-third onside. So if there is a strategy that wins in two major cases, it must include king-ten fourth offside. The strategy that meets our criterion is Low-Hook. It wins against both king-ten fourth offside and against king-small onside. So, if our goal is to take maximum tricks, we continue low if the queen holds and hook against the ten if it's covered, winning in six cases out of ten.
Now see what Jazlene does on this board at JazPlaysBridge. Be sure to watch until 21:34. Don't stop when Board 9 shows up, since Jazlene circles back to Board 8 for some afterthoughts.