In this post, we will look at how a slam was bid, looking at
just one hand at a time. North holds the following hand
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North |
It has 11 points in high cards and can count 2 points in
distribution. That is good enough for an opening bid. North bids 1 diamond.
South responds with 2 hearts. North thinks, “Wow! That’s a jump shift. My
partner has 19 or more points. We are forced to game and could easily be in
slam.” Now, North needs to choose a rebid. The best way to approach the rebid
is to make the same bid that she would have chosen after a 1 heart response,
only at a higher level. South is only promising a 4-card heart suit, so North can’t
support hearts. South could have both major suits, though. North chooses to bid 2
spades. South responds with 3 spades. OK, good deal. They have found a trump
fit. Now, the team needs to figure out if they have enough strength for a slam.
North doesn’t know. If South has a minimum jump shift of 19 points, the team
might be a little short of slam. North chooses to show a minimum opening hand
by bidding 4 spades. Remember that the jump shift forces North to continue
bidding until a game contract is reached, or the opponents are doubled for
penalties. The opponents have been silent.
The auction could end here, but South continues with 4 no
trump. That is the Blackwood ace-asking convention. North doesn’t have any
flexibility in her responses. She just bids according to her ace count. She has
1 ace, so she bids 5 diamonds. South continues the Blackwood convention by
bidding 5 no trump to ask for kings. North has 1 king, and bids 6 diamonds.
South signs off at 6 spades. North is required to pass, here. South was in
charge of the bidding, and has set the contract.
Now, try to forget what North held and look at the bidding
from the South hand. South holds
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South |
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That's 21 points in high cards and 1 in distribution. South was thinking of opening the bidding with 2 no trump, but to his surprise and delight, his partner opened 1 diamond. South is thinking, “Wow! With partner’s 13 points and my 21, we should at least have a small slam. I need to jump shift to show my strength and make sure the bidding stays open.” South responds with the same suit he would have bid with a weaker hand, but one level higher—2 hearts.
North responds with 2 spades. South is delighted. Now, they have found a trump fit. Since the jump shift keeps the bidding open until a
game contract is reached, there is no reason to hurry. He bids 3 spades to show
that he has 4 of them to go along with partner’s 4. South intends to bid on to
reach a slam at his next turn. North is
forced to bid, again, so South will get another turn. North responds with 4
spades. At this point, South expects that his partner has just a minimum
opening hand. The team has already reached a game contract, so North can pass at her next turn if she wants. South already knows that the side has enough strength for 6
spades, and he knows that the side is not off two aces. He could just bid 6
spades at this point. However, South tries to picture the sort of hand that
North might hold. Her 13 points need to fit in somewhere. If she holds the
missing ace and all 3 missing kings, a grand slam is possible. A missing queen
of hearts might require a finesse, but grand slam is worth investigating.
South bids 4 no trump, the Blackwood convention, to ask for aces. Even if partner responds with 5 clubs showing zero aces, South will bid a small slam. North replies 5 diamonds, showing the missing ace of spades. South continues the Blackwood convention by bidding 5 no trump. He wants to know if North holds all the missing kings. Some readers might be thinking, “Suppose North responds 6 clubs. Then, you are missing three kings and would need two finesses to make the small slam.” Well, yes, that is true, but North needs to fit 13 points somewhere. With 1 ace and no kings, there are still 9 points to put somewhere. There aren't enough queens and jacks out to make up the difference.
North responds 6 diamonds. Well, nuts. You are missing 2 kings. South is committed to a small slam at this
point, but he was planning to bid at least a small slam from the moment his
partner opened the bidding. He bids 6 spades and North passes.
Playing the Hand
West leads the 4 of diamonds. Let’s plan the play of the
hand. It might be a challenge.
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Dummy |
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Declarer |
Declarer starts by counting his losers. With a reasonable split,
he doesn’t have any losers in spades. From the view of the declarer hand, he
has a potential loser in hearts, and one in clubs. That’s one too many. There
is an extra winner in diamonds in dummy, but that won’t get rid of enough
losers in the declarer hand. There are 7 diamonds. Should they break 3-3,
declarer could discard the queen and jack of clubs on the small diamonds,
allowing him to give up a heart loser and making the contract. That possibility
is somewhat less likely because West chose to open with a diamond. She might
have led from 3 to the Jack. In any case that is one possibility that allows
the contract to make. What else?
If the trumps break 3-2, both hands will hold a trump when
the 4th diamond is led. Declarer could ruff the 4th
diamond and get back to the board by ruffing a club.
If East holds the king of hearts, dummy can lead the queen.
If East holds the king and covers, all the hearts are good. Declarer can afford
to lose the club king. If West holds the king and ducks, declarer ducks with
the Jack. We’ll see why he doesn’t play small in a minute. Next, he can lead
the 9 of hearts. If East ducks again, declarer plays his carefully preserved 6 of
hearts so he can stay on the board for one more heart lead. He leads the 8 of
hearts. If East started with 4 cards to the king, he can duck again. No
problem. The king will fall on the ace whenever declarer wants to play it. Even
if East started with 5 or 6 hearts to the king, declarer will make 4 heart
tricks. He should be able to ruff when
East tries to take his king later. OK, that’s one more way to make. What else?
Picking up the king of clubs in a finesse is tricker. Dummy
can only lead clubs once. If East holds the king, he can duck the club lead.
Declarer plays the queen in the declarer hand and still has a club loser. That’s
not a big problem. There should be a trump left in dummy to ruff the jack. OK,
that’s one more way to make.
There is probably a better way to avoid a club loser. Declarer
could play the ace of clubs and ruff both the queen and jack in dummy. That
plan requires both opponents to hold at least 3 clubs, or for the hand with
short clubs to also hold at most 2 spades. Declarer will not be able to finish
pulling trumps before ruffing the clubs. The opponents hold 9 clubs between
them, so getting them to follow suit to three rounds seems reasonable.
There is also the possibility of a ruffing finesse in clubs.
Declarer could cash the ace of clubs and lead the queen, intending to discard an
off-suit if West doesn’t cover. If West covers, dummy ruffs, setting up the
jack.
So far, it looks like declarer will need a lot of bad luck
for all these plans to fail. The next thing we need to consider is
transportation and pulling trump. We can’t run the diamonds until all the trump
are out. We also need an entry to dummy to run them. Likewise, we can’t try the
heart play until all the trumps are out, and we need an entry to dummy.
Of all the plays, the choice of ruffing two clubs in dummy
seems most likely to succeed. It only requires the 9 clubs that the opponents
hold to break no worse than 6-3. On the other hand, it requires two leads to
the declarer hand before trumps are pulled. The finesses are only 50-50
chances, but they both need to fail for the contract to fail. That makes a 75%
chance of success, if you have the entries. Running the diamonds works if
trumps break 3-2 and the diamonds break no worse than 4-2, or if the diamonds
break 3-3. The advantage of the latter plays is that we try each of them and go
on to plan B and plan C if they don’t work. I can’t do all of the probability
calculations in my head. Let’s just pick one and get started.
Recall that we are facing an open lead of the 4 of diamonds.
We play the 6 from dummy. East follows with the 3! If we only had a small
diamond in our hand, we could play that to win the trick, and the hand would be
easier, but no such luck. Declarer plays the ace.
We start by pulling trump, leading the queen. We want to
preserve our entries to the board. Both opponents follow. Now, declarer leads
the 2 to the ace on the board. Both opponents follow suit.
We know, now, that the trumps break 3-2. Can we afford to
pull the last one before trying our other ideas? If the heart finesse works,
the contract makes. We’ve already discovered that by preserving the 6 of hearts
in the declarer hand, we can stay on the board to repeat the finesse as many times
as necessary. If the finesse loses, we will usually create an entry in hearts
to try to run the diamonds. If West holds Kxx in hearts and waits until the 3rd
round to take the king, we don’t have the extra entry. Can West figure that
out? It’s more likely that West would take the king at the first opportunity. I
think we can finish pulling trumps. Dummy leads the king. East discards a small
club. The trumps are gone. Now it is time to try the heart finesse. Dummy plays
the queen. East follows with the 3. Declarer wisely follows with the jack. West
takes the king. Now, declarer needs to try one of his other chances.
West returns the 2 of hearts. There goes one of the entries
that declarer so carefully created. Dummy plays the 8. East follows suit, and
declarer takes the ace, maintaining one entry in hearts.
The remaining cards are
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Dummy |
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Declarer |
and declarer is in his hand. The plan, now, is to see if we
can set up the diamonds, and if that doesn’t work, try a club finesse. Declarer
cashes the ace of diamonds. West follows with the 2. Dummy plays the 7. East
discards a small club. Crud! Declarer plays the ace.
There is no way to set up diamonds. The only chance left is
a club finesse. There are two ways to try it. We could try a normal finesse by
leading the 8 from dummy, planning to play the queen if East ducks. If that
works, we can cash the ace and ruff the jack. If it doesn’t work, c’est la
vie.
The other alternative is to try a ruffing finesse by cashing
the ace. There is a tiny chance that an opponent started with the singleton
king. Don’t back on it, but that is another chance to make. Presuming that the
king doesn’t fall. Declarer leads the queen, ruffing if West covers with the
king, and discarding if she doesn’t.
Which is the better choice? Let’s consider how many cards
each opponent has that we know are not the king of clubs. West started with 3
spades and 5 diamonds. She has played 2 hearts. That leaves 3 unknown cards in
hearts and clubs. East started with 2 spades and 1 diamond. He has discarded 2
clubs and followed to 2 hearts. That leaves 6 unknown cards in hearts and
clubs. Therefore, it is twice as likely that East holds the king of clubs.
We lead our carefully preserved 6 of hearts to the 9 on the
board. West discards a club and East follows suit with a small heart. We still
have a chance to change our mind. Let’s reassess the new information that we
have gathered. This last trick has given us the complete distribution for all
the hands. We know that West has 3 diamonds left, no hearts, and no spades.
That leaves two clubs. East has no spades, 1 more heart, and no diamonds. That
leaves 4 clubs. OK, we are not going to change our minds. It is still twice as
likely that East holds the king of clubs. We lead the 8 from the board. Declarer
plays the queen. East takes the king.
Some days you just can’t win.
Epilogue
Wait! Yes you can. As I was proof-reading this, I found the way to make the hand. Let's go back to the original planning stage.
West leads the 4 of diamonds. Let’s plan the play of the hand.
Dummy |
Declarer |
Declarer starts by counting his losers. With a reasonable split, he doesn’t have any losers in spades. From the view of the declarer hand, he has a potential loser in hearts, and one in clubs. That’s one too many. There is an extra winner in diamonds in dummy. You can use that to discard a losing club, and you can ruff a club in dummy. We can try the heart finesse, but it isn't necessary to make the contract.
We play the 6 from dummy. East follows with the 3. Declarer plays the ace.
We start by pulling trump, leading the queen. We want to preserve our entries to the board. Both opponents follow. Now, declarer leads the 2 to the ace on the board. Both opponents follow suit.
We know, now, that the trumps break 3-2. Declarer pulls the last trump by leading the king on the board.
Next, we move on to the clubs. Declarer leads the 8 of clubs from dummy and takes with the ace. Trumps are gone, so it is safe to cash the K of diamonds. East shows out. No problem, really. Had East followed suit to three rounds of diamonds, we could have discarded 3 hearts on the good diamonds in dummy. You can't have everything.
Now, lead the jack of clubs and ruff it on the board. Declarer has no more diamonds, and the lead is in dummy. Declarer plays the queen of diamonds and discards the last club.
The hand now looks like this:
Dummy |
Declarer |
One More Variation
Suppose the trumps break 4-1. What is the plan, then? We start out as before, playing for the 3-2 trump break.
Dummy |
Declarer |
Declarer starts by counting his losers. With a reasonable split, he doesn’t have any losers in spades. From the view of the declarer hand, he has a potential loser in hearts, and one in clubs. That’s one too many. There is an extra winner in diamonds in dummy. You can use that to discard a losing club, and you can ruff a club in dummy. We can try the heart finesse, but it isn't necessary to make the contract.
We play the 6 from dummy. East follows with the 3. Declarer plays the ace.
We start by pulling trump, leading the queen. We want to preserve our entries to the board. Both opponents follow. Now, declarer leads the 2 to the ace on the board. East discards a club. Now, you have a spade loser. There is no way to keep from losing a spade trick. We'll stop pulling trumps for now. You will see why later.
Now, we need to keep from losing a heart. We continue with the plan as before. Lead to the ace of clubs, and cash the king of diamonds. East shows out on the diamonds. Too bad, but it doesn't matter. Even a 3-3 break in diamonds would not create enough winners to discard 3 hearts and a club. We need the heart finesse to work.
It doesn't. That was still a pretty good try. It only required a 3-2 trump break (a 68% chance) or for the king to be in the East hand (a 50% chance). You miss both chances just 16% of the time.
