Counting to Improve Declarer Play

I’m playing in a club game with a regular partner. In fourth seat, I pick up:
♠ Q873
42
A54
♣ A1097

Dealer passes, partner opens 1C, and RHO overcalls 1S. I bid 1N, showing a weak, balanced hand with a spade stopper and no interest in hearts. Partner raises to 2N, and I’m at the top of my range and happy to accept the invitation to 3N, which everyone passes. LHO leads the queen of diamonds, and I get to see dummy:
♠ KJ102
K97
963
♣ KQ2

About 6 HCP lighter than I expected! I later asked my partner why he bid 2N instead of just passing 1N with a balanced minimum opener like this, and he said he wasn’t thinking, and this was a mistake. Okay, we’re in the wrong contract, but sometimes that happens at our level (I consider both of us intermediate-to-advanced players), and I should try my best anyway. Let’s see what I can figure out.

Optimistically, I’ve got 3 spade tricks, 1 heart trick on the finesse, 1 diamond, and 4 clubs if I can find the jack. I’ve got a chance here, but anything even slightly off will mean I’m down; I need to play very carefully.

From RHO’s overcall, spades split 0-5. From the lead, RHO also has the king of diamonds, but LHO has the queen, jack, and likely the 10. The Rule of Seven suggests holding up for one trick before taking my ace, but that’s a crude tool: if diamonds split 5-2, I should hold up once, whereas if they’re 4-3 I should hold up twice (the goal being to hold up until the opponent with short diamonds is out, so that if they win a trick they can’t lead a diamond to their partner).

I play low from dummy, and RHO overtakes their partner’s trick with the king, which I duck. RHO then returns a low diamond. That looks like unblocking to me: I now suspect diamonds split 5-2. Time to hop up with the ace, and make some avoidance plays so LHO never gains the lead.

It’s easy to do this by playing spades. RHO can win one of them, but doesn’t have an obvious way to get to his partner. On a spade to dummy’s jack, LHO discards a heart as RHO holds up. On dummy’s king of spades, RHO holds up again and LHO discards another heart.

It’s now unsafe to continue spades: if RHO holds up the third spade trick, they can cash 2 spades as soon as they get in, so both LHO and RHO will have become dangerous opponents. Time to focus on clubs instead.

On the king of clubs, everyone follows suit, but on the queen of clubs, RHO discards a spade. The good news: spades are once again a safe suit to lead, since RHO can take at most 1 trick in it. The bad news: clubs cannot be picked up, because the only remaining finesse is guaranteed to be wrong. The brilliant news: I now have a complete count of the opponents’ hands! LHO is 0=3=5=5, and RHO is 5=5=2=1.

It’s a good thing I didn’t try finessing in hearts, as it would almost surely lose. New plan: endplay RHO into leading away from their heart suit! Since LHO has already discarded 2 hearts, they have only 1 (likely spot) card left in the suit, and this plan should be easy if I can just get to my hand to lead a heart and cover whatever LHO plays. but first I’ll need to strip RHO of their safe exit cards by switching back to spades.

RHO wins dummy’s 10 with their ace (as an attempt to avoid being endplayed: if they held up the third round, I could throw them in with a fourth spade, and they would have only hearts to lead back), as LHO discards the 10 of hearts. RHO exits with a fourth spade to my queen (LHO discarding a low club), and I’m ready to duck a heart to endplay RHO. On this heart trick, LHO discards a diamond, and RHO covers dummy’s 7 with the jack.

Once RHO exits, they’re likely never to get in again, so they cash the ace of hearts before leading a low heart to dummy’s now-singleton king. On these tricks, LHO discards the 10 of diamonds and 8 of clubs. Here’s the position just before that third heart trick:

Me:
♠ –

5
♣ A10
               Dummy:
♠ –
K
9
♣ 2

Perhaps this looks familiar: it’s a standard squeeze! The threat cards are the 9 of diamonds and 10 of clubs. Check BLUE: LHO is Busy holding both guards, there is one Loser remaining, the diamond threat sits Upper of the squeeze victim, and there is an Entry to the other hand in clubs. The squeeze card was the heart that RHO played to dummy’s king: my first suicide squeeze in a sanctioned tournament!

I’ve been counting well enough to know that LHO still has the jack of diamonds, so I play a club to the ace, dropping LHO’s other jack, and my 10 wins the last trick. Contract made (see the full play), for a top board! and not just a cold top in our local club game, but a result in the 99.75th percentile across 810 tables throughout the ACBL (see board 17 from that day).

Double-dummy, I should have been down 2 tricks on a diamond lead. What went wrong for the defense? At trick 2, my RHO can see 8 hearts including the ace, king, queen, and jack. Furthermore, he knows that I have at most 3 hearts (due to my lack of negative double during the bidding), so the suit splits favorably for him. If he switches to a heart, dummy’s king will win a trick, but he’ll later take 1 spade and 4 hearts in addition to the initial diamond trick. However, I think RHO got greedy: if I take the heart finesse, he’ll get 5 hearts and set us an extra trick. So, he didn’t attack hearts early, which cost a trick against perfect offense. However, this isn’t an obvious mistake: there are many deals in which declarer would indeed be forced to take the heart finesse later, and RHO attacking hearts himself would give up a trick. Part of why bridge is so interesting is that can be very difficult to see what the correct play actually is.

So, after RHO returns a diamond at trick 2, I ought to be down 1. How did I make it? When I attacked spades, LHO needed to discard 4 times. They knew they needed to keep a club stopper, and their diamonds were set up to be a great source of tricks if they ever got in again, so the obvious discards are hearts. However, that 10 was key: if they keep it, I can’t endplay RHO! If they play the 10 on the first heart trick, I can either play low (letting them win the trick and run the diamonds), or cover with the king (in which case RHO takes his ace and runs the hearts). When LHO discarded the 10 of hearts, her partner became vulnerable to the endplay, thus giving me a chance to make the contract. Note that if LHO’s top heart was lower than dummy’s second-highest heart (e.g., swap the 9 and 10), it would be useless and discarding the hearts doesn’t matter. I don’t see any obvious way for her to recognize that the bare 10 of hearts is so important. Furthermore, I expect she could infer her partner’s strength in the suit (he’s got points somewhere, and they’re seemingly not in the minors or spades), and was happy to discard the hearts knowing her partner had the suit locked up.

Remember when RHO cashed out with the ace of hearts before playing a heart to the king? An interesting play is to just lead a low heart instead. Dummy will win, but can’t lead hearts again or else RHO will run the rest of the tricks. The correct play here is a suicide strip squeeze: if trick 10 is a heart to dummy’s king, declarer can watch what LHO discards. If they come down to 1 diamond and 2 clubs, play a diamond to throw them in and force them to give a free finesse in clubs in the last 2 tricks, whereas if they come down to 2 diamonds and 1 club, declarer can run the clubs and concede a diamond afterwards. Either way, LHO gets a diamond trick to make up for the heart trick RHO forewent, but it takes a top-notch declarer to see this, and lesser players might mess it up and give extra tricks to the defense. Would I have gotten it wrong? Very possibly: I had rough ideas of the count of every suit, but was not thinking about it so explicitly. Counting is still something I aspire to improve.

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