## Counting the hand

I’m playing in a Just Declare tournament on Bridge Base Online, which means the hand has been bid by 4 robots, and I’m taking over the South seat after the auction has finished. The bidding is complicated:

W N E S
Pass Pass 1 1♠
Dbl 1N 2♣ Pass
Pass 2 Pass 2♠
3♣ 3 Dbl Pass
Pass 3♠ Pass Pass
Dbl Pass Pass Pass

The 4 of diamonds is lead (robots play fourth best from length), and I see dummy:
♠ K4
984
A10832
♣ KJ10

and my own hand:
♠ A7652
K7532
J7
♣ 5

There’s a lot going on in the bidding, so let’s see what we can figure out. East has at least 5 hearts for their opening bid, so hearts must split 0-5. West is at least 4-4 in the minors for their Negative Double. East also has at least 4 clubs for their second bid, so clubs are 4-5 or 5-4. West raised clubs later, so it’s likely they have the 5-card suit, but not a guarantee.

Usually, you’d expect West to lead the suit in which they and partner have a fit, but West didn’t lead a club, implying that they have the Ace in that suit. West instead lead a low card in a suit where I’m missing the King and Queen, so West doesn’t have both missing honors (they would have lead the King in that case), but probably has one of them (with neither honor, they’d probably lead something else), and thus East has at least (and probably only) one of the diamond honors. and since West lead their lowest diamond and their length leads are fourth best, diamonds must split 4-2.

So, I’ve got guesses of how hearts, diamonds, and clubs split, and thus can guess how the spades split, too: before I’ve even played my first card, I suspect West is 4=0=4=5 with the Ace of clubs and a diamond honor, and East is 2=5=2=4 with a diamond honor! East must also have at least one of the black queens for their opening bid (they’ve got 7 HCP in hearts, 2-3 HCP in diamonds, and thus at least a couple points elsewhere).

I play low from dummy, and East wins their King. I unblock my Jack on this trick, because I’ve now got a marked finesse against West and don’t want to have transportation problems later (if I play low at this trick and later play the Jack, West might play low, and although the Jack will win, I’ll need to find another suit besides diamonds to get to dummy to cash the Ace). East switches to a club, giving me a finesse I already knew I could have taken against West’s Ace (which the robot plays here at trick 2).

West switches back to a diamond, and I take the marked finesse and play the 10, noting East’s play of the 9 (which should be their last diamond). Time to pull some trump. Since I’m expecting a 4-2 break and can’t pull them all, I’ll settle for pulling 2 rounds (so East is out), ending in dummy, and taking a heart finesse. I won’t have transportation back to dummy on my own afterwards, but I expect West to win some trump tricks later and then be forced to lead a minor suit for me. By leaving the minor-suit winners for now, I maintain control of those suits later, and West won’t be able to run them when they get in with their trump.

I make a small mistake here: West played 2 high trump, and I played the 2 under the King of spades. Double-dummy, this would cost me a trick, due to a throw-in (which I’ll discuss later)! I know that you should play your spot cards in trump to have transportation to either hand after trump are drawn, but it hadn’t occurred to me to leave the option of ducking a trump later. However, playing a high spot card under the King would have cost me nothing, and in this case would have gained something later on.

On the marked heart finesse, East rises with the Ace as West discards a club. East continues with a low heart, and I’m happy to let it ride around to West’s ruff or dummy’s 9. West actually chooses to ruff low, which was a mistake that cancelled out my earlier mistake! If they had ruffed high, they could then play their remaining low trump to throw me in, and I’d never have an entry to the board to cash the winners in diamonds and clubs! I could have avoided this by saving my 2 of spades until now, and ducking it under West’s 3, avoiding the throw-in and forcing West to lead a minor-suit card for me into dummy.

The robot didn’t see this play, though, and ruffed the heart low, then switched to a club. There’s still one remaining top trump out, but the rest of the tricks are mine: top club (discard a heart), top diamond (discard a heart), then I’ve got 3 not-quite-top trump and the top heart left in my hand. Down one (I lost a diamond, a club, a heart, a heart ruff, and a trump). You can see the full play here.

In this Just Declare tournament, 151 people played the hand. My result put me in the 97th percentile for the board: 7 other people played the way I did, and the other 143 were down additional tricks!

I’ve felt for a while that the next way to improve my game is to improve my counting, and this hand is a taste of what it’s like to count well. I was practically playing the whole thing double-dummy, because even before it started, I knew the opponents’ exact shape. I realize that not every hand gives this much information, but I suspect that this sort of reasoning is much of what separates the experts from the intermediate players, and I hope to achieve that consistently some day.