So Cool ... And Kind of Mean
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## The setup

Every Wednesday morning my kids and I play Minibridge at the local bagel place before school. I'm not sure if the way we play is the "official" way to play Minibridge, but here's what we do (there are three of us):

1. Each player announces their high card points (HCP)
2. We figure out the HCP of the fourth hand using "mathematics."
3. The partnership with the most points is the declaring side, and the partner with the greater number of points is the declarer.
4. Dummy is displayed.
5. The person who held dummy's hand (if any) moves to take the fourth hand.
6. Declarer selects a trump suit (or notrump) after looking at dummy.

This is a great way to work on your card play, because there are no bidding misunderstandings, and you know each defender's exact HCP during the play, which is incredibly valuable.

Today, my 12-year-old daughter found herself at the helm facing this play problem, and I thought there was enough "stuff" going on on this hand to warrant sharing with you all:

Dummy
Q10
752
A1053
7632
Hero
AK43
A86
QJ62
KQ

Here's everything you know about the hand:

2. Your RHO is an experienced national champion (the mixed pairs, but still...) holding 12 HCP.

Declarer selected notrumps, and received the lead of a low spade. Dummy's ten held the trick, and RHO followed suit.

Your goal on this hand is to make 9 tricks. Please think about how you would actually play the hand before clicking through to the next page.

## The thought process

Dummy
Q10
752
A1053
7632
Hero
AK43
A86
QJ62
KQ

As always, count your tricks. You've got four spades (after the ten holds trick one), and the two red aces for six, so you need three more from somewhere.

There are only two realistic ways to get three more tricks (there's some psychological value in trying a club at trick two, but I'm not going to consider that here):

1. Score three more diamond tricks
2. Score two more diamond tricks and a club trick

Let's look at each of these options in order.

Score three more diamond tricks?

Barring a singleton K, the only way to do this is to cross to your hand with a heart to take a finesse. This means that if the finesse loses, you're now wide open in hearts, so when RHO wins the K, the opponents will be able to cash at least three hearts and the A to beat you.

Furthermore, you will have to lead the Q to finesse; in theory you'd LIKE to lead a low one to the 10 (in case the K is singleton onside) but you don't have another quick entry to your hand to finesse again. This means that you can only really handle Kx or Kxx onside. So while the K being onside is 50% (ignoring what we know about the HCP distribution for a second), you can't handle all situations when the K is onside, making this line of play (slightly) less than 50% (again, ignoring what we actually know about the hand).

Score two more diamond tricks and a club trick?

If we're not going to finesse diamonds, we should just play the A immediately and continue the suit to knock out the K. This guarantees two more diamond tricks (and sometimes the K is singleton and now we'd be playing for an overtrick!), and we still have our heart stopper. If the opponents now switch to hearts, we can't just grab our A right away because we're still going to have to lose a trick to the A to get our total up to 9, so if we grab the A prematurely the opponents can just win the K, A, and at least three hearts to beat us. So we should plan to duck two hearts, win the third, and hope that the A is in the same hand as the shorter heart holding (so when they win the A they won't have another heart to play). Of course if the opponents DON'T switch to hearts, or don't play three rounds of hearts, we are making the contract immediately. A standard hold up play.

Which line is better?

Independent of what we know about the HCP distribution, the second line of play is better. The first one works slightly less than 50% of the time, but the second one must be more than 50%. All it requires is that the hand with fewer hearts also holds the A. But by virtue of holding fewer hearts, there's more room for the A, so this line has to be a little better than 50%.

But we actually know a LOT about the hand. Most of the HCP are on our right, so the diamond finesse is a huge underdog, and the play at trick one strongly suggests that the J is on our left (remember, the 10 held trick one). If the J is on our left, and LHO only has three HCP, it's 100% that the diamond finesse will fail.

## A little knowledge can be a dangerous thing

My daughter isn't a very experienced declarer, but she generally knows enough to count the HCP and know when a finesse is "guaranteed" to fail. So she worked it all out and triumphantly played A and another diamond, intending to duck the A twice.

The full hand:

Sister
8762
1094
K84
1085
Dummy
Q10
752
A1053
7632
J95
KQJ9
97
AJ94
Hero
AK43
A86
QJ62
KQ
D

She was so proud of her reasoning, followed by a frustrated and loud "DADDY WHY DIDN'T YOU PLAY THE JACK OF SPADES?" A fair question, I thought, as the nice lady at the next table looked over to see what the ruckus was.

I also know that my partner has exactly three high card points (in real bridge, South would be known to hold 18-19 HCP, so I would also have the information that partner is very limited. Of course, in real bridge the South hand, if dealer, would likely be dummy, making this a very different hand). If those points happen to be the K, it's possible that ducking the J could be embarrassing when partner just has a bunch of spades to cash, but my 8-year-old hates leading away from honors and is one of the most passive defenders I've ever met. I would put the odds of her having the K on this hand at about 5%, which is uncoincidentally roughly the odds that she forgot that she had the K in between the time when she counted her points and the time that she selected her lead. (As a side note, I'd much rather defend with someone who is far too passive than someone who is far too active, although obviously neither is my preference)

I was pretty sure that if I showed declarer the J and my partner's whole hand was the K, declarer would just take the diamond finesse, since she's not really experienced enough to work out that the finesse is a worse play when it might work. So I decided to convince her that it couldn't work and force her into the technically correct (but fatal) line of play.

As I was dropping them off at school, she said to me:

Daddy, bridge is a really great game; the way you tricked me with the jack of spades was so cool... and kind of mean.

I started to try to convince her that it was a compliment, since I knew that she would count the cards enough to avoid a line of play that "couldn't" work, but she had already gotten out of the car and was trotting off to class.