Deal Analysis – How to count a hand in bridge

This article was written by the blogger, bridge player and Funbridge player Adrien Rahier. You can find the original French version on his blog 

A short time ago, I got the amazing book “Jouez un tournoi avec moi” (Play a tournament with me) written by Pierre Saporta.
The idea behind this book is both very simple and attractive. You play a tournament as a member of Pierre Saporta’s team (multiple Champion of France) and at the end of each round, he shares his analysis and advice.

To get straight to the point, this book is not at everyone’s level. Indeed, it lays down as a basic principle that you already know how to play bridge (well).

I thought it is a shame that this book is limited to that audience, so I came up with the idea of writing this article which, I hope, will help you better understand how problems are solved in bridge.

BEFORE STARTING, LET’S REVIEW A FEW BASIC RULES:

As bridge is not really one of the easiest games to master in terms of rules, I will do my best to keep things simple here.

Here are the main points you need to know before you continue reading:

• Bridge is played with four players sitting at a table. The players across from each other form two partnerships.
• A bridge game consists of several units called “deals”. On each deal, you play a contract. The contract means that one pair has contracted to make a certain number of tricks. If you take more tricks, then good for you, you will get extra points. If you are not able to take the number of tricks agreed, the contract “fails”.
• In bridge, each player has a hand consisting of 13 cards. The card order is Ace, King, Queen, Jack, 10, 9, etc. However, unlike other games such as belote or coinche, what matters here is only the number of tricks taken, not the number of total points. Following this reasoning, you understand that taking a trick with an Ace or a 4 means the same result.
• Once there is a final contract, the game starts and one of your opponents leads. Then your partner places his hand face up on the table. During the rest of the game, the other three players will see his hand and he remains inactive. And you as his partner will tell him which card to play on each round.

THE PROBLEM

Without going into the technicalities, let me simply tell you that on this deal my partner and I have decided to play 6NT¹.

In a simplified language, it means taking 12 tricks out of 13. 
Spade Jack lead. As expected, your partner places all his cards face up on the table and waits patiently for your instructions.

Your pair’s hands:

A K 9  J 3 2  Q 9 3  Q 10 6 3

–  –  –  –

–  –  –  –

Q 8 6  A Q 10  A K 4 2  A K 4

On this figure you are at the bottom. No-one, except yourself, can see your hand. But everyone can see your partner’s hand (at the top of the figure). And you can’t see your opponents’ hands either. The players play in turn in clockwise rotation. The one who takes the trick starts the next trick.

What do you tell your partner to play to take the 12 tricks of the contract?

THE SIMPLE SOLUTION

IN THEORY

Let’s try to imagine what is going to happen:

• In spades, you will probably take the Jack from your opponents and take three tricks.
• In hearts, you don’t really know where the heart King is so you can only rely on one sure trick so far.
• In diamonds, you have three sure tricks.
• In clubs too, you have three sure tricks.

3+3+3+1 = 10. Two tricks are missing for you to make the contract. Where are you going to find them?

Maybe you have guessed that the answer is in hearts. If the heart King is in your RHO’s hand, you are very likely to make your contract.

In details:

Let’s imagine that you take the spade Jack with your partner’s Ace on the first round. Then he has to play again. Now ask him to play the heart 2.

• If your RHO (the one you think has the heart King) plays his King indeed, you cover with the Ace and make your contract (you take the extra two tricks you needed in hearts with the Queen and Jack).
• But if your RHO stubbornly plays small, you play the 10 from your hand and hope that you will take the trick.

IN PRACTICE

In practice, your RHO plays the 4 (second instance here), so as expected, you play the 10 and you LHO plays the 5. Therefore you take the trick.

Here the idea is to repeat the manoeuver to oblige the opponent to play his King or small. You have to get over to your partner’s hand using spades to be able to play the heart 3 from his hand. Once again, the RHO plays small (heart 9) and you take the trick with the Queen.
With the heart Ace, you now count 12 tricks. Your contract is made.

Tip to shine in society: this manoeuver is called “finesse”.

THE STROCK OF GENIUS

So far, so good. All you needed to make your contract was common sense (and a bit of luck). The vast majority of players will actually win 12 tricks here.

Now, you are young, talented and willing to take tricks, so why not consider maximising your chances to take 13 tricks out of 13?

IN THEORY

First, you may have noticed that I have used the word “maximise” here. Indeed, there are several ways to manage to take 13 tricks.

1. You have 7 clubs together with your partner. As there are 13 cards in a suit, there are 6 left elsewhere. But if these cards split 3-3, your last card will take the trick at the fourth round of clubs.
2. Same thing in diamonds: if opponents’ cards split well, you win.
3. Finally, still in clubs, you can also use the same manoeuver as in the previous section and hope that the club Jack will be in your RHO’s hand.

Let’s now see how you can cumulate chances.

Without committing ourselves, we can already say that we are not taking too much risk by playing three rounds of diamonds to see how they split. In the worst case scenario, if they don’t split well, we will fall back on clubs.

Let’s talk about clubs precisely. To take 13 tricks, your objective will be to know if it is better to focus on how they split or a finesse. You concentrate and count all your LHO’s cards carefully to try to know how many clubs he holds.

IN PRACTICE

Here is what happens at the table:

• In spades, your LHO follows suit three times whereas his partner discards on the third round. So he had 5 spades.
• In hearts, he follows suit twice, then he discards a spade. So he had 2 hearts.
• In diamonds, he follows suit twice, then he discards a club. So he had 2 diamonds (hence you can no longer rely on diamonds splitting 3-3).
• In clubs, he follows suit twice…

You still have two cards to play. Here is the position. So finesse or split?

–  –  –  Q 10

–  –  2  4

If you have followed well, at this stage of the game, you can deduce that your LHO had 4 clubs (13 cards in total – (5 spades + 2 hearts + 2 diamonds)).

By inference, it means that you can kiss goodbye to clubs splitting 3-3 at the last trick.

However, good news is that two rounds of clubs have already been played and your opponent has also discarded another club on a diamond.

(4 cards in hand – 3 cards already played) = your LHO has no more clubs in hand!

Since the other opponent no longer holds any clubs (due to the 4-2 split), no more worries.

You quietly play your club 4, the Jack drops as expected, taken by the Queen². Your last club is a master card. You get 1,020 points here. Joy and excitement in the frenzied crowd!

The full layout was:

A K 9  J 3 2  Q 9 3  Q 10 6 3

J 10 7 5 4  7 5  J 10  J 9 8 2

3 2  K 9 8 6 4  8 7 6 5  7 5

Q 8 6  A Q 10  A K 4 2  A K 4

CONCLUSION

Here you can see the evil side of the thing. With a little bit of logic, you have been able to fully reconstruct one of your opponents’ hands without even seeing it!

In short, if you liked this example, feel free to share this article. You will see that bridge beyond clichés is a very interesting game.

¹6NT means “6 no trump”. Indeed, in bridge it is also possible to play in a specific suit (among clubs, diamonds, hearts and spades) prevailing over others. It is called a “trump”. In our example, it is very simple. There is no trump and each suit has the same value.

²You may have noticed that if your LHO had not discarded a club on a diamond (and still had two clubs at the end), you would have simply played the club 10 (a finesse again!) and then the Queen on the last round. Doomed to be successful!