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Counting Tricks & Calculating Wins:

Intro to Contract Bridge

What is bridge? Why bridge?

Self-introduction

Bridge basics + practice hands

Probabilities in bridge

More Resources

Jonathan Yue, Amber Lin,�& Kevin Rosenberg

Nov 18th, 2023

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Bridge is derived from Whist

Bridge is a trick-taking game of playing cards originating from Whist (UK, 16^th century)

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Around the World in 80 Days (Jules Verne, 1873)

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Bridge has a short history

Modern contract bridge was designed by Vanderbilt in 1925

Every board has two stages:

1. Auction to form a contract

2. Play to make the contract

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Cards on the Table (Agatha Christie, 1936)

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Celebrities who play bridge

Bill Gates and Warren Buffett play bridge

2010 ACBL Honorary Members

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Celebrities who play bridge

During WWII, Winston Churchill was informed about the German invasion of Soviet Union on a bridge table

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Dwight Eisenhower held Saturday night games at the White House

Jimmy Cayne (CEO of Bear Sterns) was supposedly playing bridge when his company went down in 2008, a big part of the financial crisis

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Bridge has tournaments and professionals

Bermuda Bowl – Would Championship for national teams

NABC (North America Bridge Championship)

Asian Games

Regionals / Sectionals

Clubs

Switzerland won the 2022 Bermuda Bowl

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Bridge has tournaments and professionals

Collegiate!

4^th in 2022 Collegiate

1^st in 2018 & 2019 Collegiate

Kevin Rosenberg

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Bridge is a way to socialize

Make friends! (Photos from the 2023 Collegiate Bridge Bowl)

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Health benefits

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Intellectual stimulus

• Probability, memory, deduction, planning, etc.
• Humans are still better than computers

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Suit and Rank

Bridge uses 1 deck (52 cards, no Jokers)

Cards are evenly divided between 4 players: 13 each

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There are 4 suits, each suit has 13 cards:

Cards should be sorted by suits

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Suit and Rank

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Within each suit,

Ace (A) > King (K) > Queen (Q) > Jack (J) > 10 > … > 2

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Table and Pairs

The 4 players on the table are usually called North (N), East (E), South (S), and West (W)

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North and South are in a team, West and East are in a team. There are no individual scores: your score is the same as your partner’s

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Table and Pairs

If you sit South, then North (your teammate) is your partner

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West and East are your left-hand opponent (LHO) and right-hand opponent (RHO)

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Trick

Every trick starts with a player plays (leads) a card, and then each other player plays a card clockwise

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Main Rule of Bridge: Follow Suit

if you have card(s) in the suit

led, you must choose a

card in that suit to play

Lead

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Discard

If you have no card in the suit led, you choose any other card to play

The highest card in the suit led

wins this trick

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The trick is won by a pair,

but the player who wins

will lead for the next trick

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Lead

Winner

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Keeping Scores (Tricks)

After every trick, the cards are turned over

If your pair wins, you put your card vertically in front of

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you , otherwise horizontally

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After all 13 tricks, count how many tricks your pair has won. Every trick has equal value

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Your pair won 9 tricks

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Your turn!

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Contract, Declarer, and Dummy

The contract is a bet by a pair to win at least a certain number of tricks.

It has 2 components: a number between 1 and 7, and a trump suit.

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(6 + level of contract) is the number of tricks that the declaring side needs to take (out of 13).

One player of the pair becomes the declarer, and their partner becomes the dummy. The LHO of the declarer leads for the first trick (opening lead).

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Dummy

After the first lead, the dummy lays out their hand

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and the declarer plays dummy's hand (declarer names the card that the dummy is going to play)

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Your turn!

There are 3 boards to play.

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Keeping Scores (Points)

If the declarer takes what they have bet, the contract is made. The declarer pair win points, and the other pair (defenders) lose the same amount of points

E.g. 2NT takes 9 tricks, declarer wins 50+40+30+30 = 150 points

If the declarer fails, the contract goes down, declarer loses a certain number of points for each insufficient tricks

E.g. 2NT takes 6 tricks, declarer loses 50+50 = 100 points

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Duplicate bridge

Bridge is not a game of luck!

After every board, players put their cards

back into this box, and this box is transferred

to another four players. Results are compared between tables

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2NTS+1, 150

2NTS=, 120

3NTS-1, -50

Winner

Winner

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5-min Break?

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Restart at 3:17pm

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Next, we are going to talk about cardplay strategy & probabilities!

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Planning

You see the dummy’s hand, and what?

Take 30 seconds to a minute to think!

Count the number of top tricks before playing any card!

Ex: if the contract is 3NT, you need to take __ tricks

If you have can count 9 tricks,

If you have can count 7 tricks,

you need to develop 2 more

you can just cash them!

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How many tricks can you establish?

2

2

1

3 or more

2 or more

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Try some real bridge!

The contract and declarer is:

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How many tricks can you take?

If each defender has 3 cards, you get

5 tricks (3 top + 2 established)

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If one has 4 and one has 2, you get

4 tricks (3 top + 1 established)

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Depends on the distribution!

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How many tricks can you take?

If 3-2 break, you get 5

If 4-1 break, you get 4

If 5-0 break, you get only 3

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If 2-2 break, you get 3

If 3-1 break, you get 2

If 4-0 break, you get only 1

Tricks can come from long suits! (> 3 cards)

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Probabilities

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Try some real bridge!

The contract and declarer is:

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FRIDAY

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Choosing which suit to attack

1. Which suits can you get more tricks in?

2. Which suits do the opponents want you to play? (Don’t play them!)

Ex: BridgeMaster Level 1 A-2

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Trumps

In certain cases, there will be a suit dedicated as the trump suit.

When you run out of a suit, you can play a trump card. A trump card beats any non-trump card.

The highest trump in a round wins the trick.

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Let’s learn some helpful techniques in Trump suit play.

1. Draw the opponent’s trump
2. Use your trump to ruff losers

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Drawing trumps

Often, in a trump contract, you will have many trumps than your opponents (8+)

A good strategy is to draw trumps, where you play multiple rounds of trumps until the opponents run out

It’s important to keep track of how many trumps they have left

Unless you have reasons not to (there are plenty), you should draw trumps asap

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Your turn!

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The purpose of bidding

Recall the power of the trump suit

We want more trumps rather than fewer

But a suit that our side is long in is one that our opponents are short in, and vice versa

The two sides will not come to an agreement

Unless …

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The auction

All players bid for the final contract

Each bid is an offer for the final contract

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The highest bid becomes the contract

3S

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The auction

Starting with the dealer (predetermined), clockwise

When it’s your turn, you can

• pass (and still come in later).
• Make a higher bid

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Higher means larger number or equal number, but higher suit.

Bidding ends with 3 consecutive passes.

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The auction

The contract and declarer is determined by an auction

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The highest bid becomes the contract (5C)

The first person in the pair that bid the strain of the contract becomes the declarer (North declares this 5C)

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High Card Points

High Card Points (HCP): A = 4, K = 3, Q = 2, J = 1

More high cards -> stronger hand

An (imperfect) heuristic for measuring the strength

[?] HCPs in a suit, [?] HCPs in a deck

A hand with [?] HCP is average

♠ ：A963 

♥ ：KQ75 

♦ ：KJ3 

♣ ：A6

♠ ：Q72 

♥ ：J543 

♦ ：10875 

♣ ：K4

♠ ：AJ6 

♥ ：KQ94 

♦ ：AQ72 

♣ ：AK

17 HCP

23 HCP

6 HCP

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How many HCPs are required to play a contract?

Game contract: 3NT, 4H, 4S, 5C, 5D, or higher

Need 25 points between you and your partner to play 3NT, 4H, or 4S. Need 29 points to play 5C or 5D

Small slam: 6 level contracts

Need 33 points

Grand slam: 7 level contracts

Need 37 points

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Golden Fit

You would like to have a lot more cards in a suit than your opponent to play a suit contract in that suit

If your side has 7 cards in a suit, then your opponents only have 6 cards. If you trump once, you don’t have an advantage anymore

If your side has 8 cards in a suit, then the opponents only have 5 cards. This lead is significant

An 8-card fit is called a golden fit. One of the most important goal in bidding is to find whether your side has a golden fit

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Bidding is a language

♠ ：J86

♥ ：93

♦ ：AT765  

♣ ：A62

♠ ：3 

♥ ：AKJT73

♦ ：KQ98

♣ ：T3

1♥ : I have 5+ hearts, 12+ HCP

1NT: I have 6-12 HCP, but usually don’t have 3 hearts

2♦ : I have 4 diamonds, and no more then 18 HCP

3♦ : I also have 4 diamonds, but fewer than 10 points

3♥ : I have 6 hearts but not a lot of points, Is this useful?

4♣ : Yes it is! I have very good diamond support and ♣A or K, and no ♠A or K, do you have slam interest?

4♠ : I do. And I have a spade singleton, do you have extra value?

6♦ : Yes, and I think 6♦ is the correct place

Pass: OK, let’s play 6♦ then

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Practice “mini-bridge” with bidding!

1) Everyone will count their High-card Points (HCP) and recite outloud

2) The side with the most HCP will get to decide the contract. The player on that side with the most HCP will be declarer.

3) The declarer gets to look at dummy and decide the contract. We can start low for now!

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APPENDIX

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Today we learned:

• A brief history of bridge
• Why we play bridge
• Basic rules of bridge (tricks, contracts, declarer, dummy)
• Establishing length, finesses, & probability calculations in bridge

If we have time:

• Introducing trumps

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Uncertain winners

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If W has SK5, can you

win two spade tricks?

What will happen if E has SK?

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Uncertain winners

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If W has SK5, can you

win two spade tricks?

What will happen if E has SK?

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Probability play

For finesses to succeed:

1. play from the correct hand
2. have favorable distribution (50% here)

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You can also play A, hoping W or E has singleton K!

P(finesse) = 50%; P(singleton K) < 3%

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8 ever, 9 never

If you have 8 cards and missing Q, the best way to win all tricks is to play A or K and then finesse – you need to guess which side has Q!

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If you have 9 cards and missing Q, the best way to win all tricks is to play A and K – do not finesse!

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8 ever, 9 never

For 8 cards…

How many possible holdings are there?

C(5,0) + C(5,1) + C(5,2) + C(5,3) + C(5,4) + C(5,5)

1 + 5 + 10 + 10 + 5 + 1 = 32 possible holdings

We group the holdings by the honor card to make it easier to think about when the finesse vs. drop works:

Finesse = 16 / 32 = ~50% & Drop = 10 / 32 = ~31%

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8 ever, 9 never

For 9 cards… it’s a closer exercise…

16 Possible Holdings

Finesse = 8 / 16 = ~50% & Drop = 8 / 16 = ~50%

BUT when it is close, you need to account for the probability of breaks!

The 2-2 break (xx - Qx) that the Drop picks up is more likely than the 3-1 break (Qxx-x) that the Finesse picks up…

So the Drop becomes ~53%!

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Today we learned:

• A brief history of bridge
• Why we play bridge
• Basic rules of bridge (tricks, contracts, declarer, dummy)
• Establishing length, finesses, & probability calculations in bridge

If we have time:

• Introducing trumps

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Play Live Bridge

Berkeley Bridge Club

Sundays 1 pm, Hearst Field Annex B5 with free food!

East Bay Community Bridge Center (Oakland)

Bi-monthly beginner (“99er”) games (with adults)

Center for Bridge Education (San Francisco)

Youth bridge every Saturday afternoon w/ free tacos!

Silicon Valley Youth Bridge (Mountain View)

Youth bridge every Friday night w/ free pizza!

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Learn from Online Programs

BridgeWhiz - free beginner classes with teachers

Tricky Bridge (mobile app) - all the basics

Kida Puzzles (mobile app) - cardplay

Bridge Master - declarer play

Play Against Robots & Friends

Bridge Buddies - great for beginners

Bridge Base Online - most popular bridge site

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Please take a flyer and sign-up for the Berkeley Bridge Club mailing list on your way out!