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Contract Bridge

Learning contract bridge—it is quite interesting.

Bidding

System Notes

  • Game-forcing bids
  • Game invitations
  • Do not bid a slam without sufficient reason
  • Do not stop below five of a major without a reason; bid 3NT directly and use a minor-suit bid as a force
  • Defense
    • A low card encourages
    • Discards: odd cards encourage
    • Suit-preference signals: high for the higher suit, low for the lower suit
    • Count signals: high-low shows an even count; low-high shows an odd count

4-4-3-2 is the most likely distribution.

4-4-3-2 is more likely than 5-3-3-2.

Standard American Yellow Card

Under Standard American Yellow Card, an opening bid is determined jointly by high-card points and distribution:

Opening bidHCP rangeDistributionMeaning
1♣12–21At least 3 clubs, sometimes 2Natural; clubs or a balanced hand with no better opening
1♦12–21At least 3 diamondsNatural diamond suit
1♥12–21At least 5 heartsNatural five-card major opening
1♠12–21At least 5 spadesNatural five-card major opening
1NT15–17BalancedNo five-card major; a five-card minor is possible
2♣22+ or a strong hand close to gameAnyArtificial and forcing, the sole artificial strong opening
2♦6–10Six diamondsWeak two, preemptive
2♥6–10Six heartsWeak two, preemptive
2♠6–10Six spadesWeak two, preemptive
2NT20–21BalancedNo five-card major; stronger than 1NT
3♣/♦/♥/♠6–10Seven-card suitPreemptive opening intended to obstruct opponents
3NT25–27BalancedGambling 3NT, occasionally used

Requirements for opening 1NT:

  1. 15–17 HCP under SAYC
  2. A balanced distribution: 4-3-3-3, 4-4-3-2, or 5-3-3-2, with any five-card suit being a minor
  3. No five-card major; with five hearts or spades, normally open 1♥ or 1♠

Stayman Convention

OpenerResponder
1NT2♣ asks for a major, with majors taking priority
2♦: no major
2♥: 4–5 hearts
2♠: 4–5 spades and at most 3 hearts		With enough strength, bid game at 3NT or 4♥/4♠; otherwise invite with 2NT or 3♥/3♠

Jacoby Transfers

OpenerResponder
1NT2♦: 5+ hearts
2♥: 5+ spades
4♦: 6+ hearts
4♥: 6+ spades
2♥ accepts the transfer
2♠
4♥		With enough strength, bid game at 3NT or 4♥/4♠; otherwise invite with 2NT or 3♥/3♠
  • The first round identifies the suit.
  • The second round uses point strength to decide whether to bid game.

Bid good hands slowly; place weak hands quickly.

Roman Key Card Blackwood

4NT asks for aces/key cards.

Todo

Mathematical Bidding System (SJTU)

First Round

  1. 1♣ opening
    1. 16+HCP
    2. Two suits headed by AK, 14+ HCP (8W)
  2. 1♦: 10–15, no more than four cards in a major; game forcing
  3. 1M: 10–15, at least five cards in the major; game forcing
  4. 1NT
    1. Both vulnerable: 13–15
    2. Unfavorable vulnerability: 15–17

Second-round responses:

2M to stop.

2♦ game forcing.

2♣ invites game.

Competitive and Defensive Bidding

First Defensive Call

double：

Two-Suited Overcalls

Non-vulnerable: no weak two-suited hands.

Vulnerable: at least 6W.

Cue Bids

  • (1Y → 2Y): cue-bidding a minor shows two 5+ card major suits
  • (1M → 2M): shows the other major
  • (1Y → 2NT): shows the two highest-ranking suits other than Y

Ways to Establish Tricks

Opening lead:

Lead high from weakness and low from strength.

1. High-Card Tricks

2. Long-Suit Tricks

  • In notrump, an established long suit wins tricks directly.

  • In a trump contract, a long suit can discard losers and establish tricks.

Notrump

Long-suit tricks exploit length. If declarer and dummy hold seven spades, the defenders hold six. Provided there is an entry in another suit, the final spade can win a trick even if it is the two.

Trump Contracts

Discarding Losers on Dummy’s Long Suit

Suitable when at least two of these three conditions hold:

  1. Dummy has a sufficiently long and strong suit

    • Length: at least five cards; six or more can almost always be established
    • Strength: ideally honors such as AKQ—for example, dummy’s ♣AKQxxx. Even one honor such as ♣Axxxx may work, but requires more finesse or development

  2. Declarer has unavoidable losers

    • Losers that cannot be removed by a finesse or ruff—for example, three heart losers with no heart honors and no spare trumps

  3. Declarer can draw all opposing trumps

    • For example, if declarer holds ♠AK and the opponents have only two trumps, drawing them prevents the defenders from ruffing the established long suit

Steps:

  • Draw trumps first so they cannot interfere with the long suit
  • Establish the club suit by cashing its honors
  • Use the remaining clubs to discard small losers in other suits
Establishing Declarer’s Long Suit by Ruffing

Best when all three conditions hold:

  1. Declarer has a long suit without honors

    • Length: at least five cards, such as ♦xxxxx
    • Strength: lacks AKQ-type honors; the opponents may hold ♦AKQ while declarer has only small diamonds

  2. Dummy is short in that suit

    • At most two cards, ideally one or two, allowing dummy to ruff the opponents’ honors

  3. There are spare trumps available

    • Retain at least two trumps for ruffing—for example, with five trumps, two may be used or drawn while three remain for two ruffs

Clearly unsuitable situations:

  • Dummy has three or more cards in the suit, so it cannot ruff early enough
  • Too few trumps remain—only one, for example—to ruff repeatedly
  • The opponents are short in the suit, in which case repeated ruffing is unnecessary

Procedure:

  • Do not draw trumps first; lead a small card and let the opponents win a trick
  • Regain the lead and ruff the next round in dummy
  • Continue leading small cards from the long suit and ruffing
  • After the opposing honors have been exhausted, draw trumps and cash the established long-suit winners
Crossruff
Elimination and Endplay

After drawing the opponents’ trumps, eliminate one suit from your own hand while retaining a strong suit and trumps.

  • If the opponent leads a trump or a suit in which you are void, ruff in one hand and discard from the other.
  • If the opponent leads your strong suit, you receive a free finesse.

3. Finesse

A finesse attempts to win a trick with a card below an opponent’s missing honor, based on placing that honor in the left- or right-hand opponent’s hand.

Finessing with AQ Against the King

Lead a small card toward AQ. If the king lies between the leader and the AQ hand, the finesse succeeds, with a prior probability of 50%.

1. Declarer Holds AQ and Leads Low from Dummy
  1. The king is with the right-hand opponent:
    1. If they play the king, cover with the ace and secure two tricks
    2. If they do not, play the queen and secure two tricks
  2. The king is with the left-hand opponent: playing the queen cannot successfully finesse it
    1. If the opponent covers, only one trick is immediate
    2. If they do not cover, the queen wins for now
2. Dummy Holds AQ and Declarer Leads Toward It
  1. If declarer’s left-hand opponent plays the king, dummy covers with the ace and wins two tricks.
  2. If that opponent does not play the king, dummy plays the queen, hoping the king is not on dummy’s right.

“Eight Ever, Nine Never”

Conditions:

  1. Declarer and dummy jointly hold eight or nine cards in a suit
  2. The missing key card is the queen
  3. The goal is to win every trick in the suit

Strategy:

  1. With eight cards, finesse:
    1. A queen finesse succeeds about 50% of the time.
    2. Cashing AK drops the queen only when it is singleton, roughly 14.3% under the simplified estimate.
  2. With nine cards:
    1. Cashing AK succeeds about 76.2% when the queen is singleton or doubleton.
      1. With a singleton queen, the king drops it immediately.
      2. With a doubleton queen, the king draws a small card and the ace captures the queen next.
      3. With a three- or four-card queen holding, AK will not drop it and one trick is lost; this is estimated at about 23.8%.
    2. A simple queen finesse succeeds only 50% of the time.

Defense

Against strength, lead length; against weakness, lead shortage. With strength nearby, attack nearby; with weakness nearby, attack farther away. Attack dummy’s strong long suit according to position.

Discard from three, retain four; third hand plays high, second hand plays low. A three-card holding may be discarded from, while a four-card holding is preserved as a possible long suit.

Signaling System

  1. Count signals

    1. High-low shows an even count; low-high shows an odd count.

  2. Attitude signals

    1. When following suit, low encourages and high discourages.

    2. On discards, odd encourages and even discourages.

      1. With an even discard, a low card indicates preference for the lower-ranking suit.

  3. Suit preference: high asks for the higher-ranking suit and low for the lower-ranking suit, often used when arranging a ruff.

Trump Contracts

Do not underlead an ace; an ace lead promises the ace. Lead a strong long suit to create a ruff for partner.

​

Entries and Communication

The ability to transfer the lead between declarer’s hand and dummy.

To be continued.