FUNDAMENTALS

The ideas underneath every system.

A bidding system tells you what a call means. It does not tell you how much your hand is worth, what game actually requires, or whether to bid one more at the three level. Those questions are the same whether you play 2/1 or Standard American, and getting them right matters more than any convention on the other pages.

ORIENTATION

System-independent by design

Everything on this page applies as written whether you have selected Standard American. A system is an agreement about what bids mean; these are the judgements the agreement cannot make for you.

The through-line is that point count is a starting approximation, not an answer. It is a remarkably good approximation (good enough that it has survived a century) but every idea below exists because there is a class of hand where raw HCP misleads you, and knowing which class you are holding is most of what separates a good bidder from an accurate counter.

EVALUATION

High card points, and where they lie to you

Ace = 4The only card that is certain to take a trick no matter who holds what.

King = 3Takes a trick unless the ace sits behind it and the suit is played from the wrong side. Overvalued singleton, undervalued opposite partner's length.

Queen = 2Needs help. A queen with two small cards behind an ace-king is gold; a bare queen is often worth nothing at all.

Jack = 1Almost always an overbid on its own. Jacks pull their weight only next to other honours, QJ together is worth more than the 3 points suggests, J432 is worth less.

40 in the deck10 per suit, 10 per hand on average. Half the deck (20) is not enough for game; roughly 25 is.

The 4-3-2-1 scale was designed to be simple enough to use at the table, and it buys that simplicity by being slightly wrong in predictable directions: it undervalues aces, ignores tens, and treats a jack as though it were a third of a king. Recognising the predictable errors is more useful than replacing the scale.

EVALUATION

Long suits take tricks

Why length beats pointsA fifth or sixth card in a suit is frequently a trick, because after three rounds the opponents are out. Two small cards in a six-card suit will often take two tricks; the same two cards in a doubleton take none.

Counting length pointsA common convention is +1 for each card beyond four in a suit. It's a rough guide, not a rule: the value depends entirely on whether the suit is likely to become trumps or run.

Rule of 20Add your HCP to the lengths of your two longest suits. If the total reaches 20, the hand is worth opening even below 13 HCP. This is what lets 5-5 and 6-4 hands with 11 points into the auction, where a flat 11 stays silent.

Rule of 15 (fourth seat)In fourth seat, add HCP to your spade length; open with 15 or more. Passing the hand out costs nothing, so the tiebreaker is whether a contested auction would leave you owning the spade suit.

EVALUATION

Voids, singletons and doubletons

Only with a fitThis is the single most misapplied idea in hand evaluation. A singleton is worth points because you can ruff with your trumps. No trump fit, no ruffing, no extra value: opposite a notrump contract a singleton is a liability, not an asset.

Void = 5, singleton = 3, doubleton = 1Added to HCP once a trump fit is agreed, and only for shortness outside the trump suit. Shortness in your own trump suit is not an asset.

Shortness opposite honoursA singleton king is worth far less than 3 points. So is a hand whose points are concentrated in its short suits, KQ doubleton opposite partner's singleton is close to worthless. Points sitting in your long suits are worth more than the same points scattered.

The mirror problemTwo balanced hands facing each other take fewer tricks than their combined HCP suggests. Two hands with complementary shortness take more. 26 HCP with 4-4-4-1 opposite 4-4-1-4 will beat 28 HCP of 4-3-3-3 opposite 4-3-3-3 nearly every time.

Shortness and length are two views of the same fact: a hand with a void has extra cards somewhere else. What makes shortness worth counting separately is that its value is entirely conditional on a trump fit, which is why a hand can be worth 12 points opposite one opening bid and 16 opposite another.

EVALUATION

Revaluing as the auction goes

UpgradePartner bids your long suit; you hold a good five-card suit of your own; your honours are aces and kings rather than queens and jacks; you hold two suits rather than a flat 4-3-3-3.

Downgrade4-3-3-3 shape with no fit found; honours in the opponents' suits; queens and jacks sitting under the bidder; a hand whose values are all in short suits.

Aces and tensThe 4-3-2-1 scale undervalues aces and ignores tens entirely. A hand with three aces and a ten is worth more than its raw count; a hand with four queens is worth less. Many strong players add a fraction for each ace and each ten.

Position mattersThe same king is worth more sitting behind the opponent who bid the suit than in front of them. Late in a competitive auction, this is a real consideration in whether to bid on.

A hand does not have a fixed value. It has a value given what you now know, and every call partner makes changes it. The habit worth building is to re-count after each round of bidding rather than deciding at trick zero what the hand is worth and defending that number for the rest of the auction.

EVALUATION

Suit quality

What makes a suit goodTwo of the top three honours, or three of the top five. AQJ32 is a suit you want as trumps; A5432 is a suit you'd rather not name twice.

Why it matters more at higher levelsA one-level overcall on a ragged suit costs little. The same suit at the two level, doubled and vulnerable, is how a good session ends. Suit quality requirements tighten as the level rises.

Solid, semi-solid, brokenA solid suit (AKQxxx) runs opposite a void. Semi-solid (AKJxxx) needs one card from partner. Broken (AQxxxx) needs two. This is what decides whether a long suit is a source of tricks or just length.

EVALUATION

Losing trick count

The countLook at the first three cards of each suit. Every one that is not the ace, king or queen is a loser. A suit shorter than three cards can only hold as many losers as it has cards: that's how shortness enters the arithmetic directly.

Worked example♠AKQ32 ♥A54 ♦K32 ♣43, spades AKQ = 0 losers, hearts A54 = 2, diamonds K32 = 2, clubs 43 = 2. Seven losers.

Using itAdd your losers to partner's estimated losers and subtract from 24. The result is the number of tricks the partnership should take. 7 opposite 7 = 24 − 14 = 10 tricks, which is four of a major.

Rough guide16 combined losers → partscore. 15 → invitational. 14 → game. 12 → small slam. 10 → grand slam.

The catchLosing trick count assumes an eight-card trump fit. Without one it is actively misleading, because it credits shortness that you have no trumps to exploit. Never apply it before a fit is found.

Losing trick count is the most useful second opinion available once a fit is found, precisely because it measures something HCP cannot: it counts what you are missing rather than what you hold, so shortness and length show up directly instead of through a correction table.

EVALUATION

Controls and quick tricks

Counting controlsAce = 2, king = 1. Eight controls between two hands is the rough minimum for a small slam; twelve is the full complement, since the deck holds 4×2 + 4×1 = 12.

First and second roundFirst-round control of a suit means the ace or a void, the opponents cannot take the first trick. Second-round control means the king or a singleton. Slam bidding is largely the business of establishing that no suit is missing both.

Why points aren't enough33 HCP is the traditional small-slam benchmark, but two hands with 33 points and no ace in one suit are down one before declarer plays a card. The count tells you whether you have the strength; the controls tell you whether you have the tricks in the right places.

Quick tricksA different measure, used mainly for opening and doubling decisions. AK = 2, AQ = 1½, A = 1, KQ = 1, Kx = ½. Roughly, a sound opening bid holds two or more.

TARGETS

What game and slam actually require

3NT, 25, or 26 when both hands are shapelyNine tricks with no trump suit to protect you, and shape works against you here rather than for you: distributional hands need nearer 26, because the tricks a shortage wins in a suit contract are simply losers you cannot ruff. The exception is a strong six-card suit that runs. Once it does, the count barely matters: six tricks off the top plus three stoppers is a game on far less than 25.

4♥ / 4♠, about 25 HCP, and often far lessTen tricks, but the fit does the work the points cannot. A 5-3 fit with a singleton often makes on 23; a ten-card fit with a singleton or void opposite a good 20 is a game nobody should be inviting. Two flat hands can fail on 26. This is judgement, not convention: no system documents it, because it is true in all of them.

5♣ / 5♦, about 29 HCPEleven tricks is a big ask, which is why minor-suit game is usually the last resort. With a minor fit and 25-28 points, look hard at 3NT first.

6 of anything, about 33 HCPTwelve tricks, meaning you can afford to lose exactly one. The point count is necessary but not sufficient: you also need first-round control of at least three suits, which is what the ace-asking conventions are for.

7 of anything, about 37 HCPAll thirteen. You need every ace, and a plan for every trick. In practice grands are bid on a source of tricks (a solid suit) rather than on point count alone.

PartscoreBelow about 23 combined, stop as low as the opponents will let you. The most common bidding error is not missing games; it's bidding them on 22 because the hand looked pretty.

These numbers are targets for balanced hands with a normal fit. Every one of them moves with shape. The reason the targets are worth memorising anyway is that they tell you which question you are asking: below 23 you are choosing a partscore, at 23-27 you are deciding about game, and above 30 you have stopped asking whether and started asking how high.

LANGUAGE

Forcing, invitational, sign-off

Sign-off"Pass this." Partner is expected to leave it alone regardless of what they hold. A jump to game and a retreat to two of a minor are both sign-offs.

Invitational"I have a bit extra, you decide." Roughly the top third of the range partner has already announced. Accepting on a minimum and declining on a maximum are equal and opposite errors.

Forcing for one roundPartner must bid again, but the partnership is not committed to game. A new suit by responder is the classic case.

Game forcingNeither partner may pass below game. This is the premise of the two-over-one response in Standard American, and it's what buys the room to explore slowly.

Forcing passIn a game-forcing auction where the opponents have bid on, passing can itself be forcing, it says "I have no clear action, you choose whether to double or bid." Advanced, and worth an explicit partnership agreement.

More auctions go wrong through disagreement about whether a bid was forcing than through disagreement about what suit it showed. When in doubt between two readings of partner's call, the safer error is to treat it as forcing: passing a forcing bid ends the auction permanently, while bidding over a non-forcing one usually just costs a partscore.

COMPETITION

The Law of Total Tricks

The statementThe total number of tricks available on a deal is approximately equal to the total number of trumps held by both sides in their best suits. If you have nine hearts and they have nine spades, about eighteen tricks are available between the two contracts.

What it's forIt answers "should I bid one more?" in a competitive auction without knowing whose hand it is. With nine trumps, compete to the three level. With ten, compete to four. With eight, stop at two.

Why it worksIt is not a law but an empirical regularity, and a good one. The reasoning is that extra trumps mean extra ruffing tricks for whoever holds them, so total trumps and total tricks move together.

Where it breaksIt is least reliable when the honours are concentrated in the short suits, when either side has a double fit (both sides fitting two suits inflates the total), and at high levels. Treat it as a tiebreaker in close decisions, not as arithmetic.

Counting their trumpsYou cannot see the opponents' hands, so you infer: a raise usually shows three, a jump raise four or more, a preempt six or seven. Partner's shortness in their suit implies extra length elsewhere.

The Law is at its best exactly where judgement is hardest: a contested auction at the three level where nobody knows whose hand it is. It converts an unanswerable question (“can we make this?”) into a countable one (“how many trumps do we have?”). See Competitive bidding for the machinery that gets you the information.

COMPETITION

Preemption

The purposeTo consume bidding space before the opponents have used any. A preempt is not an attempt to make the contract: it is an attempt to make the opponents guess, at a level where guessing wrong is expensive.

Rule of 2 and 3Bid to the level at which you would go down two doubled if vulnerable, three if not. The arithmetic: down three non-vulnerable doubled is 500, cheaper than their vulnerable game at 620.

RequirementsA good six-card suit for a weak two, seven for a three-level preempt. Values concentrated in the long suit, and typically fewer than 11 HCP: you are describing shape, and a hand with defence outside is worth more played constructively.

DisciplinePreempt once. Having taken away their room, you have already made your bid; bidding again with the same hand tells partner you had something you did not.

PositionPreempting is most effective in first and second seat, where two unknown hands still have to find each other. In third seat, with partner already a passed hand, you can stretch. In fourth seat a preempt makes little sense: you can pass the hand out instead.

COMPETITION

Vulnerability changes the arithmetic

What it changesThe size of your penalties and the value of your games. Vulnerable game is worth about 500 more than partscore; non-vulnerable, about 300 more. That gap is why aggression pays when vulnerable and sacrifice pays when not.

Favourable (them vul, you not)The best vulnerability for aggression. Sacrifices are cheap, preempts can stretch a level, and light overcalls cost little when they go wrong.

Unfavourable (you vul, them not)The most dangerous. Doubled undertricks are 200 each after the first, and the opponents are not being paid enough for their game to make a sacrifice worthwhile. Discipline here is worth more than flair.

Sacrifice arithmeticA sacrifice is right when the cost is less than the value of their contract. Against a vulnerable game worth 620, going down three doubled non-vulnerable at 500 is a good trade: down four at 800 is not.

Vulnerability is shown on every practice deal for a reason. It does not change what your bids mean, but it changes which of two reasonable actions is right, and at the margins that is most of competitive bidding.

Put it to work

Reading about evaluation is the easy part. Bid some hands and see which of these ideas you actually apply under pressure.

Practice a hand