The Value of a Hand

High-Card Points

        Most players determine the value of a bridge hand by counting the high-card points (HCP). Here's how it works:

EXAMPLE:

AK85 J742 K9 Q74

This hand has 4 + 3 + 1 + 3 + 2 = 13 HCP.

Distribution Points

        Most players also count points for having good distribution. For example, consider the following two hands:

JT43		JT743
Q64		Q64
AQ3		AQ643
T43		—

They both have 9 HCP, but the second hand is far better than the first. In a spade contract, for example, the second hand will be able to ruff any club tricks, and may be able to establish tricks from the long diamonds.
        I recommend the following system of counting distribution points:

For example, the first hand above is worth only 9 points (with 0 distribution), while the second hand is worth 12 total points (adding 3 points for the void).

9843 8 Q8765 AK5

This hand is worth 11 total points:         2 for the heart singleton,         2 for the diamond queen,         5 for the club honors.

KQ97 AK A942 542

This hand is worth 17 total points:         5 for the spade honors,         8 for the heart suit,         4 for the diamond ace.

Problem Suits

        High cards are worth less in short suits. For example, consider the following hand:

KQ532    K    J7652    T2

The king of hearts will be useful if partner has the ace, but is likely to drop if the opponents have the ace. Clearly the heart suit is not worth a full 5 points.
        There are many more such "problem" suits:

My recommendation for such suits is:

For example, a KQ doubleton is worth 5 points (for the K and Q), and a J singleton is worth 2 points (for the singleton).

Q8654 KJ86 KJ 62

This hand is worth 11 total points:         2 for the queen of spades,         4 for the heart honors,         4 for the diamond suit,         1 for the club doubleton.

AKJT9 KJ73 K8 Q2

This hand is worth 18 total points:         8 for the spade honors,         4 for the heart honors,         4 for the diamond suit,         2 for the club suit.

Bidding

        There are two main questions to answer while bidding:
                1.    What type contract should we play: partscore, game or slam?
                2.    Which suit should be the trump suit (or should be play in notrump)?

Contract Types

        There are four different types of contracts:

Partscores	Games	Small Slams	Grand Slams
1, 2, 3, 4	5	6	7
1, 2, 3, 4	5	6	7
1, 2, 3	4 and 5	6	7
1, 2, 3	4 and 5	6	7
1NT and 2NT	3NT, 4NT, 5NT	6NT	7NT

Let's talk a little about each kind:

        Partscores.    A partscore is any contract below game. As long as you make your contract, the value of a partscore is determined solely by the number of tricks you take:

For example, 2 making 3 and 3 making 3 are both worth 50 + 3 × 30 = 140 points.
        Note then that there is no advantage to playing in 3 instead of 2. Playing in a higher-level partscore simply increases the chance of going down.
        Why then do people sometimes bid 3 voluntarily? The answer is simple: they are exploring the possiblity of game.

        Game.    There are three different kinds of game contracts:

Game Contracts

4 of a major (4 or 4).

5 of a minor (5 or 5).

3NT.

Bidding and making a game contract is worth bonus points:

EXAMPLES:
        1.    4 making 4 is worth 50 + 4 × 30 + 250 = 420 points non-vulnerable, or 620 vulnerable.
        2.    5 making 5 is worth 50 + 5 × 20 + 250 = 400 points non-vulnerable, or 600 vulnerable.
        3.    3NT making 3 is worth 50 + 3 × 30 + 10 + 250 = 400 points non-vulnerable, or 600 vulnerable.

        Note that you must bid a game contract to get the game bonus. Hence 4making 4 is worth 420 points, but 3 making 4 is worth only 170 points.

        Slam.    Contracts at the 6-level known as small slam, and contracts at the 7-level are known as grand slam. Such contract are worth a huge number of extra bonus points:

(NOTE: The points listed above are in addition to the partscore value and game bonus.) As with game, you must bid a slam to get the bonus points.

EXAMPLE:    6 making 6 is worth 50 + 6 × 30 + 250 + 500 = 980 points non-vulnerable.

        Which Kind?    To determine whether you and your partner can make game, you should add the value of your hand to that of your partner's and compare with the following chart:

Game Contract	Points Required
Major-Suit Game (4 or 4)	25 points
Minor-Suit Game (5 or 5)	28 points
Notrump Game (3NT)	25 HCP

Note that only HCP are helpful for notrump: since you cannot trump anything, short suits are not an asset in a notrump contract.
        Though it is not as accurate, you can also use point-count to figure out whether you and your partner have slam:

(NOTE:    The point requirements given are for a suit slam. Notrump slams require 33 or 37 HCP.)
        Much of the purpose of bidding is to determine whether the partnership has enough points for game or slam. For example, consider the following auction:

1 — 2 — 3 — 4

Here is what each of the bids means:
        1:    "I have 13-21 points and a nice spade suit."
        2:    "Partner, I have 6-10 points and support for your spades."
        3:    "I have between 16 and 18 points. If you are in the upper half of your range we may have game."
        4:    "Partner, I am in the upper half of my range (with 8-10 points), so I accept your invitation to game."

Suits and Notrump

        The second important goal of bidding is determinre which strain to play: clubs, diamonds, hearts, spades, or notrump. Here is a good rule to follow:

(NOTE:    An 8-card fit is a suit in which you and your partner have at least 8 total cards.) This rule has many exceptions of course, but it is good as a general principle.

        Finding an 8-card Fit.    The standard procedure for finding an 8-card fit is as follows:

EXAMPLE:    Suppose the two players have the following distributions:

Player 1:	ooo    oooo    oo    oooo
Player 2:	oo    oooo    oooo    ooo

Then the auction should proceed:

1 — 1 — 1 — 2

at which point both partners are aware of the 8-card heart fit, and may concentrate on conveying their strength.

        Finding Asymmetric Fits.    Of course, the procedure above is very good at finding 4-4 fits (fits in which each partner has 4 cards), but will not work for finding 5-3 fits or 6-2 fits, etc.
        Here is the procedure for finding these asymmetric fits:

By the way, you can show a 7-card suit by bidding it three times, and an 8-card suit by bidding it four times.

EXAMPLES:

        1.    Suppose the two players have the following distributions:

Player 1:	oooo    ooo    oo    oooo
Player 2:	ooo    ooooo    ooo    oo

Then the auction should proceed:

1 — 1 — 1 — 1NT — 2

Player 2 is now aware of the 8-card heart fit, and may bid 3 next to make Player 1 aware. (If Player 2 only had 4 hearts, he would bid 2NT instead.)

        2.    Suppose the two players have the following distributions:

Player 1:	oooo    o    oo    oooooo
Player 2:	ooo    ooooo    ooo    oo

Then the auction should proceed:

1 — 1 — 1 — 1NT — 2

Player 2 is now aware of the 8-card club fit, and may bid 3 next to make Player 1 aware. (If Player 2 had a singleton club, he would bid 2NT instead. He should not rebid his hearts with only 5.)

        The Order of Bidding Suits.    When your hand has two suits, obey the following rules for bidding:

EXAMPLES:    For the following two examples, assume that your partner starts with a bid of 1.

        1.    Suppose the two players have the following distributions:

Player 1:	ooo    oo    oo    oooooo
Player 2:	ooooo    oooo    ooo    o

Then the auction should proceed:

1 — 1 — 2 — 2

Player 1 is now aware of the 8-card spade fit, and should bid 2 next. (Player 1 knows that Player 2 has 5 spades since he originally skipped over hearts to bid spades.)

        2.    Suppose the two players have the following distributions:

Player 1:	oo    ooo    ooo    ooooo
Player 2:	ooooo    ooooo    oo    o

Then the auction should proceed:

1 — 1 — 1NT — 2 — 2NT — 3

Player 1 is now aware of the 8-card heart fit (since Player 2 has shown 5 hearts).

        Minors vs. Majors.    In reality, it is much more important to find major-suit fits than minor-suit fits. There are two reasons for this discrepancy:
        1.    Major-suit contracts are worth more (30 points / trick vs. 20 points / trick).
        2.    Major-suit game requires fewer tricks (10 tricks vs. 11 tricks).

ASIDE:    In fact, minor suits are so disadvantageous that players often elect to play in 3NT instead of minor suit game, even if they have a minor-suit fit. Note that the two contracts are worth the same amount (400 points), but that minor-suit game requires two more tricks!

        Because of this discrepancy, players have adopted the following convention:

The purpose is make it easier to find 5-3 fits in the majors. However, the tradeoff is that the first player must sometimes open in a 3-card minor suit. There are exactly four distributions where this occurs:

Distribution	Opening Bid
oooo    ooo    ooo    ooo	1
ooo    oooo    ooo    ooo	1
oooo    oooo    oo    ooo	1
oooo    oooo    ooo    oo	1

EXAMPLES:

        1.    Suppose the two players have the following distributions:

Player 1:	ooo    ooooo    oo    ooo
Player 2:	ooo    ooo    ooooo    oo

Then the auction should proceed:

1 — 2

Both players are now aware of the 8-card heart fit. (Since the 1 bid promised 5, Player 2 was allowed to raise immediatelt with 3-card support.)

        2.    Suppose the two players have the following distributions:

Player 1:	ooo    ooooo    oo    oooo
Player 2:	oooo    oo    ooo    oooo

Then the auction should proceed:

1 — 1 — 2 — 3

Both players are now aware of the 8-card club fit. Player 1 should probably bid 3 next to check for an 8-card major suit fit. (Note that the 1 bid still only promised 4 cards. A major-suit bid only promises 5 if it is the opening bid.)

        3.    Suppose the two players have the following distributions:

Player 1:	oooo    ooo    ooo    ooo
Player 2:	oooo    oooo    o    oooo

Then the auction should proceed:

1 — 1 — 1 — 2

Both players are now aware of the 8-card spade fit. Note that player 2 did not raise the clubs immediately: he knew that Player 1 might only have 3, and he wanted to search for a major-suit fit first anyway. By the way, there is no reason for Player 1 to bid hearts at this point (since a major-suit fit has already been found).

The Opening Bid

        Most opening bids require opening strength — at least 13 total points. (Remember to count both HCP and distribution.)

        Suit Openings.    You must have 13 points to open 1, 1, 1, or 1. Remember the follwing rules when deciding which suit to open:

• Opening in a major suit promises at least 5 cards in the suit.
• If you don't have a 5-card major, you should open the most convenient minor.
• With a strong hand, always bid your longest suit first.

Also remember to open notrump with a balanced hand, if possible.