Hand Evaluation, Opening Bids, and Rebids

Hand evaluation — starter points

The standard deck of cards for the game of bridge contains fifty-two cards. The cards are organized into suits — spades ([??]), hearts ([??]), diamonds ([??]), and clubs ([??]). The sequence spades, hearts, diamonds, and clubs represents the rank order of the suits within the deck. Thus, spades is higher ranking than hearts; hearts is higher ranking than diamonds, etc. The major suits are spades and hearts, and the minor suits are diamonds and clubs.

Each suit contains thirteen cards as follows:

A K Q J 10 9 8 7 6 5 4 3 2

The ace (A), king (K), queen (Q), jack (J), and 10 are called honor cards.

A bridge hand is created by dealing the fifty-two cards to four players, one at a time, so that each player has a total of thirteen cards. Partnerships at the game are the two persons sitting north- south and those sitting east-west. To evaluate the value of your hand, independent of rank, the standard/traditional method promoted by Charles Goren in the late 1940s is to assign values to the honor cards:

Honor Value
Ace 4
King 3
Queen 2
Jack 1
Ten 0
_____________
10

The evaluation method is referred to as 4-3-2-1-0 point count system. Using this method, one observes that a bridge deck contains a total of 40 high card points (HCP). Hence, an "average" hand consists of 10 HCP While the method of assignment is accurate, a computer analysis of bridge hands shows that the point count system (4-3-2-1-0) tends to undervalue aces and tens and to overvalue queens and jacks. Only kings are correctly valued. Using only HCP, a hand with at least 12 HCP is usually opened. More later!

To compensate for the over and undervaluation using the Charles Goren's "standard/ traditional" method, Marty Bergen, ten-time national champion, developed the Adjust-3 method. His 2008 book, Slam Bidding Made Easier, published by Bergen Books, devotes the first one hundred pages to his proposed method. Why adjust three? Because the accuracy of the HCP in a hand depends on the difference of overvalued and undervalued honors by the value of three.

Let's see how the process works. With a dealt hand, one goes through six simple steps to employ the Adjust-3 method:

Step 1: Add up your HCP using the table presented earlier.

Step 2: Count the number of aces and 10s (undervalued honors).

Step 3: Count the number of queens and jacks (overvalued honors).

Step 4: Subtract the smaller number from the larger number.

Step 5: Evaluate the difference:

If between zero and two, make no adjustment.

If within the range three to five, adjust by 1 point.

If six plus (rare), adjust by 2 points.

Step 6: If the number of aces and 10s is more, add;

If the number of queens and jacks is more, subtract

We next apply the method to a few examples.

Hand 1 Hand 2 Hand 3 Hand 4 Hand 5
[??]AKQ105 [??]AK9 [??]A67 [??]A104 [??]K78
[??]10982 [??]KJ3 [??]KQ54 [??]10543 [??]AQ9852
[??]6 [??]J105 [??]Q7 [??]KJ67 [??]A109
[??]J67 [??]5678 [??]J678 [??]K10 [??]A

Hand 1: 10 HCP

three (undervalued) 10A10; two (overvalued) honors QJ

3 - 2 = 1; no adjustment

The adjusted total for the hand is 10.

Hand 2: 12 HCP

three aces and 10s (undervalued); two Js (overvalued)

3 - 2 = 1 no adjustment, but skewed in undervalued honors The adjusted total for the hand is 12.

Hand 3: 12 HCP

three queens and jacks (overvalued); one ace (undervalued)

3 - 1 = 2 no adjustment, but skewed in overvalued honors The adjusted total for the hand is 12.

Hand 4: 11 HCP

four undervalued honors; one overvalued honor

4 - 1 = 3; add 1 HCP; more overvalued honors

The adjusted total for the hand is 12.

Hand 5: 17 HCP

four undervalued honors; one overvalued honor

4 - 1 = 3; add 1 HCP; more undervalued honors

The adjusted total for the hand is 18.

Using the Adjust-3 method of hand evaluation, one may consider opening hands 2-5. However, is there more to the story? Yes. Clearly, if a suit includes AKxxx and another suit contains Axxx, one may take two tricks with the first and only one with the second. Thus, in addition to HCP, one must consider suit length.

After the Adjust-3 process, you must apply the following rule to modify your points for suit length, provided the suit contains at least one honor card: A/K/Q/J/10.

ADD FOR SUIT LENGTH

One additional point for a five-card suit

Two additional points for a six-card suit

Three additional points for a seven-card suit, etc.

In summary, add 1 additional point for each card in a suit over four that contains an honor. However, in addition to suit length, one has to consider dubious honors since they are overvalued.

Subtract 1 point for hands with the following doubletons or singleton honors:

Doubletons: AJ, KQ, KJ, QJ, Qx, Jx (quick tricks = 1, ½, or 0)

Singletons: K, Q, J (½, or 0 quick tricks)

Note that AK, AQ, Ax, and Kx are excluded doubletons.

Last, you must adjust for quality suits — a suit with 3+ of the top-five honor cards.

Add 1 additional point for each quality suit.

In summary, one proceeds through the following steps to obtain the total value of a hand:

Step 1: HCP

Step 2: Adjust-3 (add or subtract)

Step 3: Suit length (add for length)

Step 4: Dubious honors (subtract)

Step 5: Suit quality (add)

Step 6: Total starting points

Completing steps 1–4, one has what Mr. Bergen calls starting points. To open the bidding in the game of bridge (one of a suit), a hand is opened if it has at least 12 starting points in the first seat. There is more to a hand than simply high card points (HCP).

One final comment: in a suit contract, if your shape is 4-3-3-3, 5-3-3-2, 6-3-2-2, or 7-2-2-2, you should downgrade your hand by 1 point for "flatness."

If the shape is 4-3-3-3 and one is considering a notrump bid, also subtract 1 from the total starting points.

Returning to hands 1-5, we apply the process outlined above.

Hand 1 Hand 2 Hand 3 Hand 4 Hand 5
[??]AKQ105 [??]AK10 [??]A67 [??]A104 [??]K78
[??]10982 [??]KJ3 [??]KQ54 [??]10543 [??]AQ9852
[??]6 [??]J105 [??]Q7 [??]KJ67 [??]A109
[??]J67 [??]5678 [??]J68 [??]K10 [??]A

Hand 1: HCP 10
Adjust-3 0
Suit length add 1
Dubious honors none
Suit quality add 1
Starting points 12

Hand 2: HCP 12
Adjust-3 0
Suit length none
Dubious honors none
Suit quality none
Flatness subtract 1
Starting points 11

Hand 3: HCP 12
Adjust-3 0
Suit length none
Dubious honors subtract 1
Suit quality none
Starting points 11

Hand 4: HCP 11
Adjust-3 1
Suit length none
Dubious honors none
Suit quality none
Flatness subtract 1
Starting points 11

Hand 5: HCP 17
Adjust-3 1
Suit length add 2
Dubious honors none
Suit quality none
Starting points 20

Counting only HCP, one would have opened hands 2, 3, and 5; however, using Bergen's starting points method, one only opens hands 1 and 5. Also observe that the hands have at least two quick tricks.

Basic rule: Open a bridge hand one of a suit with at least 12-21 starting points and two quick tricks (in the first or second seat). The rule is relaxed in the third seat, more on this later.

The first step at the bridge table is that all players evaluate their hands; the process begins by the person designated dealer. The person with 12 starting points opens the auction by bidding (there are exceptions called preemptive bids and strong two-level bids to be discussed later). As the auction progresses, the value of your hand may increase or decrease depending upon what you learn from your partner and your opponents. To keep the process simple at this juncture, suppose one person has a sufficient number of starter points to open a hand one of a suit with no interference.

Many players will open a hand with only 11 starter points (seats one and two). This is a modern- day practice, since it is important to get your bid in as soon as possible. However, one should have two quick tricks and a five-card suit. Never open a balanced 11-point hand.

Another facet of the game one must consider when bidding is vulnerability. In general, there are four situations. The two pairs are nonvulnerable, two pairs are vulnerable, one pair is vulnerable, and the other pair is nonvulnerable. The value of tricks (won or lost) depends upon the vulnerability of your pair. More on this later!

Opening notrump bids

Having sufficient starting points to open, the first goal is to describe your hand to your partner. When you open, you may have a balanced hand, an unbalanced hand, or a semibalanced hand. A hand with a singleton or a void is, by definition, unbalanced (35.7 percent). The patterns that do not contain a singleton or a void are 4-4-3-2, 5-3-3-2, and 4-3-3-3 (47.6 percent) and are called balanced hands; semibalanced hands are hands with the following patterns: 5-4-2-2, 6-3-2-2, and 7-2-2-2 (16.7 percent). A frequency table of hand patterns follows.

When you open the bidding, you first want to communicate to you partner whether you have a balanced or nonbalanced (unbalanced or semibalanced) hand. However, if the semibalanced hand has honor cards (AKQJ) in two of its doubletons, it may be considered balanced. When hands are balanced, one usually opens the hand with an opening notrump (NT) bid. Because roughly 50 percent of the hands dealt are balanced, many hands are opened using the notrump bidding scheme. In addition, it is used to describe rebids by an opener when bidding one of a suit. When bidding notrump, you are saying to your partner, "I have a balanced hand"; suit bids often convey nonbalanced hands.

Playing bridge the 2/1 way, the notrump ranges for NT bids and rebids follow.

Opening notrump bids Opener notrump rebids

1NT = 14/15-17 starter points 1NT = 12-14 starter points

2NT = 20-21 starter points 2NT = 18-19 starter points

Opener may make an artificial and forcing opening bid of two clubs and then rebid notrump with 22-24 starting points; more on this in chapter 4. Interference is common over 1NT openings; bidding strategies are discussed in chapter 9.

While some will open 3NT with 25-27 starting points, this will not be the case in this book. We will use the Gambling 3NT bid. Playing 2/1, the Gambling 3NT bid shows a solid seven-card suit and denies holding an ace or a king (in the third or fourth seat, it may include an outside ace honor); more on opening 2[??] and 3NT in chapter 4.

An opening bid of 1NT usually shows stoppers in at least three suits where a minimum stopper is defined as Qxx. However, never open 1NT with Jxx or less in a major.

When opening 2NT, you should have all suits stopped; however, some may open it with an honor doubleton, hoping his partner has the suit stopped. To reach game in a notrump contract, the bid is 3NT (for example, the bidding sequence may be simply 1NT-2NT-3NT), both hands combined usually require 26 starting points; however, with long suits and points balanced between the two hands, only 24 starting points may be needed. To make a game in notrump, you must take a minimum of nine tricks out of thirteen.

If you take twelve tricks (the bid is 6NT), you have made what is known as a slam. To make a (small) slam usually requires 33 starting points in the two hands. And if you take all thirteen tricks (the bid is 7NT), you have taken all of the tricks, a grand slam; to make a grand slam normally requires approximately 37 starting points. The goal of a partnership when bidding is to determine whether one has enough points for a partial notrump contract, a game notrump contract, a small slam contract, or grand slam contract.

Let's apply our methodology (yes, it applies when opening a major or notrump).

Step 1: HCP

Step 2: Adjust-3

Step 3: Add for suit length

Step 4: Subtract for dubious honor doubletons/singletons

Step 5: Add for suit quality

Step 6: Total starting points

A few more examples:

Example N1 Example N2 Example N3 Example N4
[??]KJ [??]KJ6 [??]K9 [??]98
[??]AQ4 [??]A104 [??AQ5 [??]AKJ2
[??]A108 [??]AQ8 [??]K8 [??]102
[??]Q10854 [??]AK96 [??]K109874 [??]AKJ42

Example N1

Step 1: 16 HCP

Step 2: (Undervalued honors = 4) - (overvalued honors = 3) = 1; no adjustment

Step 3: Add 1 for suit length

Step 4: Subtract 1 for dubious doubleton

Step 5: Add 0 for suit quality

Step 6: Total: 16 starting points

Open the bidding 1NT (balanced 5-3-3-2)

Example N2 Step 1: 21 HCP

Step 2: (Undervalued honors = 4) - (overvalued honors = 3) = 1; no adjustment

Step 3: Add 0 for suit length

Step 4: No dubious doubletons

Step 5: Add 0 for suit quality

Step 6: Flatness subtract 1

Step 7: Total: 20 starting points

Open the bidding 2NT (balanced 4-3-3-3)

Example N3

Step 1: 15 HCP

Step 2: (Undervalued honors = 2) - (overvalued honors = 1) = 1; no adjustment

Step 3: Add 2 for suit length

Step 4: No dubious doubletons

Step 5: Add 0 for suit quality

Step 6: Total: 17 starting points

Open the bidding 1NT (semibalanced 6-3-2-2)

Example N4

Step 1: 16 HCP

Step 2: (Undervalued honors = 3) - (overvalued honors = 2) = 1; no adjustment

Step 3: Add 1 for suit length

Step 4: Subtract 0 for dubious doubletons

Step 5: Add 2 for suit quality (hearts and clubs)

Step 6: Total: 19 starting points

With 19 starting points, you should not open the bidding 1NT (if partner is a passed hand; some may open 1NT with 18 starting point in the fourth seat). With 20 points, you would not open the hand 2NT when holding two worthless doubletons and good suits. You must open the bidding one of a suit.

Before discussing suit bids, one needs to understand what it means to "take tricks" in notrump. To set our ideas, suppose you open 1NT and all other players at the table pass. You have won the contract (1NT), and to succeed, you must take seven tricks. The first six tricks are called your book; hence, to make a 1NT contract, you must take book plus one trick. Similarly, for a contract of 3NT, you must take book plus three tricks or nine tricks.

To capture tricks in notrump, each card in a suit is of decreasing value from the ace down to the 2 (A K Q J 10 9 8 7 6 5 4 3 2). However, the values are only meaningful for the suit led. If you lead, for example a club, only clubs are played, and four cards constitute a trick. The highest valued card in the club suit is the [??]A. When you are unable to follow suit, you may discard any card in your hand; however, if you get in the lead later, you must be careful when discarding. One generally discards cards in other suits with low value.

Because there are no trumps in "notrump contracts," they are the most difficult contracts to make. Tricks are only won with a suit led. To establish tricks in notrump, you want to take advantage of long suits, since these are the source of tricks.

Let's look at an example. You have the following hand: [??]KQ [??]A10 [??]AKQ10753 [??]KQ, and your contract is 3NT. In this hand, you have one spade trick, one heart trick, seven diamond tricks, and one club trick, or ten tricks (ten potential tricks without a heart lead); hence, you may make 4NT. Bidding only 3NT, you can make your contract plus an overtrick. In duplicate bridge, 3NT is worth 400 points if your side is nonvulnerable and 600 points if your side is vulnerable. Each overtrick is worth a score of 30 so that you have made either 430 or 630 points for the contract.