Chapter 2

Point Count

I use these counts: 

• Notrump count. 
• Suit count.  A hand has four different suit counts.
• Shorts known count.  This is a modification to suit count when the short suits in the partnership are known. 

The count rules are followed by the count required for game, slam, and grand slam.  The game and slam counts are based on a combination of bridge arguments and the results of the analysis of Ginsberg's double-dummy deals The links and Appendix 1, which are two paths to the same information, report unmodified computer counts.

Notrump Count

Ace = four, king = three, queen = 2, jack = 1 with a 1 point subtraction for a singleton king, a singleton queen, and a doubleton K-Q.  Add 1 point for a useful five-card or longer suit.

• Game is 25. 
• Slam is 32. 
• Grand slam is 36.  With no long suits in partnership, slam is 33 and a grand is 37.  The computer slam and grand slam counts are lower. 

To subtract a point for a doubleton K-Q was a surprise.

One point for a useful long suit has bridge reasons.

• If the defense fails to find the best lead, we are likely to do better when we have a long suit. 
• The hand is easier to play when we have a long suit. 
• Adding a length point leads to 25 points for a notrump game rather than 24.4 points. 

Each hand has four different suit counts, based upon the value of the hand with each suit as trump.  The suit count is based on the 4321 count, with adjustments for weak honor combinations, trump length, and short suits.

Suit Count

High cards Ace = 4, King = 3, Queen = 2, Jack = 1.  Side singleton honors.  Ace = 3, King = 1, Queen = 0, Jack = 0.  Side doubletons.  A 1-point deduction for K-Q, K-J, Q-J, Q-x, and J-x.  Trump suit length.  Take the trump length and subtract four.  Length -4. The first hand to show five or more trumps adds 1 point.  Short side suits.  Void = 4.  Singleton = 2. Doubleton = 0.  Adjust for the number of short side suits None = -1. Two = +1. Three = +2.

• 4 and 4 need a suit count of 25.
• 5 and 5 need a suit count of 28.
• 6 , 6 , 6 , and 6 need a suit count of 32. 

These agree with the computer game and slam numbers.  At suit there is less guessing of queens and jacks, and Blackwood eliminates some high-count non-slam deals.  A grand should not be based on suit count, but if I did, I would use 37.

An extra point for one player's fifth trump may seem illogical.  However, bidding is more accurate if you do.

One could save words in the suit count rules, but that would often add a step to the counting.  The most common case is exactly one short suit, and, if that is what you have, the number of short suits correction is zero.

It is an error to add your suit count to partner's notrump count.  Suit count is lower than the notrump count in many balanced-hand situations.

• With a 4-3-3-3 pattern, the suit count is one point lower in the four-card suit, and two points lower in the three-card suits.
• With 4-4-3-2 and 5-3-3-2, the suit count is usually one point lower in a three-card suit.  If the hand has a soft doubleton, the suit count is two points lower. 
• With 4-4-3-2 and 5-3-3-2, the suit count is three points lower in the doubleton.  If the doubleton is soft, then a point comes back. 

Partner's bidding shows a singleton or void in one or more suits.  Compute suit count as above, with the following adjustments in suits where shortness exists:

Count Opposite a Short Suit

In the short suit, count Ace = 3, King = 1, Queen = 0, Jack = 0.  Add two points with three or more cards opposite the shortness, as there is some fit. Reduce (short suit) count by one with a singleton or void opposite the shortness, as there is duplication of short values.

• To make 10 tricks, the partnership needs 25 suit points.
• To make 11 tricks, the partnership needs 28 suit points.
• To make 12 tricks, the partnership needs 31 suit points. 
• To make 13 tricks, the partnership needs 35 suit points. 

For example, Q-x-x or longer opposite a singleton is neutral and the net adjustment is zero.  The queen is now worthless, but significant length opposite shortness allows the hand to retain its value.  Honors opposite a short suit are assigned the same value as singleton honors.  Obviously a singleton king opposite a short suit is zero and not one.  The value of a singleton or void opposite a short suit is reduced by one.  Thus, facing singletons add three points to the partnership, rather than four.  I was surprised that both partner's get to count something for facing shorts suits (mirror distributions).  Doing so works better.

The largest shorts known hit occurs with A-K-Q-J opposite a singleton or void.  The hand value drops by six points.  If you have two trumps in this hand, the total hit is nine points.

The analysis for the shorts-known count showed a singleton ace is closer to three than four.  For consistency, a singleton ace is three in the "pure" suit count.

The slam and grand slam numbers have decreased.  You can be pushier in bidding slams when shorts are known.

Chapter 18 applies the shorts known count to specific hands.

This will show that the three count rules can be exercised on a simple looking hand.  This is problem B of the November 2000 Bridge World Master Solvers' Club.  3NT was awarded 100.

		Q 9 2
		K Q T 2
		A 5 4 3
		Q 2
1		1
2		2
3		?

• The East notrump count is 13 points.  The HCP are unchanged, because there is no long suit or weak honor holdings for notrump. 
• The suit count at diamonds is one less.  The doubleton queen of clubs is a one point deduction.  12 points. 
• What is the count at diamonds if partner has a singleton (void) spade?  Count ten in the other suits, add two points for three or more spades, and ignore the queen of spades.  12 points. 
• What is the value at diamonds if partner is short in hearts?  Count seven in the other suits, add the two points for three or more hearts, and count one for the K-Q.  10 points. 

Opener's hand (West) has gone through the following evolution.  When we heard 1 , we thought 12 at notrump and 12 at diamonds (for a Bridge World 1 opening.)  Now I think West has a 6-4-x-x pattern with less than three hearts, and most likely, one heart.  If you accept 6-4-2-1, then 11 high, + 3 for six diamonds, 0 for the doubleton, 2 for the singleton, and 1 for two short suits.  17 suit points at diamonds.  If you argue a 5-4-2-2 pattern is possible, as someone did, then West can be as low as 14 suit points at diamonds.  As a result, it is possible that the 28 points recommended for a minor game is not present, which makes 5 unattractive.

My observations from the data in Appendix 1. 

• One should use different counts at suit and notrump.
• The classical 4-3-2-1 count is good at notrump.  It is not at suit.
• The count needed for game at IMPs is less than the count needed at matchpoints.  You need about one point less to bid a vulnerable game at IMPs than at matchpoints.
• The Appendix 1 data is a guide for developing point count schemes.  All good schemes must count a lot for distribution.
• Each additional trump in the partnership is worth one point.
• A bidding style based on short suits is better than a style based on long suits.
• The value of a short suit depends on the number of trumps.  It increases with trump length until four or five, and then is relatively constant.  Goren was wrong to assign more to a short suit in the dummy.  See Shorts vs Trump Length for more detail.  (Links are given descriptive names here, and take you to where you want to go.  Shorter names are used in the appendix.) 
• At suit, side queens are more like 1.25 points, and jacks are half of that.  Make a correction for a fistful of queens and jacks.
• Aces, at suit, are more like 4.5 points.
• Under the notrump count we need 21, 23, and 25 points to have a good chance of making 1, 2, and 3NT, respectively.  Therefore, at low levels, a trick is two points at notrump.
• Under the suit count, the 1 , 2 , 3 , and 4 numbers are 17, 19.5, 22.5, and 25 respectively.  Therefore, a trick is between 2.5 and 3 suit points.
• You want about 32 points for a small slam.  Increase this number with balanced hands as you do not find queens and jacks like a double dummy solver does.
• The points for a 50-50 play and the average points held to win a certain number of tricks are different.  The difference is over three points at a suit grand slam.  The 50-50 number matters.
• Don't base grand slam bidding on point count alone.
• Marriages, except possibly broken marriages, are no big deal!  I am amazed that, at suit, A-J and A-J-x are worth over a point more than K-Q and K-Q-x.  Suit Marriages
• Unsupported honors at notrump do not lose much.  It is almost okay to use their full value!  Notrump:  Honors and Longest
• The value of an ace depends on the model.  Most models give about 4.5 at a trump contract, but if all you did was count high cards, an ace is worth about 5.3 points.  Suit:  Just High Cards
• Don't let this stuff distract you.  If you counted points more precisely, you could improve your bidding accuracy.  The maximum improvement at notrump is a little under 1%.  It is a little over 1% at suit.  Finding out about the partnership's short suits gains another percent.
• If you use better numbers, it will affect your choice of contract on five deals in 100, and you will be wrong on two of those deals.
• If you lay down aces on defense, you are not getting your money's worth. 

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