Ginsberg's 717102 double dummy solutions can be used to determine the best point count system.  The steps in a study are: 

1. Specify the strain and declarer associated with each Ginsberg hand-pair.  Details
    
2. Propose the features in a model. 
3. Determine the value of those features.  Least Squares
4. Develop a score for the model.  Details
5. Repeat steps 2 to 4 for many models. 
    
6. Decide the accuracy for the point count rules you want, i.e. one point, half a point, or whatever.  Decide the number of points for game.  I chose one point accuracy and 25 points for game. 
7. Decide on complexity.  For example, a singleton can have one value, or its value can depend on the number of trumps. 
    
8. Formulate rules using the results of steps 2 to 5. 
9. Calculate a score for the model. 
10. Repeat the last two steps until satisfied. 

The box at the left provides links and scores for various count methods.  The box above clarifies the abbreviations to the links.  The numbers after Notrump and Suit are the number of hand-pairs in the analysis.  Click through the links and observe the value of trump honors, side suit honors, singleton honors, trump length, and short suits.

I define the batting average for N points as the score for bidding game with N or more points and not bidding game with N-1 or fewer points divided by the total cases, and converted to percent.  The score is the average of the batting averages for N = 25 and N = 26.

50-50 Play tabulates the 50-50 counts at game, slam, and grand slam for all the models.  These are computer opinions.  When I examined the notrump grands, I did not want to be in a grand slam on three out of four of those deals.

If the features considered are not obvious from their labels, then 4evanb@cox.net.

The scores improve as you read down the table.  No matter what you do, notrump accuracy does not improve by even 1%.  The links marked "Ch 2" and "NT 4321" are evaluations of my man-made count rules.  The remaining links are evaluations of counts determined through a least squares analyses.  When the counts use fractions, both hands round to the nearest number, and these are added to get the hand-pair count.  The least squares counts are normalized to 25 points for game.  This means 25 points should be a 50% play for game.

My notrump summary: 

• 224168 out of the 1434204 hand-pairs, 15.5%, were used.  In my experience about one of four hands are played in notrump.  I suspect good judgment in including more hand-pairs could shift the bid-game number downward. 
• 4321 is not bad. "NT 4321" tested this simple count.  The 50-50 play for game is 24.40 points.  The batting average using N = 24 and N = 25 is 91.66. 
• Marriages are no big deal. 
• Singleton honors are not much of a detriment. 
• The analysis argues against adding one point for a five-card or longer suit.  In some notrump tables, rows are labeled "High Cards", "Length ", and "Length ".  These are calculations of the value of a long suit as a function of high cards in the hand pair.  Each hand counted only one five-card or longer suit.  Use judgment in adding one point for a long suit. 
• Jacks are half a queen, tens are half a jack, and I suspect nines are half of a ten. 
• Two points wins one trick. 

When I was in college, we sometimes drafted a fourth.  We gave him a quick 4321 lecture, and proceeded with the game.  The "H" suit table shows what we should have told him.  Using the suit count of Chapter 2 improves this score by 3%, doing everything right improves the score by 4%, and learning about all of the short suits in the partnership increases the score by 5%.

The suit scores are in several sections.  Comparisons between sections are less meaningful. 

• All the "suit" hand-pairs.  Suit
• The same hand-pairs where now all of the short suits (suits with less than two-cards), in the partnership are known.  Shorts Known. 
• The hand-pairs without short suits.  Suit — No Shorts
• The hand-pairs with short suits.  Suit — Shorts
• Matching Shorts One hand has 0 or 1 and the other has 0 to 2 in the same suit.  Using different numbers in this experiment and the next found the best correction for matching short suits. 
• Two Stiffs/Void Both hands have 0 or 1 in the same suit. 

My suit summary: 

• 84.5% of the hand-pairs were used in this analysis. 
• Use a different count for suit and notrump. 
• Game is 25.13 points with the Chapter 2 count. 
• Trump honors are worth more than side-suit honors. 
• Aces are worth more than four, and queens and jacks are overvalued. 
• The formula is:  A queen is half a king, a jack is half a queen, and a ten is half a jack.  This has the smell of the Four Aces 6-4-2-1 count.  Listen closely.  This is a suit result and not a notrump result. 
• Short suits are second in importance.  The "HvL T SvL" link (Side honors versus length - Trump honors - Shorts versus trump length)  shows that the short-suit value depends on the number of trumps.  It increases until five trumps and then is relatively constant. 
• Continuing with "HvL T SvL", if you rounded side suit honors to the nearest point: 
  • Four of the six king cases would be reduced by one point. 
  • All of the queen cases would be reduced by one point. 
  • Three of the six jack cases would be reduced by one point. 
• Third in importance is trump length.  If you count short suits, then adding or subtracting one point for each trump over or under four is good.  If you did not count short suits, then each trump would be two-and-a-quarter points ( "H TL".) 
• The SK links are count rules when the bidding finds all of the partnership short suits.  An honor opposite a short suit is about the same as a singleton honor.  In these links you will see a "vs1Bonus", which are of the order of one point.  The hand opposite the short suit adds this bonus.  In doing my black magic, two points as a bonus worked better than one point.  Build a bidding system around determining the short suits in the partnership. 
• A little under three points wins one trick. 

Other computer studies that I have seen assign higher values to the ace.  To see if this is due to the hand-pairs used in the study, I have repeated the studies using different criteria.  Those results are summarized in the tables in this sections.  I used the "H Lng" notrump model, and the "H T S" suit model.  The results depend on the hand-pairs selected.  The hand-pairs with no fits have lower ace values at notrump.  When you sum frequent combinations of honors and then round the sum, more often than not you get the 4321 result.  The quickest way to see this is to look at the "M Lng" table.  Honor combinations always round to the 4321 answer.  If you use balanced hands, you can have nine- or ten-card minor fits, and the value of the ace increases.  On hands that (sort of) work at notrump, the value of the ace is also higher, and you succeed at game with less.  If you willy-nilly notrump on all of the deals, you need more count.  I am surprised it is only a little bit more.

Value of (non-singleton) honors and 24-25 long minor bonus

NT criteria	Notrump Hand-pairs	Ace	King	Queen	Jack	Minor Bonus	Ch 2 NT 50-50 play
No 8 + fits	15.6%	4.17	3.03	1.94	1.08	.20	24.94
No 8 + majors or 9 + minors	34.4%	4.27	2.98	1.83	.98	.27	25.24
No 8 + majors or 9 + minors or NT works	49.2%	4.47	2.99	1.77	.93	.54	24.35
No 8 + majors.  Balanced patterns.  4-3-3-3 4-4-3-2, 5-3-3-2, or 5-4-2-2.	21.5%	4.33	2.98	1.77	.93	.08	25.27
All Deals	100.0%	4.58	2.91	1.63	.84	.06	25.38

The next table is suit results and they complement the notrump results.  Though 4321 is not very good here, I cannot believe we are ever going to switch to a different count.

Value of (non-singleton) side-suit honors. 

Non notrump hand-pairs	Suit Hand-pairs	Ace	King	Queen	Jack	Ch 2 suit 50-50 play
8 + fits	84.4%	4.43	2.61	1.23	.56	25.14
8 + majors or 9 + minor fits	65.6%	4.49	2.59	1.19	.54	25.13
8 + majors or 9 + minors and NT is not okay	50.8%	4.61	2.75	1.31	.63	24.77
8 + majors or unbalanced	78.5%	4.46	2.59	1.23	.57	25.28
All Deals	100.0%	4.34	2.61	1.26	.59	25.22

Some results contradict bridge wisdom.  The most striking result is the low esteem of touching honors.  (Other computer studies agree.)  Touching honors divided between the two hands actually score slightly better at notrump.

A-x-x	K-x-x	Divided honors provide better communication between the two hands.  The ace-king combination gains when the A-K-T is in one hand.
K-x-x	Q-x-x	If they attack, they must lead twice from one specific hand, and as little as Q-9-x will sometimes stop the attack.  If you want two tricks, you prefer K-Q-x.  (At suit, K-Q-x scores better.)
Q-x-x	J-x-x	This is a sure stopper.  If you want a trick in the suit you prefer Q-J-x.

The analysis is complicated by the number of cards in the suit and whether the lower cards are twos and threes, or tens and nines.

The A-Q, A-J, and K-J do score better than the divided cards.  Of course, the double dummy solver always guesses the king-jack combination.

Others have done computer studies.  See articles in the January and February 2000 Bridge World by Alex Martelli.  He describes an investigation of the value of side-suit honors in a specific hand setting.  December 2000 has an article by Marshall Schwartz with comments by Jeff Rubens.  That article applies Martelli's suit results to notrump, which I believe is wrong.  An interesting assertion is that a notrump game is 26 points.

The September 2001 Bridge World has a letter from Doug Bennion.  He uses different criteria in defining notrump hand-pairs, and I think, a different analysis method, and surprise, gets different results.  He uses partnership holdings in the 24 HCP range.  I repeated the least square calculations using 22-26 notrump point hand-pairs, and the effect was minimal.  He defined notrump hand pairs as no singletons, voids, or six-card or longer suit, and perhaps, no eight-card or longer major fit.  He allows nine- and ten-card minor fits, and misses the notrump hand-pairs where one or both hands have a short suit.  The fourth rows of the tables that are one or two screens above here used these constraints.  The least square results are close to his.  However, at notrump, jacks are always more than half a queen, and there is no benefit to touching honors.