Once a partnership has discovered a suit fit, then the next step is that the partnership can and should re-evaluate both holdings by adding the distributional points to the total of the high card points in order to assess the possibility of a game contract. If the distributional count does not justify a game contract, then the partnership can safely play in a partscore.

There are several ways to count the distributional points, and these have been devised and used since the beginning of contract bridge. These various methods of valuating distribution with a known fit or even two known fits have been established over time. They have been put to the test at the bridge table, in blind tests comparing with other methods, or even developed during the evolution of the game from the days of Whist through to the days of Auction Bridge and then finally to the very beginnings of Duplicate Contract Bridge.

Most, if not all methods are based on the number of distributional points, which are then, in turn, based on voids and shortness of a suit or even suits.

The Goren Count

The Goren Count was devised by Mr. William Anderson of Toronto, Canada, and adopted and developed by Mr. Charles Goren. The first chart is used by the opener and the distributional points are added only to his high card points.

Void:	3 distributional points
Singleton:	2 distributional points
Doubleton:	1 distributional point

The second chart, showing the Goren Count, applies to the responder, who intends to raise the suit of the found fit of his partner.

Void:	5 distributional points
Singleton:	3 distributional points
Doubleton:	1 distributional point

The responder can also make adjustments to his distributional count, for example, deducting one point for each of the following situations:

1.	responder plans a raise with 3 trumps
2.	responder holds a 4-3-3-3 distribution
3.	responder has an insufficiently guarded high card

The responder, using the Goren Count, adds a distributional point for a King, a Queen, or a Jack in the trump suit provided this does not bring the total number of High Card Points in the trump suit to more than 4.

The Karpin Count

The Karpin Count was named after Mr. Fred Karpin, and his distributional count method was highly successful. Mr. Karpin applied distributional points for suit lengths over four. Therefore, for any 5-card suit, 1 distributional point would be added. For any 6-card suit, 2 distributional points would be added.

However, short suits are counted, when intending to raise the suit of the partner after a fit has been discovered, according to the following chart. These additional distributional points are added to the total of high card points.

With 4 or more trumps:				With 3 or more trumps:
Void:	3			Void:	2
Singleton:	2			Singleton:	1
Doubleton:	1			Doubleton:	0

It was in 1947 when Mr. Richard Miller wrote an published a simple version of the Karpin Count. As a side note, Mr. Victor Porter of Boston, Massachusetts, published a similar distributional point-count method in 1938. He allotted, however, 4 distributional points for each Singleton and Void, and 2 distributional points for each Doubleton in both hands, not only in the hand of the opener as compared to the hand of the responder.

The Culbertson Count

The method of distributional count was published by Mr. Ely Culbertson, a pioneer in the development of the game of bridge, in 1952. His method included, when opening the auction in a suit, counting each card over three in any suit as 1 point in the event that the fourth card does not count in the trump suit. Only when the opening suit has been raised by the partner does the fourth card count 1 additional distributional point. If the opener holds six or more trump, then 2 additional distributional points are added.

The responder counts also 2 additional distributional points when holding six or more trumps and makes the appropriate raise of the trump suit. The responder also evaluates his holding based on the following three guidelines.

1 point is deducted for a 3-card trump support.

1 point is deducted for a 4-3-3-3 distribution.

1 point is added for holding a void or two singletons.

As a side note, before the Culbertson Count was introduced, Mr. Ely Culbertson applied another distributional count method, which included adding distributional points for honor winners and long-suit winners. The total of the combined hands then represented the bidding level to which the partnership could safely bid. Using this method, a supporting hand counted also the ruffing values, but did not count length in any of the side suits.

The Roth Count

The Roth Count was devised and named after Mr. Alvin Roth. This count method quantifies the point-count adjustments in evaluating the hand. It applies the 4-3-2-1 Work point-count for honor cards and the basic 3-2-1 Goren Count for shortness. It adds distributional points for long suits, and 1 point for any 6-card Major suit or for a good 6-card Minor suit. For any 7-card Major suit or for a good 7-card Minor suit, 2 distributional points are added.

The Roth Count depends also upon the degree of a known fit, and the point count is altered accordingly to fit the shortness and length of side suits. The following chart describes the altered point count.

0-2 cards in partner's suit:	no distributional points are counted in a side suit.
3 cards in partner's suit:	a normal 3-2-1 scale of shortness count is applied.
4 cards in partner's suit:	1 additional point for each singleton.
	and 1 additional point if any doubleton is present.

However, if the opener supports the suit of the responder or if the opener rebids No Trump, showing a balanced to semi-balanced hand, then 1 distributional point is added for each card in the suit in excess of four.

Roth Hand Evaluation

This evaluation is based on the Roth Point Count, developed by Mr. Alvin Roth and published 1968 in the book Modern Bridge Bidding Complete by Mr. Alvin Roth and Mr. Jeff Rubens.

The Combination Count

The Combination Count was devised in England, and was developed by bridge players over time. This method uses lengths and shortages immediately. Using the Karpin Count, Karpin length points are supplemented by 2 for a Void and 1 for a Singleton. This treatment applies to both the opener and the responder in all situations and stages of the auction. There are, however, two considerations to be made.

1.	the opening bidder may not count more than 3 distributional points.
2.	in responses and rebids, no partner may count more distributional points than he has cards in the suit of his partner.

Distributional counts were devised to give the partnership a mathematical calculation as to the success of fulfilling the contract, giving the partnership also the foundation as to the level of bidding which could be attained during the auction safely, and to assist learning students. It should be noted that some partnerships do not employ distributional count, and other partnerships rely solely on distributional count. It is, however, important to evaluate and re-evaluate, when necessary, certain holdings, in order to achieve success at the bridge table.

 

If you wish to include this feature, or any other feature, of the game of bridge in your partnership agreement, then please make certain that the concept is understood by both partners. Be aware whether or not the feature is alertable or not and whether an announcement should or must be made. Check with the governing body and/or the bridge district and/or the bridge unit prior to the game to establish the guidelines applied. Please include the particular feature on your convention card in order that your opponents are also aware of this feature during the bidding process, since this information must be made known to them according to the Laws of Duplicate Contract Bridge. We do not always include the procedure regarding Alerts and/or Announcements, since these regulations are changed and revised during time by the governing body. It is our intention only to present the information as concisely and as accurately as possible.