Deal Of The Week: February 4, 2023

A Short History of Highcard Points

And the Notrump System that derives from it

Partner opens a 15-17 1NT as dealer, the next player passes, and you have this hand:

A Q T   Q J 2   A K 9   K Q 9 6  

Pretty exciting; what's the correct call? Think about your answer and we will return to it later.

The Notrump System that is a part of most natural systems is basic bridge knowledge that every player should know, and the history of counting points passes through three great names in bridge history, spanning back a full generation before the current form of the game was devised in 1925.

The first of these was a St. Louis expert player named Bryant McCampbell (1877-1927). McCampbell played mostly auction bridge, the form of the game that preceded contract bridge. In this variant, bidding to 2 and making ten tricks (two overtricks) would be good enough to score up a game, and making twelve tricks (four overtricks) would get you a bonus for a slam, even though the auction had ended at the two-level! Bidding in auction bridge usually ended quickly, except on very rare occasions when both sides competed to buy the contract. McCampbell's 1915 idea of using the 4-3-2-1 point count from a different game called Auction Pitch proved to be useful for evaluating balanced bridge hands, but among his other contributions was the invention of the most common bidding convention in the game to this day: the takeout double.

New ideas take a while to catch on in bridge and seven years after McCampbell first published his 4-3-2-1 idea in his book on auction bridge, New York expert Milton Work (1864-1934) wrote in 1923 that he thought the 4-3-2-1 point count was the best method for measuring the trick-taking potential of two balanced hands. Shapely hands were a world of their own and the first attempts at systemizing them involved honor tricks. Ely Culbertson (1891-1955) became the first bridge celebrity authority, writing a series of books defining his honor trick-based system, playing high-profile matches against other competing systems and their advocates, and developing a bridge industry with magazines, newspaper articles, and teacher accreditation programs. As the Culbertson bidding system became the most popular system in the 1930s, 4-3-2-1 took a back seat to honor trick methods, but Work was by that time the "grand old man" of bridge and continued to promote the method when evaluating balanced hands.

The Culbertson system of honor tricks attempts to determine directly how many tricks two hands will probably make, which involves adding fractions like 3½ to 5¾ and deciding whether 9¼ tricks might be enough for game. (To be fair, fractions in Culbertson are never smaller than halves, but there are many plus and minus factors to consider with some combinations of honors which amounts to the same thing as quarters.) The 4-3-2-1 system uses integers, not fractions, and maps combined highcard point totals to likely levels: 26 for game (25 perhaps for 3NT), 33 for a small slam, 37 for a grand slam. Neither system is perfect, but the final step was taken by Charles Goren (1901-1991), who was an assistant to Work in his final years. Goren's work in editing and ghostwriting Work's newspaper columns established him in the bridge world, and he met an enthusiastic Canadian player named Bill Anderson (1905-1969), an actuary who had spent several years examining Work's 4-3-2-1 system and thought that unbalanced hands might be handled by adding points for distribution when appropriate. Anderson created several other important ideas often forgotten: add a point for hands with three or four aces, which are slightly undervalued in the 4-3-2-1 system, and deduct a point for 4-3-3-3 distribution or no aces at all. Goren took these ideas and produced the 1949 book "Point Count Bidding in Contract Bridge." A much more informal writing style, with clarity over philosophy, teaching examples and useful rules, was a hit with bridge players in the 1950s, and many, many books followed, as well as newspaper and magazine articles, even TV appearances and celebrity co-authors. A young Omar Sharif learned and became hooked on the game by reading Goren's books while waiting in the Egyptian sun for the next shot to be set up by the technical crews.

So what is the Notrump System? It begins with point count totals and the levels a partnership can bid to once they discover what their combined total is. This assumes that both players have balanced hands:


The way we discover how many points partner has, is by making our opening bids and rebids that show balanced hands, promise a limited range of highcard points:

Balanced Range:Strategy:
12-14Open 1 of a suit, rebid 1NT if possible
15-17Open 1NT
18-19Open 1 of a suit, rebid by jumping to 2NT if possible
20-21Open 2NT
22-24Open 2, rebid 2NT
25+Open 2, rebid 3NT

When responder hears that opener has a balanced hand with a limited range, and responder also has a balanced hand, responder picks a middle value in opener's range and adds his or her own points to see what the indicated level is. In the hand above, partner opened a 15-17 1NT and you have a balanced 21, making the total 37, give or take a point.

Often the level will depend whether opener is minimum or maximum for the range. In that case, there are invitational bids that apply to notrump auctions:

Notrump Invite:Notrump Bidder's Choices:Scoring Tiers Involved
2NTBid 3NT with a maximum, pass with a minimumGame or Partscore
4NTBid 6NT with a maximum, pass with a minimumSmall Slam or Game
5NTBid 7NT with a maximum, 6NT with a minimumGrand Slam or Small Slam

Note that each of these is concerned with finding the correct scoring tier, from partscore to game to small slam to grand slam. The 2NT bid that invites 3NT is universally known and works quite well. The 5NT bid that forces 6NT and invites 7NT, works well but is new to most players when it comes up once or twice a decade. The 4NT bid that invites 6NT also works like a charm but is the worst of all for familiarity: it seems to clash with Blackwood, and the wide use of the ten-dollar word quantitative just confuses players. (Actually, all three of these invites can be described with the Q-word.)

There are complications. What if the opponents overcall at the two level and a 1NT rebid is no longer available? What if responder rebids notrump to show a limited balanced hand? And many more to consider. But that is the basic Notrump System that Milton Work devised on Bryant McCampbell's 4-3-2-1 idea, as contract bridge was sweeping the world in the late 1930s, and relegating auction bridge and other earlier variants to history.

More recently we have discovered two more things about balanced hand bidding: two hands of approximately the same strength will tend to do better than the same total mostly concentrated in one hand: 3NT can often be made on 12 opposite 12, but seldom on 21 opposite 4. Entry options, being able to get to dummy or declarer's hand to attack a suit from the right side, allow a good player to pinpoint the locations of missing cards and win more tricks, once the first few missing high cards appear. Another related principle is that fewer points are required when one opponent has opened the bidding: often 23 or 24 combined points are enough for 3NT if you can stop the opponent's suit and an opponent has made the opening bid: for you know where most of the missing high cards are before dummy even appears.

And then came Stayman. Experts leading the way in developing bidding systems eventually discovered that balanced hands where a 4-4 fit in a major happened to exist, usually played a trick better in the suit than in notrump. In money bridge the difference between 620 and 600 was trivial, but in matchpoint scoring it could easily and often be the difference between 80% on a board and 25%. The solution was to use a 2 response to 1NT (3 over 2NT) to ask, and a diamond bid to deny. The name came from the writer of the first article on the convention in 1945, New York expert Sam Stayman, although it was thought up by others on both sides of the Atlantic.

Until Stayman became one of the universally-used conventions, a 2 response to 1NT was a signoff, as were 2-bids in the other suits. The main drawback of Stayman is that to escape to clubs you need to go to the three level. All conventions impose these tradeoffs and the advantage of being able to find a 4-4 major suit fit is worth more than the loss of the escape into 2.

One surprising lesson is that the 2 bid does not gain with two types of hands: 4-3-3-3 responding hands tend to play better in notrump even if partner has a fit for the four-card suit, and responding hands that put the partnership in the 28-31 point range, even if there is a 4-4 fit in hearts or spades, will often make the same number of tricks in notrump as in a suit (sometimes with a little risk to get the extra trick needed).

Stayman is exclusively played after notrump openers but there are ways to play it after opener rebids 1NT or 2NT. Checkback Stayman and New Minor Forcing allow responder to check for 5-3 fits in responder's major, as well as uncovered 4-4 fits in unbid majors after opener rebids 1NT or 2NT. Both are useful conventions that will come up often and help get to the best strain; well worth a look (Wikipedia and many online bridge sites have good descriptions) and some partnership discussion.

The final step in the Notrump System came with the adoption of transfer bids, which emerged in the 1950s and slowly were added to convention cards by experts and scientists first, then gradually by most duplicate players by the 1980s. Mistakes in these bids can be costly and send you into distant danger like the hyperspace button on a 1980s Asteroids console! It's vital that both players agree to play them and discuss which competitive sequences include them.

But they work. Having the opening lead come around to the stronger hand is worth an extra trick on many hands, and the latest transfer technology can find games and slams with less than the normal requirement of points. Transfer bids remove completely the 2-level signoff calls, replacing them with signoffs in majors only (responder transfers and passes when opener bids the actual suit held); with a weak hand in clubs and diamonds, escape is only possible at the three level, and toughing it out in 1NT instead has become more common, occasionally producing nightmare scores!

Like all systems, notrump bidding has tweaks and adjustments (with balanced hands, these are far smaller than the adjustments we make to unbalanced hands to get a more accurate point count picture) that many players use to try to make things even more precise, and we'll discuss those in future. But a basic knowledge of the Notrump System is a good asset for a developing player. Once you learn the numbers in the tables above, you won't have to consult or memorize the much longer tables of responses that newer players rely on; you can work out the best response from your familiarity with the system.

Partner opens a 15-17 1NT as dealer, the next player passes, and you have this hand:

A Q T   Q J 2   A K 9   K Q 9 6  

Partner bid 7NT and my hand was:

K 3 2   A K 8 3   Q 7 4 3   A 2  

I counted winners and came to 13 (three suits with the AKQ and a fourth heart) and claimed at trick one. Was partner correct to bid 7NT by the Notrump System?

Not quite, but it is debatable. 5NT would have been a better call, forcing at least 6NT, and I would probably have bid 7NT with a hand on the good side of 16 (mostly aces and kings, stoppers in all suits). 21 opposite a minimum 15 might have left an opponent with a cashable ace. But it is a great 21-count, with tens and nines and no dubious honours, so maybe 7NT was a brilliant stroke after all!

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