These opening bids were devised by Mr. Erich Friedman of De Land, Florida, United States, and are based on the Ultimate Club bidding system, and is therefore a variation. Mr. Erich Friedman is a member of the Math and CS Department of the Stetson University in DeLand, Florida, United States. The date of origin is unknown.

Note: Mr. Erich Friedman operates Erich's Place online. A short biographic synopsis is presented at Erich Friedman, whereby he explains that he grew up playing games, including chess, poker, bridge, backgammon, go, and mah jongg, and now teaches a popular game theory course. He enjoys puzzles, and now owns the largest puzzle collection in Florida.

The concept is that an opening of 1 Club is followed by control-showing responses whereas all other openings on the one level are followed by relay bidding. Note that no opening bid has either a variable or multiple meaning.


Opening Bids Only

Bid Strength Meaning
1 : 16 plus high card points Shows any shape.
1 : 11-15 high card points Promises 3 plus Diamonds.
1 : 11-15 high card points Promises 5 plus Hearts.
1 : 11-15 high card points Promises 5 plus Spades.
1 NT: 13-15 high card points Shows balanced shape.
2 : 11-15 high card points Promises 5 plus Clubs.
2 : 11-15 high card points Distribution: 4-4-1-4 or 4-4-0-5 or 4-3-1-5 or 3-4-1-5.
2 : 6-10 high card points Promises 5 plus Hearts and 4 plus Clubs.
2 : 6-10 high card points Promises 5 plus Spades and 4 plus Clubs.
2NT: 14-15 high card points Promises 5 plus Diamonds and 4 plus Clubs.

Note: Mr. Erich Friedman, as as student of the Rose-Hulman Institute of Technology together with his co-student Mr. Doug Jungreis of Harvard University, wrote a Theorem while visiting the University of Minnesota, Duluth, Michigan, United States, regarding the subject How Many Bridge Auctions? This theorem can be found on the Internet and is also only archived and preserved on this site in .pdf file format for future reference.

Below is the entire thesis including the mathematical formula.

How Many Bridge Auctions?

Erich Friedman
Student, Rose-Hulman Institute of Technology

Doug Jungreis
Student, Harvard University

In normal games of bridge, only a small fraction of the possible auctions (that is, sequences of bids and passes) are ever used. One might therefore might be surprised at the actual number of distinct auctions.

The game of bridge is played with four players comprising two teams, North-South, and East-West. We will assume that North opens the bidding, which proceeds clockwise. Each player bids or passes. The 35 possible bids are (in increasing order) 1 club, 1 diamond, 1 heart, 1 spade, 1 no trump; 2 clubs, . . . 2 no trump; . . . ; 7 clubs, . . . 7 no trump. Each bid must be higher than the preceding bid. The bidding terminates if all four players pass on the first round, or when 3 consecutive passes occur after the first bid. In place of a pass or bid, a player may "double" the last bid provided that this bid was not made by his partner. For example, South cannot double North's bid if East passes. Following a double, a player may "redouble" provided that he does not redouble his partner's double. There can be no more doubling of a bid after a redouble is made, unless a subsequent bid is made - in which case it too may be doubled and then redoubled.

Theorem: There are (4 (22)35-1) / 3 distinct bidding auctions.

Proof: There are 35 possible bids other than passes, doubles, and redoubles. Every auction involves exactly one subset of these 35 bids. Once the subset is determined, the order of the bids is determined.

Suppose we are given a subset of size b (0<b35). The first of these b bids may be preceded by 0, 1, 2, or 3 passes (four possibilities). In between each of the two bids, there are twenty-one possibilities: three in which no one doubles, six in which someone doubles but no one redoubles, and twelve in which someone redoubles. (Recall that one may not double or redouble one's partner.) After the last of the b bids, there are seven possibilities: everyone passes, or either opponent doubles followed by three passes, or either opponent doubles and either of the last bidder's team members redoubles. This provides the total of 4 x 21b-1 x 7 = 4 (21)b / 3 possible auctions, each of which involves precisely b bids. If b=0, there is one possible auction (everyone passes). Therefore, the total number of possible auctions is:

Acknowledgement: This was written while the authors were visiting the University of Minnesota, Duluth. They were each funded by the NSF (Grant Number DMS-8407498).



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.