Computer Oriented Bridge Analysis is the result of feeding a computer certain elements of the evaluation and distributional factors of card combinations by Mr. E. Torbjörn Lindelof of Sweden. To some degree the Cobra system is related to the Schenken Club after certain refinements were made to the computer result. Note: Mr. Torbjörn Lindelöf has a personal website.

Evaluation Method via Computer

The Cobra system adheres to its own hand evaluation methods, which were entered into the computer for analysis, and these methods set precise limits on bids. However, the high card point ranges are to a degree only approximations, give or take a few percentages. This is not the case relating to the ranges for No Trump and the 2 Diamonds openings.


The following is quoted from his website:

I learnt the Bridge basics from a book by Charles Goren and became really interested after reading Howard Schenken, Better Bidding in 15 Minutes. This happened during the first years of my first marriage to Berit, around 1960. We just enjoyed a good game with friends, at home, during the days when Bridge was still commonly played as a domestic pastime.

When I arrived in Geneva in the mid-sixties I started a games club at CERN, including a Bridge section, and became interested in the game from a theoretical point of view. I had access to a small computer, normally switched off at night, and used it to design an optimal bidding system which I called COBRA, later published by Victor Gollancz, London (1983).

Bridge and the COBRA bidding system
Mostly for addicts

I am not a great bridge player, not even a good one by national standards. The reason I mention Bridge is that I have written a book, a widely appreciated study of my own, on the art and technique of bidding bridge hands.

Bridge bidding is an activity which requires skill. I have developed a bidding system, called COBRA (an acronym for Computer Oriented BRidge Analysis), published in 1983 by Victor Gollancz, London under the title: The Computer-Designed Bidding System COBRA.

COBRA was developed with the aid of main frame computers, using a technique for studying the trick-winning ability of various cards and combinations of cards, as a function of a number of suggested properties of the whole hand. This study eventually formed the basis for a highly successful hand evaluation method, around which it was comparatively easy to build a complete bidding system. COBRA has few really innovative features, except that it performs at a level of skill which is unusual, even among international masters.

Its strength lies in a strong relationship between bidding rules and hand evaluation as the auction proceeds. The human user of COBRA is not required to take any action whatsoever during the auction except to "calculate" the next bid, just as a computer will perform this menial task.

To be a perfect COBRA user one has to devote quite some time to practice and study. The system is based on a set of very well defined concepts, which have to be understood before one can undertake to use the COBRA Hand Evaluation method, and the bidding rules.

The system is thought to be simple enough, however, for humans to learn. Experience has shown that already the strict application of a proper subset of the COBRA system is often enough to make a "palooka" bid like a master. Experience has also shown that many bridge players cannot believe that a computer could possibly know the right bid in every situation. After having bid something else they often discover that it would have been better to bid just as COBRA dictated!

The original COBRA book is out of print. However, I can send you a pdf-file (you must have Acrobat Reader 4.0 or later) of the around 120 pages COBRA description. To cover cost of distribution and assembly I ask for the equivalent of US $15 in US, Swiss or Swedish banknotes. This also makes you a member of the COBRA Friends informal association, which simply means that you will receive notes from other COBRA users, collected over time.

You may also download two key chapters of the book, Concepts and Definitions, and Hand Evaluation where the unique COBRA hand evaluation method is described.

Torbjörn Lindelöf
Storgatan 7
S-582 23 Linköping

Email Address:

Concepts and Definitions - This is a .pdf file link, which will be automatically opened by your browser in a new window.

Cobra Evaluation - This is a .pdf file link, which will be automatically opened by your browser in a new window.

Mr. Torbjörn Lindelöf, in the following excerpt, gives a review of his devised COBRA bidding system:

COBRA: The Computer-Designed Bidding System
By Torbjörn Lindelöf, published 1983.

"In the very rich fauna of existing bidding systems for contract bridge it is clearly futile to look for one single system that could be said to be better than al other system. One reason is that bridge bidding is too complicated an activity to have been described in the context of a coherent formal theory (based on axioms etc.) and, therefore, that the only way to evaluate a system is to gain experience of it and to study its performance in actual play...

"Using an electronic computer, however, impartial bidding statistics can be obtained for large numbers of deals... The computer can produce the experimental equivalent of many years of actual play in a comparatively short time and thus supply the bridge theoretician with material which he can use to test new ideas...

"COBRA (acronym for "Computer Oriented BRidge Analysis"), is a bidding system which...may be regarded as the result of applying the classical scientific method (i.e. an appropriate combination of analysis, predictions and experimental verification) to the problem of bridge bidding...

"Bridge bidding has been computerised before COBRA, but I believe COBRA to be the first successful attempt to develop a new bidding system designed for and by a computer. Earlier reports of similar work only mention the successful realisation of biding programs based on existing bidding systems, however, the reported success achieved with such programs has never (as far as I know) been said to compete with the achievements of leading world bridge experts. Based upon COBRA performance with a large number of hands from various bidding contests, I claim, however, that COBRA bidding is of world expert standard...

"The book does not describe the COBRA system completely...Instead, the book concentrates on describing the solid bidding framework: unambiguous bidding rules and well-defined concepts; which is basic to the COBRA program. A player who understands this framework will be able to determine, uniformly and unambiguously, the correct bid in any situation."

Besides the personal website of Mr. Torbjörn Lindelöf, we have included several Internet references regarding summaries of COBRA, which the reader might find interesting. However, if the reader would prefer the original concept, then it is strongly suggested that he/she purchase the published book.

Mr. David Grabiner

From Thu Aug 25 19:52:47 1994
Subject: COBRA system summary

COBRA is quite similar to the Schenken system, as described in Schenken's Better Bidding in 15 Minutes; even some of the specific criteria are similar or identical. The COBRA system was optimized by computer. Additional conventions were not introduced if they made a difference of less than .01 IMPs per board. I don't know whether the author of COBRA automatically started with the Schenken system as his basic framework before optimizing the system; it looks as though he may have, since several bids have exactly the same limits, and the responses to 2D, although apparently non-optimal, are essentially identical to those in Schenken's book.

The book includes a system summary; I have used this as an outline but added more details so that I can describe the system rather than giving an outline for players playing against it.

The book is available from:

455 Alfreton Road
Nottingham NG7 5LX
Phone: +44 1159 422615

Hand Evaluation

COBRA evaluates hands both by HCP and PP (playing points). The PP evaluation system is dynamic; its function is to give numerical values to strong suits, well-placed honors, misfits, etc. Humans can talk about "good 14 counts"; while a computer cannot do this, it can say that a particular 14 count is now worth 15, and bid accordingly.

The system is designed so that a partnership with 28 PP can expect to make ten tricks more than half the time; each additional trick requires another three PP.

This is higher than in standard hand evaluation methods; the reasons are that values increase significantly when a fit is found, and that long suits have much greater PP value in COBRA than in conventional methods.

The value of a long suit is one point for a biddable suit (Axxx, KJxx, QJTx, xxxxx), plus one for the next card, plus two for the next card, plus three for every card beyond that. The basic PP also makes adjustments for aces, tens, and unprotected honors.

General Bidding Principles

In constructive auctions, a limiting bid is made whenever possible, with a few exceptions. Limiting bids are raises, rebids of suits, and
natural NT bids, including jumps; they are not limiting when made in forcing auctions unless they cancel the force.

Competitive bidding is based on the law of total tricks. On a competitive auction, COBRA will contract for as many tricks as the partnership holds in trumps, and then double the opponents if the strength is evenly divided and the opponents are above their total
number of tricks. Many competitive overcalls require a minimum difference between the length of the suit bid and the number of cards in the opponents' suit; this allows overcaller's partner to calculate the number of total tricks.

Constructive Bidding

All opening bids (even preempts, but preemptive hands usually reach these totals because of the points for long suits) require at least 13 PP, except in third seat.

1C opening: 18+ PP, 14+ HCP, forcing. Not made on hands suitable for 1NT, 2D, or 2NT openings. A positive response requires two aces, or 9 HCP with 1 1/2 honor tricks, or 10+ HCP; it is forcing to 3NT. Negative responder bids 1D; opener jumps in response to 1D with 23+ PP.

Over 1-level or 2-level interference, most positive hands double. Over 3-level interference, negative doubles are used, but no other

1D/1H/1S opening: Natural. Spades must be biddable, hearts at least Qxxx, diamonds at least xxx. 1NT response to a major is forcing; opener's 2D or 2H rebid shows a biddable suit, 2C is artificial. Limit raises. Weak-suit game tries in minors (partner assumes three losers).

Penalty doubles over non-jump 2-level overcalls; negative doubles over 1-level overcalls and single jump overcalls.

1NT: 15-17 HCP; third seat psyches 1NT 50% of the time if vulnerability is favorable with 18+ PP when the opening would have normally been 1D. 2C is Stayman, 2D and 2H Jacoby, 2S minor-suit Stayman, no Texas transfers. All 3-bids game-forcing; transfer to hearts followed by a 2S bid to sign off in a minor.

2C opening: Natural, rebiddable clubs; may be a preemptive club hand which does not qualify for 3NT or 4C bids. 2D is an artificial inquiry.

Penalty doubles over 2-level intervention; negative doubles over 3-level intervention.

2D opening: Artificial, either a balanced hand with 23+ HCP or a one-suited hand with 8 1/2 playing tricks. Responder shows aces, and may be asked for kings and queens as well.

2H/2S openings: Weak, 6-card or good 5-card suit. 2NT is the only forcing response.

2NT opening: Two-suited hand with singleton or void in spades, 16- HCP, 18-22 PP. Artificial responses of 3C/3D/4C with 0-3/4-7/8+ HCP; other suit responses show long suits.

No special conventions over an overcall.

3C opening: Solid 6-card club suit, hand too weak for 1C and inappropriate for 3NT or 4C. 3D response is Stayman; other responses natural.

3D through 4S: Natural, preemptive, playing strength within 2/2.5/3/3.5 tricks of bid depending on vulnerability (subtract 1/2 trick if the hand has at least a doubleton in all suits higher than the long suit). Preempts above the 4-level are not used.

3NT opening: Gambling, solid minor suit. Slam-bidding conventions: Gerber with Roman responses (4S shows two aces of same color or rank, 4NT two of same shape), 5-ace Blackwood.

Defensive Bidding

Over natural 1-bids or natural 2C: Cue-bid similar to a takeout double, but shows a void in the adverse suit; takeout double promises at least one card in the suit. Responsive doubles through 3S. 1NT shows 18-20 over 1C, 17-19 over 1D, 16-18 over 1H/1S. 2NT over 1-bid unusual, may be any two-suiter over 1S, otherwise two lower unbid suits; 2NT over 2C undefined. Weak jump overcalls.

Over strong artificial 1C or 2C: Double with strong hands, including any hand with at least the strength shown by the artificial bid, or 14+ HCP and no suit good enough to bid at the appropriate level. Jump overcalls are preemptive; simple overcalls need not be.

Over weak 1NT (minimum less than 15 HCP): Penalty double denies singleton or void; any other bid requires one. 2C shows any major-minor two-suiter, 2D shows both majors.

Over strong 1NT (minimum 15+): Penalty double denies singleton or void; any other bid requires one. All overcalls natural and preemptive.

Over preempts: Doubles are optional over 3-bids, penalty over 4H or higher (but double of 4H guarantees four spades), takeout over 4C/4D.

Mr. David Grabiner also wrote a review of the COBRA System being used in several bridge tournaments, which follows below:

COBRA is a computer-designed bridge bidding system, developed by E. T. Lindelof. The system is precisely defined, which makes it possible for computers to use it. Given the current quality of computer bridge-playing programs, it would be interesting to see if a computer can actually bid on an expert level. My analysis suggests that this is the case; COBRA bid about as well as the humans in the 1987 World Championships.

The system is similar to the Schenken Club, as described in Schenken's Better Bidding in 15 Minutes. It does include some additional refinements and conventions.

Lindelof published a book which describes the system; it is available from

455 Alfreton Road
Nottingham NG7 5LX
Phone: +44 1159 422615

The book doesn't give a complete description of the system, but the description is good enough to see how COBRA thinks and bids.

Lindelof tested COBRA on bidding challenge hands from Bridge Magazine, and the hands from the 1959 Bermuda Bowl. The Bermuda Bowl results, in 96 boards:

Italy vs. COBRA: COBRA improved the North American score by 98 IMPS.
North America vs. COBRA: COBRA improved the Italian score by 69 IMPS.

Italy actually won 214-189; thus, if these results are correct, either side could have won by a large margin if it had used COBRA as its bidding system.

The gain of nearly one IMP per board seemed unusually high, and I was suspicious of COBRA's results on a few hands, so I decided to check the results for myself. I have a book of the 1987 Bermuda Bowl and Venice Trophy, with all interesting hands from the final detailed, so I used that for the sample. My criteria were similar to Lindelof's.

I didn't make a comparison if I couldn't tell how the human bidding would continue, or on a few hands in which the description of COBRA in the book was inadequate. Also, some of the British pairs played a forcing pass system, against which I often had no idea how COBRA would defend.

If the humans at the same table reached the same denomination (but not necessarily the same level), COBRA was usually credited with the same number of tricks. I made an allowance if the auction with COBRA would have caused a different result. For example, there was one hand on which COBRA allowed the opponents to make a overcall, which directed the best opening lead; it was credited with the tricks made against this lead, rather than the tricks taken by human declarers whose auction made the overcall impossible.

If humans at other tables reached the same denomination, I tried to pick the normal result from among those results the humans reached. Again, allowances were made if necessary.

If COBRA reached a denomination not reached in any room, I worked out a reasonable result on my own, after reading the expert commentary.

After 128 boards, which was the end of the Venice Trophy, the standings (excluding penalties) were:

Bermuda Bowl: US led Great Britain 241-188.
Venice Trophy: US II beat France 254-219.

COBRA's total swings:
+15 for US men,
+43 for Great Britain,
+18 for France,
-2 for US women,
total +74.

This is in 512 boards, much less than Lindelof's +167 in 192 boards. Part of the reason may be that I don't understand COBRA fully (using the book rather than the full program). Still, it is positive (and that doesn't seem to be be due to good luck), which suggests that the COBRA system is actually capable of bidding at a world-class level when used perfectly.

I looked at all the significant swings (5 IMPs or more), and broke them down by cause, to see where COBRA gained its advantages.

A swing was attributed to luck as well as to another cause if it was not the result of reaching a better contract. For example, there was one deal on which COBRA reached a poor slam which was bid by only one of the four human pairs. When the slam made, the resulting +39 was credited to the "COBRA's judgment luck" category, because it wasn't a result of superior judgment.

System swings (fundamental differences in the system led to a different contract being reached, for reasons unrelated to judgment): +99 and -84 on thirteen boards.

System luck: -13 on one board. On this hand, COBRA systemically didn't open 4H as dealer with ATx of spades. Two humans did, fourth hand made a light takeout double, it was left in, and the contract made with overtricks. When COBRA opened 1H instead, it reached 4H with no double, as happened at the other tables.

COBRA's judgment (decisions to bid slam, play 5C rather than 3NT, etc., which were made by COBRA but not by most of the humans): +240 and -258 on twenty-nine boards.

COBRA's judgment luck: +70 and -44 on six boards. COBRA made a 50% slam (+31); went down in a good slam (-18, because two of four humans went down in games on the same bad breaks); made a bad slam (+39); went down in a good game (-6, because one of the two human pairs that avoided the game went down in a partial); avoided a bad game which made (-11); and reached a good slam which could have been made on a squeeze, but the human declarer in game made only five (-9).

Humans' judgment (COBRA agreed with the human consensus, but one human pair bid differently, or two human pairs had different results, neither of them COBRA's): +99 and -36 on eighteen boards.

Humans' judgment luck: -48 on four boards. The US women bid and made a bad slam (-13); France bid an unmakeable 3NT rather than an unmakeable 5C and then made it on misdefense (-12); and France bid and made two mediocre slams (-12 and -11).

Human misunderstandings: +27 on two boards. The US women had two misunderstandings about 4NT (one whether it was Blackwood or natural, and one whether it was five-ace or six-ace), and got to a slam off two cashing aces (+10) and a grand off the KQ of trumps (+17).

Total: +52, with small swings adding up to the remaining +22.

I had thought that COBRA's biggest gains would have been on the misunderstandings; despite the numbers above, this doesn't seem to be the case in this sample. The humans had six serious misunderstandings, but COBRA cashed in on only two. Two of the six were US misunderstandings over British ferts (one of which led to a lucky gain), which made it impossible for me to obtain a result from COBRA for comparison. The British missed one game on a misunderstanding, but COBRA missed the same game without help from a misunderstanding. And the British had one misunderstanding over their own forcing pass, but landed on their feet.

Instead, COBRA gained on the hands when one human pair made a decision which went against the consensus. This happened 24 times on 22 boards. The human was right only six times, plus one hand on which the two contracts were equally bad but the opponents misdefended against the human. COBRA gained only +15 on these boards, compared with +27 on misunderstandings, but the humans gained a lot from luck on their judgment hands and nothing on the misunderstandings. On the hands in this category, the humans reached three slams not reached by COBRA, all under 50%, and made all three.

When COBRA disagreed with all or most of the human experts, it was wrong as often as it was right, and it would have actually lost points without the benefit of luck. If the six luck hands in this category had gone the other way, they would have been -29, +40, -39, +12, +10, and +11 instead of +31, -18, +39, -6, -11, and -9, for a net gain of +7 rather than +26, and a total of -11 instead of +8 on all of these hands.

Thus it seems that COBRA's judgment may be slightly better than the judgment of any individual expert pair, and comparable to the consensus of experts.

I don't know whether humans playing COBRA could do as well; I had to keep referring back to the book to check point ranges and defensive methods. In fact, in an earlier version of this discussion, I posted two examples of COBRA auctions which reached slams. I then rechecked the book and discovered that the second example auction, which reached a mediocre slam, was incorrect; removing this example from the totals above gained an extra 29 IMPs for COBRA.

Included are also the efforts of Mr. Jan Eric Larsson, who wrote a review of the COBRA system, and which is presented below:

Jan Eric Larsson
Palo Alto, California, May 5th, 1995

1 : Promises 16 high card points and any shape.
1 : Promises 11-15 high card points and a 3-card plus Diamond suit.
1 : Promises 11-15 high card points and a 4-card plus Heart suit.
1 : Promises 11-15 high card points and a 4-card plus Spade suit.
1 NT: Promises 15-17 high card points, balanced distribution.
2 : Promises 11-15 high card points and a 5-card plus Club suit or preemptive.
2 : Promises 23 high card points plus and balanced and/or game forcing.
2 : Promises 9-12 high card points and a 5-card plus Heart suit.
2 : Promises 9-12 high card points and a 5-card plus Spade suit.
2 NT: Promises 11-15 high card points and 5-5 plus in two suits.

A 1 Diamond response after a 1 Club opening is an artificial negative response. All other responses are deemed natural. If the first response after a Major suit opening is 1 No Trump, then this response is forcing for one round.

Using the Cobra bidding system, distributional hands after two passes, in Third Seat, which would generally open the auction with 1 Diamond, will use a Psyche Bid most of the time. This position almost demands an opening of the auction, but the meaning of the opening does not always comply with the requirements of the bid when opened in First or Second Seat.

If the opener shows a large hand by bidding 2 Diamonds, the responder will show controls, the first step being the Aces and then, if possible, the location of Kings and Queens. After a rebid by the opener of 2 No Trump, promising a balanced distribution, and rebid by the responder of 3 Clubs promise 0 to 3 high card points. A rebid of 3 Diamonds promises 4 to 7 high card points, and a rebid of 4 Clubs promises 8 plus high card points.

Since the computer assigned high card point ranges to almost all opening bids, except for Psyche Bids in Third Seat, preemptive opening bids are designed to comply with these ranges by adding a count of 7 points for a good 7-card suit together with the high card points, which generally should be approximately 7 high card points. This total allows the opener to preempt on the Three Level, but if the total is weak as is the 7-card suit, then the better option is to pass and wait.

Defense Mechanisms

Defense mechanisms against Cobra openings take into account the Law of Total Tricks. This feature of defense should be the first guideline applied when considering taking any kind of defensive action. A double of a strong, artificial 1 Club or preemptive 2 Club opening generally promises a moderate to strong hand with strategically placed honors. A cuebid of a natural opening is understood to be the same as a Takeout Double, but the cuebid, in addition, shows a void. A double of a natural opening promises at least one card in the opening suit, but no void.

Any overcalls over a strong 1 No Trump opening are considered natural and preemptive, and are to be viewed as also obstructive in nature. An overcall of 2 Clubs over a weak 1 No Trump opening promises a Minor-Major two-suiter, whereas an overcall of 2 Diamonds promises both Major suits and a two-suiter.

If the opening is a preemptive bid on the Three Level, then the Optional Double is an option. If the opening is a preemptive bid of 4 Clubs and/or 4 Diamonds on the Four Level, then the Takeout Double is applied. Any double as a call after a 4 Hearts preemptive bid or higher is for penalty.



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.


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