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{{short description|Playing of contract bridge with computer software}}
{{refimprove|date=October 2016}}
'''Computer bridge''' is the playing of the game [[contract bridge]] using computer software. After years of limited progress, since around the end of the 20th century the field of computer bridge has made major advances. In 1996 the [[American Contract Bridge League]] (ACBL) established an official World Computer-Bridge Championship, to be held annually along with a major bridge event. The first championship took place in 1997 at the North American Bridge Championships in Albuquerque. Since 1999 the event has been conducted as a joint activity of the American Contract Bridge League and the [[World Bridge Federation]]. Alvin Levy, ACBL Board member, initiated this championship and has coordinated the event annually since its inception. The event history, articles and publications, analysis, and playing records can be found at the official website.

== World Computer-Bridge Championship==
The World Computer-Bridge Championship is typically played as a round robin followed by a knock-out between the top four contestants.<ref>[http://www.computerbridge.com ACBL/WBF World Computer-Bridge Championship Official Site]</ref><ref>[http://www.jackbridge.com/ewkprt.htm World Computer Bridge Championship - List of contestants and their links]</ref> Winners of the annual event are:
{{columns-list|colwidth=15em|
* 1997 ''Bridge Baron''
* 1998 ''GIB''
* 1999 ''GIB''
* 2000 ''Meadowlark Bridge''
* 2001 ''Jack''
* 2002 ''Jack''
* 2003 ''Jack''
* 2004 ''Jack''
* 2005 ''Wbridge5''
* 2006 ''Jack''
* 2007 ''Wbridge5''
* 2008 ''Wbridge5''
* 2009 ''Jack''
* 2010 ''Jack''
* 2011 ''Shark Bridge''
* 2012 ''Jack''
* 2013 ''Jack''
* 2014 ''Shark Bridge''
* 2015 ''Jack''
* 2016 ''Wbridge5''<ref>{{Cite web|url=https://www.allevybridge.com/allevy/computerbridge/2016scores.html|title=20th Ourgame World Computer-Bridge Championship|website=World Computer-Bridge Championship|access-date=3 November 2019}}</ref>
* 2017 ''Wbridge5''<ref>{{cite web |url=https://www.allevybridge.com/allevy/computerbridge/2017_scores5.html |title=21st World Computer-Bridge Championship |website=World Computer-Bridge Championship |access-date=3 November 2019}}</ref>
* 2018 ''Wbridge5''<ref>{{cite web |url=https://www.allevybridge.com/allevy/computerbridge/2018_scores.html |title=22nd World Computer-Bridge Championship |website=World Computer-Bridge Championship |access-date=3 November 2019}}</ref>
* 2019 ''Micro Bridge''<ref>{{cite web|url=http://www.allevybridge.com/allevy/computerbridge/2019_scores.html |title=23rd World Computer-Bridge Championship December 2-7, 2019 San Francisco, CA, USA at the ACBL's NABC |website=World Computer-Bridge Championship |access-date=14 December 2019}}</ref>
* 2020- championships cancelled
}}
Since 2022, "Unofficial Computer Bridge Championships" have been held.<ref>{{cite web|url=https://robot-bridge.co.uk |title=Christine Goulden's Robot Bridge Site|website=World Unofficial Computer Bridge Championship |access-date=24 December 2023}}</ref> The format is a round-robin event, followed by a semi-final and then a final, with scoring in IMPs (and Victory Points may be used to resolve ties). In 2022, due to "technical difficulties" the round-robin was replaced by a quarter-final.

Winners of the annual event are:

* 2022 ''Wbridge 5.12''
* 2023 ''Qplus 15.3''
* 2024 in preparation
== Computers versus humans ==
In [[Zia Mahmood]]'s book, ''Bridge, My Way'' (1992), Zia offered a £1 million bet that no four-person team of his choosing would be beaten by a computer. A few years later the bridge program ''GIB'' (which can stand for either "Ginsberg’s Intelligent Bridgeplayer" or "[[Charles Goren|Goren]] In a Box"),<ref>[http://www.bridgebase.com/help/3/common/text/index.html?topic=gib Bridge Base Online Help]</ref> brainchild of American computer scientist Matthew Ginsberg,<ref name="Ginsberg">[http://www.cirl.uoregon.edu/~ginsberg/ Ginsberg profile]</ref> proved capable of expert declarer plays like [[winkle squeeze]]s in play tests. In 1996, Zia withdrew his bet. Two years later, ''GIB'' became the world champion in computer bridge, and also had a 12th place score (11210) in declarer play compared to 34 of the top humans in the 1998 Par Contest (including Zia Mahmood).<ref>{{cite web| url=http://www.worldbridge.org/bulletin/98_2%20Lille/pdf/bul_02.pdf | title=Rosenberg Wins Par Contest}}</ref> However, such a par contest measures technical bridge analysis skills only{{clarifyme|date=September 2016}}, and in 1999 Zia beat various computer programs, including ''GIB'', in an individual round robin match.<ref>[http://www.msoworld.com/mindzine/news/bridge/reviews/misc/man.html Foreword to ''Man vs Machine - The Bridge Match of the Millennium''] {{webarchive|url=https://web.archive.org/web/20060514115301/http://msoworld.com/mindzine/news/bridge/reviews/misc/man.html |date=2006-05-14 }}</ref>

Further progress in the field of computer bridge has resulted in stronger bridge playing programs, including ''Jack'' <ref>[http://www.jackbridge.com/eindex.htm Jack homepage]</ref> and ''Wbridge5''.<ref>[http://www.wbridge5.com WBridge5 homepage (in French)]</ref> These programs have been ranked highly in national bridge rankings. A series of articles published in 2005 and 2006 in the Dutch bridge magazine [[List of significant bridge books and magazines|''IMP'']] describes matches between five-time computer bridge world champion ''Jack'' and seven top Dutch pairs including a [[Bermuda Bowl]] winner and two reigning European champions. A total of 196 boards were played. ''Jack'' defeated three out of the seven pairs (including the European champions). Overall, the program lost by a small margin (359 versus 385 [[International Match Point|IMPs]]).{{volume needed|date=September 2018}}

In 2009, Phillip Martin, an expert player, began a four-year project in which he played against the champion bridge program, Jack.  He played one hand at one table, with Jack playing the other three; at another table, Jack played the same cards at all four seats, producing a comparison result.  He posted his results and analysis in a blog he titled ''The Gargoyle Chronicles''.<ref>{{Cite web|url=http://thegargoylechronicles.blogspot.com/2009/09/introduction-and-board-1.html|title = The Gargoyle Chronicles: Board 1|date = 15 September 2009}}</ref> The program was no match for Martin, who won every contest by large margins.

== Cardplay algorithms ==
Bridge poses challenges to its players that are different from board games such as [[chess]] and [[go (game)|go]]. Most notably, bridge is a [[stochastic]] game of incomplete information. At the start of a deal, the information available to each player is limited to just his/her own cards. During the bidding and the subsequent play, more information becomes available via the bidding of the other three players at the table, the cards of the partner of the declarer (the dummy) being put open on the table, and the cards played at each trick. However, it is usually only at the end of the play that full information is obtained.

Today's top-level bridge programs deal with this probabilistic nature by [[Monte Carlo method|generating many samples]] representing the unknown hands. Each sample is generated at random, but constrained to be compatible with all information available so far from the bidding and the play. Next, the result of different lines of play are tested against optimal defense for each sample. This testing is done using a so-called "double-dummy solver" that uses extensive search algorithms to determine the optimum line of play for both parties. The line of play that generates the best score averaged over all samples is selected as the optimal play.

Efficient double-dummy solvers are key to successful bridge-playing programs. Also, as the amount of computation increases with sample size, techniques such as [[importance sampling]] are used to generate sets of samples that are of minimum size but still representative.

== Comparison to other strategy games ==
While bridge is a game of incomplete information, a double-dummy solver analyses a simplified version of the game where there is [[perfect information]]; the bidding is ignored, the contract (trump suit and declarer) is given, and all players are assumed to know all cards from the very start. The solver can therefore use many of the [[game tree]] search techniques typically used in solving two-player perfect-information win/lose/draw games such as [[chess]], [[go (game)|go]] and [[reversi]]. However, there are some significant differences.

* Although double-dummy bridge is in practice a competition between two generalised players, each "player" controls two hands and the cards must be played in a correct order that reflects four players. (It makes a difference which of the four hands wins a trick and must lead the next trick.)
* Double-dummy bridge is not simply win/lose/draw and not exactly [[zero-sum]], but constant-sum since two playing sides compete for 13 tricks. It is trivial to transform a constant-sum game into a zero-sum game. Moreover, the goal (and the risk management strategy) in general contract bridge depends not only on the contract but also on the form of tournament (due to differences in scoring systems affecting the optimal general strategy). However, once the game has been reduced to deterministic double-dummy analysis, the goal is simple: one can without loss of generality aim to maximize the number of tricks taken.
* Bridge is incrementally scored; each played trick contributes irreversibly to the final "score" in terms of tricks won or lost. This is in contrast to games where the final outcome is more or less open until the game ends. In bridge, the already determined tricks provide natural lower and upper bounds for [[alpha–beta pruning]], and the interval shrinks naturally as the search goes deeper. Other games typically need an artificial [[evaluation function]] to enable alpha–beta pruning at limited depth, or must search to a leaf node before pruning is possible.
* It is relatively inexpensive to compute "sure winners" in various positions in a double-dummy solver. This information improves the pruning. It can be regarded as a kind of [[evaluation function]], however while the latter in other games is an approximation of the value of the position, the former is a definitive lower bound on the value of the position.
* During the course of double-dummy game tree search, one can establish equivalence classes consisting of cards with apparently equal value in a particular position. Only one card from each equivalence class needs to be considered in the subtree search, and furthermore, when using a [[transposition table]], equivalence classes can be exploited to improve the hit rate. This has been described as ''partition search'' by Matthew Ginsberg.
{{unsolved|computer science|Is the problem of [[decision problem|deciding]] the winner in double-dummy bridge [[Computational complexity theory#Reduction|hard]] in any [[complexity class]]?}}
* Numerous strategy games have been proven hard in a [[complexity class]], meaning that any problem in that complexity class can be reduced in [[Polynomial-time reduction|polynomial time]] to that problem. For example, generalized {{math|x × x}} [[chess]] has been proven {{math|[[EXPTIME]]}}-complete (both in {{math|EXPTIME}} and {{math|EXPTIME}}-hard), effectively meaning that it is among the hardest problems in {{math|EXPTIME}}. However, since there is no natural structure to exploit in double-dummy bridge towards a hardness proof or disproof, unlike in a board game, the question of hardness remains.<ref>{{cite thesis |last=Hearn |first=Robert Aubrey|author-link=Bob Hearn |date=2006 |title=Games, puzzles, and computation |type=Doctoral}}</ref>

== The future ==
In comparison to [[computer chess]], computer bridge has not reached world-class level, but the top robots have demonstrated a consistently high level of play. (See analysis of the last few years of play at [http://www.computerbridge.com www.computerbridge.com].) However see below the Philippe Pionchon's article (1984). Yet, whereas computer chess has taught programmers little about building machines that offer human-like intelligence, more [[Intuition (knowledge)|intuitive]] and probabilistic games such as [[Contract bridge|bridge]] might provide a better testing ground.

The question of whether bridge-playing programs will reach world-class level in the foreseeable future is not easy to answer. Computer bridge has not attracted an amount of interest anywhere near to that of computer chess. On the other hand, much progress has been made in the last decade by researchers working in the field.

Regardless of bridge robots' level of play, computer bridge already has changed the analysis of the game. Commercially available double-dummy programs can solve bridge problems in which all four hands are known, typically within a fraction of a second. These days, few editors of [[List of bridge books|books]] and [[List of bridge magazines|magazines]] will solely rely on humans to analyse bridge problems before publications. Also, more and more bridge players and coaches utilize computer analysis in the ''post-mortem'' of a match.

== See also ==
* [[List of computer science awards]]
* [[Computer Olympiad]]
* [[Monte Carlo method]]
* [[Monte Carlo tree search]]
* [[Importance sampling]]
* [[Hanabi (card game)]]

== References ==
{{reflist}}

== External links ==
*[https://bridgebotchampionship.com/ World Computer-Bridge Championship – ACBL/WBF bridge-bot world championship] (official website)
* {{cite web | url = http://www.bridgeguys.com/CGlossary/Computer/CBProgrammers.pdf | last = BridgeGuys | title = Participating Computer Bridge Software for the World Computer Bridge Championship and the History of these Software Programs | date = 23 October 2013 | archive-url=https://web.archive.org/web/20161108180002/http://www.bridgeguys.com/CGlossary/Computer/CBProgrammers.pdf | archive-date = November 8, 2016}}
* {{cite web|url=https://citeseerx.ist.psu.edu/doc/10.1.1.52.2188 | id={{CiteSeerX|10.1.1.52.2188}}| first = Matthew L. | last = Ginsberg | title = GIB: Steps Toward an Expert-Level Bridge-Playing Program | year = 1999 | pages = 584–589 }}
* {{cite web | url = http://ephman.org/bridgeReview200908.pdf | first = Paul M | last = Bethe | title = The State of Automated Bridge Play | date = January 14, 2010 }}
*  {{cite web
|url=http://www.will-bridge.us/bridge/bridge-artificial-intelligence.htm
|title= Artificial intelligence and Bridge game
|author=Philippe Pionchon 
|date=1984
|work=Le Bridgeur Review
}} Classic analysis of AI applied to bridge.

{{WPCBIndex}}

{{DEFAULTSORT:Computer Bridge}}
[[Category:Contract bridge]]
[[Category:Game artificial intelligence]]
[[Category:Computer science competitions]]