Tournaments

Bridge is a game of skill played with randomly dealt cards, which makes it also a game of chance, or more exactly, a tactical game with inbuilt randomness, imperfect knowledge and restricted communication. The chance element is in the deal of the cards; in competitions and clubs the chance element is largely eliminated by comparing results of multiple pairs in identical situations. This is achievable when there are eight or more players, sitting at two or more tables, and the deals from each table are preserved and passed to the next table, thereby duplicating them for the next table of participants to play. At the end of a session, the scores for each deal are compared, and the most points are awarded to the players doing the best with each particular deal. This measures skill because each player is being judged only on the ability to bid with, and play, the same cards as other players. However very often even the most skillful play will only succeed some of the time, and the skilled player may be unlucky because an alternative, less expert play achieves a better result. But in the long run the expert player will score better. This form of the game is referred to as duplicate bridge and is played in clubs and tournaments, which can gather as many as several hundred players. Duplicate bridge is a mind sport, and its popularity gradually became comparable to that of chess, with which it is often compared for its complexity and the mental skills required for high-level competition. Bridge and chess are the only "mind sports" recognized by the International Olympic Committee, although they were not found eligible for the main Olympic program.[26] The basic premise of duplicate bridge had previously been used for whist matches as early as 1857. Initially, bridge was not thought to be suitable for duplicate competition; it wasn't until the 1920s that (auction) bridge tournaments became popular. In 1925 when contract bridge first evolved, bridge tournaments were becoming popular, but the rules were somewhat in flux, and several different organizing bodies were involved in tournament sponsorship: the American Bridge League (formerly the American Auction Bridge League, which change its name in 1929), the American Whist League, and the United States Bridge Association. In 1935, the first officially recognized world championship was held. By 1937, however, the American Contract Bridge League had come to power (a union of the ABL and the USBA), and it remains the principal organizing body for bridge tournaments in North America. In 1958, the World Bridge Federation was founded to promote bridge world-wide, coordinate periodic revision to the Laws (each ten years, next in 2017) and conduct world championships. Randomness means different things in various fields. Commonly, it means lack of pattern or predictability in events. The Oxford English Dictionary defines "random" as "Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard." This concept of randomness suggests a non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination. Applied usage in science, mathematics and statistics recognizes a lack of predictability when referring to randomness, but admits regularities in the occurrences of events whose outcomes are not certain. For example, when throwing two dice and counting the total, we can say that a sum of 7 will randomly occur twice as often as 4. This view, where randomness simply refers to situations where the certainty of the outcome is at issue, applies to concepts of chance, probability, and information entropy. In these situations, randomness implies a measure of uncertainty, and notions of haphazardness are irrelevant. The fields of mathematics, probability, and statistics use formal definitions of randomness. In statistics, a random variable is an assignment of a numerical value to each possible outcome of an event space. This association facilitates the identification and the calculation of probabilities of the events. A random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. These and other constructs are extremely useful in the probability calculus.