Analytics is the discovery and communication of meaningful patterns in data. Especially valuable in areas rich with recorded information, analytics relies on the simultaneous application of statistics, computer programming and operations research to quantify performance. Analytics often favors data visualization to communicate insight.
Firms may commonly apply analytics to business data, to describe, predict, and improve business performance. Specifically, arenas within analytics include predictive analytics, enterprise decision management, retail analytics, store assortment and stock-keeping unit optimization, marketing optimization and marketing mix modeling, web analytics, sales force sizing and optimization, price and promotion modeling, predictive science, credit risk analysis, and fraud analytics. Since analytics can require extensive computation (see big data), the algorithms and software used for analytics harness the most current methods in computer science, statistics, and mathematics.
Game theory is the study of strategic decision making. Specifically, it is “the study of mathematical models of conflict and cooperation between intelligent rational decision-makers”. An alternative term suggested “as a more descriptive name for the discipline” is interactive decision theory. Game theory is mainly used in economics, political science, and psychology, as well as logic, computer science, and biology. The subject first addressed zero-sum games, such that one person’s gains exactly equal net losses of the other participant or participants. Today, however, game theory applies to a wide range of behavioral relations, and has developed into an umbrella term for the logical side of decision science, including both humans and non-humans (e.g. computers, insects/animals).
The games studied in game theory are well-defined mathematical objects. To be fully defined, a game must specify the following elements: the players of the game, the information and actions available to each player at each decision point, and the payoffs for each outcome. (Rasmusen refers to these four “essential elements” by the acronym “PAPI”.) A game theorist typically uses these elements, along with a solution concept of their choosing, to deduce a set of equilibrium strategies for each player such that, when these strategies are employed, no player can profit by unilaterally deviating from their strategy. These equilibrium strategies determine an equilibrium to the game—a stable state in which either one outcome occurs or a set of outcomes occur with known probability.
Most cooperative games are presented in the characteristic function form, while the extensive and the normal forms are used to define noncooperative games.
In game theory, a cooperative game is a game where groups of players (“coalitions”) may enforce cooperative behaviour, hence the game is a competition between coalitions of players, rather than between individual players. An example is a coordination game, when players choose the strategies by a consensus decision-making process.
Recreational games are rarely cooperative, because they usually lack mechanisms by which coalitions may enforce coordinated behaviour on the members of the coalition. Such mechanisms, however, are abundant in real life situations (e.g. contract law).
In cooperative game theory and social choice theory, the Nakamura number measures the degree of rationality of preference aggregation rules (collective decision rules), such as voting rules. It is an indicator of the extent to which an aggregation rule can yield well-defined choices.
- If the number of alternatives (candidates; options) to choose from is less than this number, then the rule in question will identify “best” alternatives without any problem.
- if the number of alternatives is greater than or equal to this number, the rule will fail to identify “best” alternatives for some pattern of voting (i.e., for some profile (tuple) of individual preferences), because a voting paradox will arise (a cycle generated such as alternative socially preferred to alternative , to , and to ).
The larger the Nakamura number a rule has, the greater the number of alternatives the rule can rationally deal with. For example, since (except in the case of four individuals (voters)) the Nakamura number of majority rule is three, the rule can deal with up to two alternatives rationally (without causing a paradox). The number is named after Kenjiro Nakamura (1947–1979), a Japanese game theorist who proved the above fact that the rationality of collective choice critically depends on the number of alternatives.
In the card game of poker, a bluff is a bet or raise made with a hand which is not thought to be the best hand. To bluff is to make such a bet. The objective of a bluff is to induce a fold by at least one opponent who holds a better hand. The size and frequency of a bluff determines its profitability to the bluffer. By extension, the term is often used outside the context of poker to describe the act of making threats one cannot execute.
Bluffing in other games
Although bluffing is most often considered a poker term, similar tactics are useful in other games as well. In these situations, a player makes a play that shouldn’t be profitable unless an opponent misjudges it as being made from a position capable of justifying it. Since a successful bluff requires deceiving one’s opponent, it occurs only in games where the players conceal information from each other. In games like chess and backgammon where both players can see the same board, they should simply make the best legal move available. Examples include:
- Contract Bridge: Psychic bids and falsecards are attempts to mislead the opponents about the distribution of the cards. A risk (common to all bluffing in partnership games) is that a bluff may also confuse the bluffer’s partner. Psychic bids serve to make it harder for the opponents to find a good contract or to accurately place the key missing cards with a defender. Falsecarding (a tactic available in most trick taking card games) is playing a card that would naturally be played from a different hand distribution in hopes that an opponent will wrongly assume that the falsecarder made a natural play from a different hand and misplay a later trick on that assumption.
- Stratego: Much of the strategy in Stratego revolves around identifying the ranks of the opposing pieces. Therefore depriving your opponent of this information is valuable. In particular, the “Shoreline Bluff” involves placing the flag in an unnecessarily vulnerable location in hopes that the opponent won’t look for it there.
- Spades: In late game situations, it is useful to bid a nil even if it cannot succeed. If the third seat bidder sees that making a natural bid would allow the fourth seat bidder to make an uncontestable bid for game, he may bid nil even when it has no chance of success. The last bidder then must choose whether to make his natural bid (and lose the game if the nil succeeds) or to respect the nil by making a riskier bid that allows his side to win even if the doomed nil is successful. If he chooses wrong and both teams miss their bids, the game continues.
- Scrabble: Scrabble players will sometimes deliberately play a phony hoping the opponent doesn’t challenge it. Bluffing in Scrabble is a bit different from the other examples. Although Scrabble players do conceal their tiles, they have little opportunity to make significant deductions about their opponent’s tiles, and even less opportunity to spread disinformation about them. Bluffing by playing a phony is instead based on assuming players have imperfect knowledge of the acceptable word list
The use of cubical and oblong dice was common in the Indus Valley Harappan civilization (c. 2300 BC). The earliest textual mention of games in India is the Rig-Veda‘s mention of the use of dice (c. 1000 BC). Texts such as the Mahabharata indicate that dice games were popular with Kings and royalty, and also had ceremonial purposes. Cowry shells were also widely used.
Another early reference is the list of Buddha games (circa 500 BC) which is a list from the Pali Canon that Buddhist monks were forbidden to play. This list mentions games on boards with 8 or 10 rows (Ashtapada and Daśapada), games which use floor diagrams (one game called Parihâra-patham is similar to hop-scotch), dice games and ball games. Ashtapada and Daśapada were race games.
Chaturanga (which means ‘quadripartite’ and also ‘army’), the predecessor of Chess, possibly developed in the Indian subcontinent or Central Asia during the Kushan (30–375 CE) or Gupta (320–550 CE) periods from an amalgamation of other game features and was transmitted to Sassanid Persia (where it was known as Shatranj) and China through the Silk Road. The oldest text to mention Chaturanga is the middle Persian work Wizârîshn î chatrang ud nîhishn î nêw-ardakhshîr (The explanation of Chatrang and the invention of Nard, c. 600 AD). This texts tells the arrival of Chatrang in an embassy from ‘Hind‘ during the reign of Khosrau I (531–579). The name ‘Hind’ was often used to refer to eastern regions such as Balochistan. Another game named Chaturaji was similar but played with four sides of differing colors instead of two, however the earliest source for this four sided board game is Al-Biruni‘s ‘India’, circa 1030 AD. Historians of Chess such as Yuri Averbakh have surmised that the Greek board game petteia may have had an influence on the development of early Chaturanga. Petteia games could have combined with other elements in the Greco-Bactrian and Indo-Greek Kingdoms. 
Cross and circle games such as Chaupar and Pachisi may be very old games, but so far their history has not been established prior to the 16th century. Chaupar was a popular gambling game at the court of Mughal emperor Akbar the Great (1556-1605). The emperor himself was a fan of the game and was known to play on a courtyard of his palace using slaves as playing pieces.
During the 15th century card suits began to approach the contemporary regional styles and the court cards evolved to represent European royalty. Early European card games included Noddy, Ruff, All Fours, Piquet, Basset, Hofamterspiel, Karnöffel, and Primero. In 1674 Charles Cotton’s published his ‘Compleat Gamester’, one of the first books which set out to outline rules for many card and dice games. During the mid 16th century, Portuguese traders introduced playing cards to Japan. The first reference to twenty-one, the precursor of Blackjack is found in a book by the Spanish author Miguel de Cervantes. Cervantes was a gambler, and the main characters of his tale Rinconete y Cortadillo are cheats proficient at playing ventiuna (twenty-one).
The game of Cribbage appears to have developed in the early 17th century, as an adaptation of the earlier card game Noddy. Pinochle was likely derived from the earlier Bezique, a game popular in France during the 17th century. 1742 saw the publication of Edmund Hoyle’s ‘Short Treatise on the Game of Whist‘ which became one of the bestselling publications of the 18th century. Whist was widely played during the 18th and 19th centuries, having evolved from the 16th century game of Trump (or Ruff) by way of Ruff and Honours. During the French Revolution, the traditional design of Kings, Queens, and Jacks became Liberties, Equalities, and Fraternities because the revolutionary French national assembly believed the people should not play with Kings or Queens, but with the ideals of the revolution at hand. This would ultimately be reversed in 1805 with the rise of Napoleon.
While possibly dating back as far as the reign of Charles VIII of France (1483–1498), Baccarat first came to the attention of the public at large and grew to be widely played as a direct result of the Royal Baccarat Scandal of 1891, and bears resemblances to the card games Faro and Basset, both of which were very popular during the 19th century. The rules of Contract bridge were originally published in 1925, the game having been derived from Bridge games with rules published as early as 1886, Bridge games, in turn, having evolved from the earlier game of Whist.
The first documented game of poker dates from a 1834 Mississippi river steamer. The game derives from a Persian game called “as nas“, as is named after a similar French game, “poque“. During the American Civil War the game was popular with soldiers and additions were made including stud poker, and the straight. Modern tournament play became popular in American casinos after the World Series of Poker (WSOP) began, in 1970. Poker’s popularity experienced an unprecedented spike at the beginning of the 21st century, largely because of the introduction of online poker and hole-card cameras, which turned the game into a spectator sport. In 2009 the International Federation of Poker was founded in Lausanne, Switzerland, becoming the official governing body for poker.
Collectible card games or trading card games while bearing similarities to earlier games in concept, first achieved wide popularity in the 1990s. The first trading card game was the ‘The Base Ball Card Game’ produced by The Allegheny Card Co. and registered on 4 April 1904 featured 104 unique baseball cards with individual player attributes printed on the cards enabling each collector to build a team and play the game against another person. The 1990s saw the rise of games such as Magic: The Gathering and the Pokémon Trading Card Game.
Game of chance
A game of chance is a game whose outcome is strongly influenced by some randomizing device, and upon which contestants may choose to wager money or anything of monetary value. Common devices used include dice, spinning tops, playing cards, roulette wheels, or numbered balls drawn from a container. A game of chance may have some skill element to it, however, chance generally plays a greater role in determining the outcome than skill. A game of skill, on the other hand, also has an element of chance, but with skill playing a greater role in determining the outcome.
Any game of chance that involves anything of monetary value is gambling.
Gambling is known in nearly all human societies, even though many have passed laws restricting it. Early people used the knucklebones of sheep as dice. Some people develop a psychological addiction to gambling, and will risk even food and shelter to continue.
Some games of chance may also involve a certain degree of skill. This is especially true where the player or players have decisions to make based upon previous or incomplete knowledge, such as blackjack. In other games like roulette and punto banco (baccarat) the player may only choose the amount of bet and the thing he/she wants to bet on, the rest is up to chance, therefore these games are still considered games of chance with small amount of skills required. The distinction between ‘chance’ and ‘skill’ is relevant as in some countries chance games are illegal or at least regulated, where skill games are not.
Game of skill
A game of skill is a game where the outcome is determined mainly by mental or physical skill, rather than by chance. A game of skill generally has an element of chance, but skill plays a greater role in determining the outcome.
One benefit of games of skill is that they are a means of exploring one’s own capabilities. Games encourage the player to look at, understand, and experience things. They teach people lessons about themselves and possibly the world, and allow such insights to be passed on to others.
Most games of skill also involve a degree of chance, due to natural aspects of the environment, a randomizing device (such as dice, playing cards or a coin flip) or guessing due to incomplete information. Some games of skill such as poker may involve bluffing and other forms of psychological warfare.
The distinction between “chance” and “skill” has legal significance in countries where chance games are treated differently from skill games. The legal distinction is often vague and varies widely from one jurisdiction to the next.
In a number of countries like Germany, whether a game is considered of skill has legal implications with respect to whether money bets on the game’s outcome are considered gambling or not. For example poker is legally considered a game of chance in Germany (thus only allowed in casinos), whereas skat is considered a game of skill and competitions with money prizes are allowed.
The Indian Games of Pachisi, Chaupar, and Chausar
Throwing dice for money was the cause of many special laws in Rome, one of which stated that no lawsuit could be filed by a person who allowed gambling in his house, even if he had been cheated or assaulted.[
A die found in excavations at a Harappan period site. Note that the six is not opposite the one.