A mathematical game is a game whose rules, strategies, and outcomes are defined by clear mathematical parameters. Often, such games have simple rules and match procedures, such as Tic-tac-toe and Dots and Boxes. Generally, mathematical games need not be conceptually intricate to involve deeper computational underpinnings. For example, even though the rules of Mancala are relatively basic, the game can be rigorously analyzed through the lens of combinatorial game theory.

Mathematical games differ sharply from mathematical puzzles in that mathematical puzzles require specific mathematical expertise to complete, whereas mathematical games do not require a deep knowledge of mathematics to play. Often, the arithmetic core of mathematical games is not readily apparent to players untrained to note the statistical or mathematical aspects.

Some mathematical games are of deep interest in the field of recreational mathematics.

When studying a game's core mathematics, arithmetic theory is generally of higher utility than actively playing or observing the game itself. To analyze a game numerically, it is particularly useful to study the rules of the game insofar as they can yield equations or relevant formulas. This is frequently done to determine winning strategies or to distinguish if the game has a solution.

Blaufränkisch (German for blue Frankish) is a dark-skinned variety of grape used for red wine. Blaufränkisch, which is a late-ripening variety, produces red wines which are typically rich in tannin and may exhibit a pronounced spicy character.

The grape is grown across Central Europe, including Austria, Czech Republic (in particular southern Moravia where it is known as Frankovka), Germany, Slovakia (where it is known as Frankovka modrá), Croatia (frankovka), Slovenia (known as modra frankinja), and Italy (Franconia). In Hungary the grape is called Kékfrankos (also lit. blue Frankish) and is grown in a number of wine regions including Sopron, Villány, Szekszárd, and Eger (where it is a major ingredient in the famous red wine blend known as Egri Bikavér (lit. Bull's Blood) having largely replaced the Kadarka grape). It has been called "the Pinot noir of the East" because of its spread and reputation in Eastern Europe. In America this grape is grown in Idaho, Washington State and the Finger Lakes region of New York State, where like in Germany it is known as Lemberger, Blauer Limberger or Blue Limberger.

A simulation video game describes a diverse super-category of video games, generally designed to closely simulate aspects of a real or fictional reality.

A simulation game attempts to copy various activities from real life in the form of a game for various purposes such as training, analysis, or prediction. Usually there are no strictly defined goals in the game, with players instead allowed to freely control a character. Well-known examples are war games, business games, and role play simulation.

From three basic types of strategic, planning, and learning exercises: games, simulations, and case studies, a number of hybrids may be considered, including simulation games that are used as case studies.

Comparisons of the merits of simulation games versus other teaching techniques have been carried out by many researchers and a number of comprehensive reviews have been published.

History

While many credit simulation games beginning with Will Wright and SimCity in 1989, the true progenitor of the genre was "Fortune Builder", released in 1984 on Colecovision. Certain games such as SimLife and SimEarth were subsequently created and are capable of teaching players the basics of genetics and global ecosystems.