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== Strategy and tactics == {{See also|Backgammon match strategy}} [[Image:Backgammon-set from American civil war.jpeg|thumb|Backgammon set, 19th century]] Backgammon is played in two principal variations, ''money'' and ''match'' play: * Money play means that every point counts evenly and every game stands alone, whether money is actually being wagered or not; sometimes it is called ''unlimited'' play. * Match play means that the players play until one side scores (or exceeds) a certain number of points. The format has a significant effect on strategy. In a match, the objective is not to win the maximum possible number of points, but rather to simply reach the score needed to win the match, so optimal play may depend on the match score. In money play, the theoretically correct checker play and cube action would never vary based on the score. Backgammon has an established [[Backgammon opening theory|opening theory]], although it is less detailed than that of chess. The [[Game tree|tree]] of positions expands rapidly because of the number of possible dice rolls and the moves available on each turn. Recent computer analysis has offered more insight on opening plays, but the midgame is reached quickly. After the opening, backgammon players frequently rely on some established general strategies, combining and switching among them to adapt to the changing conditions of a game. There are several strategies or "game plans" to achieve a win: * The ''running game'' is a strategy minimizing or breaking contact while ahead in the race.<ref name="magriel">{{cite book|last=Magriel|first=Paul|author-link=Paul Magriel|title=Backgammon|year=1976|publisher=Quadrangle/The New York Times Book Co|isbn=978-0-8129-0615-8}}</ref> * <div>The ''holding game'' is holding a point on the opponent's side of the board, called an anchor. As the game progresses, the player may gain an advantage by hitting an opponent's blot from the anchor or by rolling large doubles that allow the checkers to escape into a running game.<ref name="magriel"/></div> * The ''priming game'' involves building a wall of checkers, called a prime, covering a number of consecutive points. This obstructs opposing checkers that are behind the prime. A checker trapped behind a six-point prime cannot escape until the prime is broken.<ref name="magriel"/> * <div>The ''attacking game'', sometimes called a ''blitz'', is a strategy of covering the home board as quickly as possible while hitting one's opponent and keeping them on the bar. Because the opponent has difficulty re-entering from the bar or escaping, a player can quickly gain a race advantage and win the game, often with a gammon.<ref name="robertie-winners"/></div> A ''backgame'' is a strategy that involves holding two or more anchors in an opponent's home board while being substantially behind in the race.<ref>{{cite web|url=http://www.bkgm.com/gloss/lookup.cgi?back+game%20game|title=Backgammon Glossary/Back Game|publisher=Backgammon Galore!}}</ref> The anchors obstruct the opponent's checkers and create opportunities to hit them as they move home. The backgame is generally used only to salvage a game wherein a player is already significantly behind. Using a backgame as an initial strategy is usually unsuccessful.<ref name="robertie-winners"/><ref name="magriel"/> ''Duplication'' refers to the placement of checkers such that one's opponent needs the same dice rolls to achieve different goals. For example, players may position all of their blots in such a way that the opponent must roll a 2 in order to hit any of them, reducing the probability of being hit more than once.<ref name="robertie-winners"/><ref name="magriel"/> ''Diversification'' refers to a complementary tactic of placing one's own checkers in such a way that more numbers are useful.<ref name="magriel"/> The ''[[Pip (counting)#Dice|pipcount]]'' is number of pips needed to move a player's checkers around and off the board. Many positions require a measurement of a player's standing in the race, for example, in making a doubling cube decision, or in determining whether to run home and begin bearing off. The difference between the two players' pip counts is a measure of the leader's racing advantage. For cube decisions, a number of formulas have been developed over the years,<ref>{{Cite web |title=Backgammon Articles: When and How to Use the Doubling Cube |url=https://www.bkgm.com/articles/page04.html#pip_counting |access-date=2024-10-11 |website=www.bkgm.com}}</ref> including the Thorpe count,<ref>{{Cite web |title=Backgammon Cube Handling in Races |url=https://www.bkgm.com/rgb/rgb.cgi?view+772 |access-date=2024-10-11 |website=www.bkgm.com}}</ref> the Ward count, the Keith count,<ref>{{Cite web |title=Cube Handling in Noncontact Positions |url=https://www.bkgm.com/articles/CubeHandlingInRaces/#comparing_the_formulas |access-date=2024-10-11 |website=www.bkgm.com}}</ref> and iSight.<ref>https://bkgm.com/articles/Reichert/insights-with-isight.pdf</ref> These calculations enable a player to determine whether to offer or take a double based on the pipcount in non-contact positions. ===Cube handling=== Two theoretical models provide a basis for cube handling, i.e. when to offer a double and when to accept an offered double. Both ignore the effects of gammons and backgammons. * The ''dead cube model'' ignores the advantage the taker gets from having sole access to the cube. It estimates that the ''takepoint'' (i.e. the minimum game winning chances to accept a cube) is 25% and the doubling window opens at 50%. * The ''live cube model'' assumes a maximum value for sole cube access (i.e. that the taker may use the cube most efficiently by either raising the stakes or doubling out the opponent). It estimates that the takepoint is 20% and the doubling window opens at 80%. In practice, the takepoints and doubling points are somewhere in between, since while cube ownership cannot be ignored, assuming maximal efficiency for a re-cube is also not a valid assumption.<ref>https://www.bkgm.com/articles/Janowski/cubeformulae.pdf</ref> Ignoring gammons and backgammons, the takepoint in money play is about 22%.<ref>{{Cite web |title=GAMMONLIFE.COM - Backgammon Cube Strategy Made Simple |url=http://www.gammonlife.com/writers/simple-backgammon-cube-strategy.htm |access-date=2024-10-11 |website=www.gammonlife.com}}</ref> All of the above ignores gammons and backgammons for either side, so in practice the calculation of takepoints is more complicated.<ref>https://www.bkgm.com/articles/Simborg/WhenToDouble/index.html "I wish there were as good a law for when to take the cube. No one I know has come up with a simple solution for this ..."</ref>
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