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Markov chain
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===Games and sports=== Markov chains can be used to model many games of chance. The children's games [[Snakes and Ladders]] and "[[Hi Ho! Cherry-O]]", for example, are represented exactly by Markov chains. At each turn, the player starts in a given state (on a given square) and from there has fixed odds of moving to certain other states (squares).{{cn|date=January 2025}} Markov chain models have been used in advanced baseball analysis since 1960, although their use is still rare. Each half-inning of a baseball game fits the Markov chain state when the number of runners and outs are considered. During any at-bat, there are 24 possible combinations of number of outs and position of the runners. Mark Pankin shows that Markov chain models can be used to evaluate runs created for both individual players as well as a team.<ref>{{cite web |last=Pankin |first=Mark D. |title=MARKOV CHAIN MODELS: THEORETICAL BACKGROUND |url=http://www.pankin.com/markov/theory.htm |access-date=2007-11-26 |url-status=usurped |archive-url=https://web.archive.org/web/20071209122054/http://www.pankin.com/markov/theory.htm |archive-date=2007-12-09 }}</ref> He also discusses various kinds of strategies and play conditions: how Markov chain models have been used to analyze statistics for game situations such as [[bunt (baseball)|bunting]] and [[base stealing]] and differences when playing on grass vs. [[AstroTurf]].<ref>{{cite web |last=Pankin |first=Mark D. |title=BASEBALL AS A MARKOV CHAIN |url=http://www.pankin.com/markov/intro.htm |archive-url=https://web.archive.org/web/20010513164045/http://www.pankin.com/markov/intro.htm |url-status=usurped |archive-date=May 13, 2001 |access-date=2009-04-24 }}</ref>
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