Abstract:
Games are simple models of decisionmaking. Understanding games should help us
understand decisions. Mathematical games
provide opportunities for building self-concept
and reducing the fear of failure and error.
Progressively finite game is one of the
mathematical games. This paper proposes the
system which analyses the nature of progressively
finite games such as the simple takeaway game
and nim game by means of generating winning
strategies. The system starts with the introduction
of takeaway game, nim games and ends with
producing their winning strategies. A winning
strategy is a rule that tells the player which move
to make the player will eventually win.
Progressively finite games of winning strategies
are based on the grundy value. Grundy values 0
are in the winning strategy. The system uses the
Digital Sum and Sprague-Grundy function of
Combinatorial Game Theory to find grundy value.
Experimental results are show by means of
probability theory as well as Bayes’ rule.
