Mathematics of the game Snakes and Ladders

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the cumulative probability of finishing game of snakes , ladders turn n


any version of snakes , ladders can represented absorbing markov chain, since square odds of moving other square fixed , independent of previous game history. milton bradley version of chutes , ladders has 100 squares, 19 chutes , ladders. player need average of 39.6 spins move starting point, off board, square 100. two-player game expected end in 47.76 moves 50.9% chance of winning first player.


in book winning ways authors show how treat snakes , ladders impartial game in combinatorial game theory though far natural fit category. end make few rule changes such allowing players move counter number of spaces, , declaring winner player gets last counter home. unlike original game, version, call adders-and-ladders, involves skill.








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