Editing Snakes and ladders (section)

==Mathematics of the game==
[[Image:Probability of winning Snakes and Ladders by turns.svg|thumb|400px|The cumulative probability of finishing a game of snakes and ladders by turn N]]
Any version of snakes and ladders can be represented exactly as an [[absorbing Markov chain]], since from any square the odds of moving to any other square are fixed and independent of any previous game history.<ref name="Mathematical Gazette">{{cite journal |last1=Althoen |first1=S.C. |last2=King |first2=L. |last3=Schilling |first3=K. |title=How Long Is a Game of Snakes and Ladders? |journal=The Mathematical Gazette |publisher=The Mathematical Association |volume=77 |issue=478 |pages=71–76 |date=March 1993 |jstor=3619261 |doi=10.2307/3619261|s2cid=65071163 }}</ref> The Milton Bradley version of ''Chutes and Ladders'' has 100 squares, with 19 chutes and ladders. A player will need an average of 39.2 spins to move from the starting point, which is off the board, to square 100. A two-player game is expected to end in 47.76 moves with a 50.9% chance of winning for the first player.<ref>{{cite web |first=Daniel |last=Audet |title=Probabilités et espérances dans le jeu de serpents et échelles à deux joueurs |url=http://archimede.mat.ulaval.ca/amq/bulletins/dec12/Serpents.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://archimede.mat.ulaval.ca/amq/bulletins/dec12/Serpents.pdf |archive-date=2022-10-09 |url-status=live |publisher=Bulletin AMQ |date=Dec 2012 }}</ref> These calculations are based on a variant where throwing a six does not lead to an additional roll; and where the player does not need to roll the exact number to reach square 100; if they overshoot, the game has still ended.