Average length of a Snakes and Ladders game by Ciro Santilli 34 Updated 2024-11-15 Created 1970-01-01
Since Snakes and Ladders is nothing but a Absorbing Markov chain, the results are exactly the same as for that general problem.
www.jstor.org/stable/3619261: How Long Is a Game of Snakes and Ladders? by Althoen, King and Schilling (1993), paywalled.