It is not possible to climb ladder1 or ladder80 more than once in a game.
According to the wikipedia article you quote, a player who rolls 3 sixes in a row starts all over again. Which makes it possible to use ladder1 more than once.
What fascinating statistics can you dial up?
The same article says that a player rolls again after rolling a six. Which means you can finish in less than 7 turns
. Perhaps you should make a histogram on turns as well.
But the most important statistics is missing. The entire game is almost without decisions (except that you are allowed to skip a roll when rolling 6, and aren't forced to climb a ladder). Which leaves one big decision: do you go first, or second? Obviously, going first increases the chance of winning, but by how much? Said it differently, if you play chutes and ladders (2 player game), the loser paying the winner 1 USD, how much would you pay to go first?