It's not too hard to compute perfect cube action for that game. I suspect that one of the players in your chouette had done this. People made some money years ago by calculating perfect cube action for one-checker-each backgammon, and then playing it with people whose cube action contained errors.
You can solve a set of 10000 simultaneous equations, but the iterative way is simpler. The problem is that the game contains loops, because of the chutes. So break the loops by computing and storing all the probabilities for the modified game where you go down a chute, you lose. Now use these values to compute the values of the game where when you go down a second chute, you lose. Continue to iterate in this way until the values aren't changing, because "Chutes and ladders modified by the rule that if you go down 50 chutes, you lose" is pretty much the same game as Chutes and ladders, since that never happens.
I forget what happens when you roll (spin?) too large to get to 100, but if that doesn't move you forward, you'll have to treat that the same way you treat the chutes. This will slow convergence a bit, but it will still be fast.
The harder part is the data visualization exercise of figuring out how to describe the resulting 100 by 100 table in a way that is memorizable.