Pardon me but is that really for parents or am I just a dumb? I am an undergraduate student but I'd expect a more human friendly explanation on this topic.
Basically, for each turn you calculate the probability that the pawn is on a given square. You can then calculating the probabilities for the next turn by applying all possible moves to all possible positions, while weighting for the chance of the position and the chance of the move.
For parents that were mathematics majors
They come up with an expected number of rolls-to-complete of 32. This surprisingly large number is why that game tends to drag on forever.
It is not that surprising. If you leave out all the snakes and all the ladders, the rolls-to-complete is 100/3.5, or about 28.5. So, it seems the average loss due to snakes is larger than the average gain due to ladders.
Yes, I realized this simple explanation only after doing the Markov chain analysis myself a couple years ago.
But for some reason, looking at the game, you don't think it will take so long.