stochastic simulation, markov chain program

I assume for simplicity that you are the only player of this board game. Start at square 1 and move at each step to one, two, or three squares ahead according to the outcome of spinning a roulette. If you land at the bottom of a ladder, immediate climb it. If you land on the head of the snake, slide 5 down to the tip of the snake's tail. The game ends at reaching square 12. The only way to reach 12 from squares 10 and 11 is by drawing 2 or 1, respectively; if the roulette gives a higher number than necessary, stay where you are. We wish to run a stochastic simulation of this game by using the Markov chain program. (a) What is the expected number of steps to go from 1 to 12? (b) On average, how many limes will a player climb a ladder? (c) On average, how many times will a player slide down a snake? Before writing your program, convince yourself that my transition probabilities diagram given below correctly interprets the rules of the game. The simulation consists of running the game till finish a large number of times and obtaining the three average values asked in the