Snakes & Ladders is a board game.
It involves throwing a dice to move from a starting point off the board through the squares to the final square.
Along the way, the player is aided by ladders, but hampered by snakes.
Landing upon a square with a ladder transports you up the ladder.
Landing on a snake will bring you sliding down to the squares at the end of the snake.
A miniature snakes and ladder board is attached.
And we use a coin (not a dice) because it is only a small game.
Heads: Move forward one space (probability 0.5)
Tails: Move forward two space (probability 0.5)
Rolling a head or tail moves the player onto the board.
HINT
In this game there are 9 game states (the 9 squares) and 1 state off the board (State 0) where play begins.
This equals 3 * 3 + 1 = 10 states in total.
REQUIREMENT
(a) What is the minimum number of moves required to win the game?
(b) Plot the ‘cumulative distribution function.’
This graph should show the number of moves on the x axis, and the probability that the game has been won on the y axis.
