Chutes And Ladders Game Analysis

Chutes and Ladders, originally called Snakes and Ladders is an ancient Indian board game that is known worldwide. The game itself is exceedingly simple. Players start on an undefined square zero and take turns rolling a dice. They move their pieces on the board the value that the dice shows on their turn. If the player lands on a space with a chute, their piece is moved back a set number of spaces as defined by that chute. If the player lands on a space with a ladder, the player is moved forward a set number of spaces as defined by the ladder. The first player to reach space one hundred is the winner. As defined by the rules above, Chutes and Ladder is a game of luck. This concept of luck was the original defining concept of the game, with parents playing the game with their children used in order to teach their children the power of good versus evil actions and the resulting karma of those actions. In order to win Chutes and Ladders, the player does not have to have any sort of skill. Thus, teaching an artificial intelligence to play the game optimally would be underwhelming at best. In order to make the project more interesting, we need to change the rules of the game.

Figure 1.This is a picture of the board from the game Chutes and Ladders.

In regards to this project, the rules of Chutes and Ladders are now as follows.

We will be using four different algorithms in order to “solve” this problem. First, we use Dynamic Programming to solve the game optimally offline. Then, we use Monte Carlo in order to set up random simulations to determine average moves for each play through of the game. Finally, we use the on-policy Reinforcement Learning technique, SARSA, and the off-policy Reinforcement Learning technique, Q-Learning, to determine if there is a more optimal way to solve the