The Probabilistic Wumpus World

AI basics explained in a game

Rachael Ferguson
4 min readFeb 3, 2023

The Probabilistic Wumpus World is a type of artificial intelligence problem that provides a framework for reasoning about uncertainty and decision-making in a simple, yet representative environment.

A simplistic troll-like monster with brown smell lines coming off of him. Next to him is the text “Wumpus World”
From 2016 Wumpus World PC game. 📷: Cite

It is a popular subject in the field of AI and is widely used for teaching, research, and experimentation. A lot of its recent popularity comes from its inclusions in what is known as the “the most popular artificial intelligence textbook in the world,”Artificial Intelligence: A Modern Approach.

The Wumpus World is a two-dimensional grid, where the agent (the player) starts at a certain location and has to navigate the world to reach a goal. The world is populated with various elements, including pits, gold, wumpus, and walls, each with its own characteristics and behaviors. The goal of the agent is to find the gold while avoiding the wumpus and pits, which can kill the agent. The agent has a limited set of actions available to it, such as moving forward, turning left, turning right, and shooting an arrow.

A 4x4 grid showing the Wumpus World. One cell contains the Wumpus monster. 3 cells contain pits. One cell contains gold. And one cell contains the agent.
The Wumpus World visualized. 📷: Cite

For more info about the Wumpus World setup, see my previous article “What is the Wumpus World?

The key aspect of the Probabilistic Wumpus World is that the agent faces uncertainty about the world. For example, the location of the wumpus and the pits is not known to the agent. Additionally, the agent must rely on its sensors to observe the state of the world. The sensors can provide information such as the presence of a breeze (indicating the presence of a pit), the smell of a wumpus, or the glitter of gold. The information provided by the sensors, however, is noisy and not always accurate.

The probabilistic nature of the Wumpus World means that the agent must deal with uncertainty when making decisions. For instance, the agent may not be sure about the location of a pit based on the breeze it feels, or the presence of the wumpus based on the smell it detects. In such cases, the agent must use probabilistic reasoning to update its beliefs about the world and take actions that minimize its uncertainty.

What your agent is doing before taking every step. 📷: Cite

One approach to solving the Probabilistic Wumpus World is to use a Bayesian network. A Bayesian network is a graphical model that represents the probabilistic relationships between variables. In the case of the Wumpus World, the variables can be the location of the wumpus, the pits, and the gold, as well as the state of the sensors. The Bayesian network can be used to update the beliefs about the world as new information becomes available.

Example of a Bayseian network showing the relative probabilities of WetGrass based on previous information.
Example of a Bayesian Network. 📷: Cite

Another approach to solving the Probabilistic Wumpus World is to use Partially Observable Markov Decision Processes (POMDPs). POMDPs are a mathematical framework for decision-making under uncertainty. They model the decision-making process as a Markov decision process, where the state of the world is a Markov process and the actions of the agent are influenced by the current state of the world. In a POMDP, the agent’s observations of the world are treated as partial observations, and the agent must update its beliefs about the world based on these observations.

A graph with arrows showing the thought process of a little robot as it makes a decision, decides if that was a good decision, and updates its internal logic with the information it learned from making that decision.
An example of an iterating POMDP. 📷: Cite

The usefulness of the Probabilistic Wumpus World lies in its simplicity and generality. The Wumpus World provides a simple and intuitive environment for teaching and experimenting with artificial intelligence. It allows students and researchers to explore various AI techniques, such as probabilistic reasoning, decision-making, and planning, in a simple and accessible environment. Moreover, the Wumpus World can serve as a starting point for more complex AI problems, such as robotics and autonomous systems.

In conclusion, the Probabilistic Wumpus World is a useful tool for teaching, research, and experimentation in the field of artificial intelligence. Its simplicity and generality make it an accessible environment for exploring various AI techniques, such as probabilistic reasoning, decision-making, and planning.

If you liked the above, please consider following or checking out my other articles below! Thanks!

Other Wumpus World articles by me:

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