# Adventure Games and Eigenvalues

DevFeed: [Adventure Games and Eigenvalues](<https://devfeed.tech/articles/adventure-games-and-eigenvalues-37881.md>)

Original publisher: [Read original article](<https://www.evanmiller.org/adventure-games-and-eigenvalues.html>)

Author: Evan Miller

Published: 2017-04-23T10:10:00Z

Content type: tutorial

Language: en

Sources: [Evan Miller](<https://devfeed.tech/sources/evan-miller.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>), [Formal verification](<https://devfeed.tech/topics/formal-verification.md>), [Graphs](<https://devfeed.tech/topics/graphs.md>)

Tags: [eigenvalues](<https://devfeed.tech/tags/eigenvalues.md>), [formal-verification](<https://devfeed.tech/tags/formal-verification.md>), [graph-theory](<https://devfeed.tech/tags/graph-theory.md>), [matrix](<https://devfeed.tech/tags/matrix.md>), [state](<https://devfeed.tech/tags/state.md>)

## AI overview

This article explains how Markov theory and matrix manipulation can prove the absence of dead ends in a small adventure game and quantify the risk of reaching invalid states. It compares this approach with formal verification and graph-based route-finding algorithms, while noting that all approaches become impractical for large state spaces.

## Source excerpt

Identifying and quantifying dead ends, the bane of all adventure game players: Adventure Games and Eigenvalues