Simulating Keystroke and Computing the Theoretical Probability of Infinite Monkey Theorem with Markov Process

TL;DR

This paper models the probability of randomly typing Shakespeare's Hamlet using a Markov process, estimating the expected time to occur and comparing it with theoretical calculations, revealing surprisingly lower estimates.

Contribution

It introduces a Markov process-based simulation to estimate the expected time for the Infinite Monkey Theorem, providing empirical data and comparison with theoretical predictions.

Findings

Estimated time for Hamlet typing is about 10^34 minutes.

Empirical simulation yields lower expected time than theoretical calculations.

The approach demonstrates the use of character transition probabilities in modeling random typing.

Abstract

The Infinite Monkey Theorem states that if one monkey randomly hits the keys in front of a typewriter keyboard during an infinite amount of time, any works written by William Shakespeare will almost surely be typed out at the end of the total text. Due to the seemingly low chance of typing the exact literature works, our group are motivated to find out the expected time the Hamlet, our target text, being typed out by simulated random typing on a standard keyboard. For finding the answer, 30 users randomly typed characters into a file. Then, the frequency of each characters occurred following the previous character is calculated. This conditional probability is used to build the Markov matrix by considering all 128 times 128 cases. Finally, the expected time we estimated is about 10 to the power of 34 (min), which is surprisingly lower than the theoretical computation, and not achievable at all even in the cosmic time.