[Paper Review] A Crude Analysis of Twitch Plays Pokemon

Scott Deeann Chen|arXiv (Cornell University)|Aug 21, 2014

Artificial Intelligence in Games3 citations

TL;DR

This paper models Twitch Plays Pokemon's anarchy mode as a continuous-time Markov process to analyze how player count affects winning probability and expected game time. It finds that while collaboration without coordination helps reduce time, excessive players cause input collisions that drastically increase expected playtime, with a theoretical limit of 46 expert players for guaranteed wins under given parameters.

ABSTRACT

We model and study the game mechanisms and human behavior of the anarchy mode in Twitch Plays Pokemon with a pure-jump continuous-time Markov process. We computed the winning probability and expected game time for $1$ player and $N$ players and identified when collaboration helps. A numerical plug-in example is also provided.

Motivation & Objective

• To model the anarchy mode of Twitch Plays Pokemon as a pure-jump continuous-time Markov process.
• To compute winning probability and expected game time for both single-player and N-player scenarios.
• To identify conditions under which collaborative input from multiple players improves or hinders game progress.
• To quantify the impact of human reaction time, input delay, and input quality on game duration and success.
• To evaluate the trade-off between player count and expected game time, especially in the absence of coordination.

Proposed method

• Models game progression as a birth-death process with absorbing states at n good moves (win) and m bad moves (lose).
• Uses the gambler's ruin problem to derive winning probability P and expected number of moves M under symmetric transition rates λ and μ.
• Incorporates human behavior via exponential reaction times (λₕ⁻¹) and input delay (Tₔ) to compute effective input rates.
• Adjusts input quality q to account for duplicate inputs in N-player scenarios, defining effective quality q′ = q × P_c where P_c = e^(-λₕ(N-1)Tₔ).
• Derives expected game time T_gN as a function of N, λₕ, Tₔ, q, and n, using M(t + Tₔ) with t = 1/(λ+μ).
• Applies numerical parameters (q=0.99, Tₔ=0.15, λₕ=0.1, n=100) to compute time growth and identify the N=46 threshold for guaranteed win.

Experimental results

Research questions

• RQ1 How does the expected game time scale with the number of players in Twitch Plays Pokemon’s anarchy mode?
• RQ2 Under what conditions does increasing player count improve or degrade game progress efficiency?
• RQ3 What is the theoretical upper bound on player count that still guarantees a win, given input delays and reaction times?
• RQ4 How does input duplication due to multiple players affect the effective quality of inputs and game outcome?
• RQ5 In what scenarios does uncoordinated crowd-sourcing outperform single-player play despite chaotic inputs?

Key findings

• Expected game time drops by approximately 7-fold when increasing from 1 to 19 expert players, indicating early efficiency gains from collective input.
• The expected game time grows exponentially with player count when 2qe^(-λₕ(N-1)Tₔ) > 1, and becomes infinite when this condition is violated.
• With q=0.99, Tₔ=0.15, λₕ=0.1, and n=100, the maximum number of players that still guarantees a win is 46.
• Beyond 46 players, the system no longer guarantees a win due to excessive input collisions overwhelming progress.
• Even without coordination, collaboration helps in early stages due to shared learning from successful inputs.
• The model shows that democracy mode would likely reduce expected game time significantly compared to anarchy mode, though this remains for future work.