It turns out that players don't always need to defeat the Ender Dragon themselves. Minecraft YouTuber RedLogic has demonstrated that, under the right circumstances and given an almost incomprehensible amount of time, the game can indeed beat itself.
This feat required a specific world seed and a complex setup. RedLogic created a simulation to find a Minecraft seed with a sufficiently close and accessible End Portal. The simulation then employed a Monte Carlo method to condense billions of in-game ticks into statistically sampled waiting times. This allowed for the progression of events that would eventually lead to the Ender Dragon's defeat.
The Long Road to Victory
Running the simulation on Minecraft world seed -535646876083114041, the process began in year 33,477 when an Enderman picked up a pumpkin. This pumpkin was later used to create a snow golem, which could attack mobs. Two years later, this snow golem provoked a Creeper, blowing open a section of the path to the End Portal.
By year 35,510, further Creeper explosions, triggered by snow golems, fully opened the path, allowing surface mobs to enter the End. It took until year 1,300,000 for Endermen to start entering the End and placing blocks that gradually created pathways to the End Crystals. The first snow golem entered the End in year 3,000,000 and managed to destroy an End Crystal.
Progress continued slowly, with 8 out of 10 End Crystals destroyed by year 122,415,210. A snow golem managed to destroy the ninth crystal in year 181,000,000. After an additional 18 million years of wandering, it finally destroyed the last End Crystal in year 199,000,000.
The Final Blow
The first Creeper explosion damaging the Ender Dragon occurred in year 227,000,000. For nearly two billion years, the Ender Dragon's health was gradually reduced by a combination of snow golem attacks and Creeper explosions. The final blow that defeated the Ender Dragon and thus completed the game occurred after an astonishing 1.975 billion years.
The result of this multi-billion-year endeavor is a surreal End dimension filled with stacked blocks and scarred by Creeper explosions, with no visible signs of life. However, for RedLogic, the completed game was a worthy outcome.