BioShock Infinite Ending Explained
2013's "BioShock Infinite" saw the series transition from the ocean city of Rapture to the beautiful skies of Columbia, where Booker DeWitt and Elizabeth Comstock must work together to escape from the control of Father Comstock. While the story sprinkles in hints toward its mind-bending ending throughout the game, the final cutscene can be sensory overload with how much information it throws at you. These narrative chances paid off, as "BioShock Infinite" received a 94 on metacritic for the PC version of the game, garnering nearly universal praise when the epic sequel was released.
After a lengthy battle on the barge near the end of the game, Booker uses Songbird to destroy the siphon that has been limiting Elizabeth's powers. However, once the siphon is destroyed, Booker loses control of Songbird, which starts to attack them. Elizabeth opens a tear in reality to take herself, Booker, and Songbird to Rapture. With Elizabeth's powers now at full power, she is able to explain to Booker what exactly is going on.
The keys to the multiverse
Elizabeth leads Booker through Rapture to a Bathysphere, which takes them to the lighthouse from the original "Bioshock." This leads to an area where there are a seemingly infinite number of lighthouses. Elizabeth explains that there are infinite variables, but only three constants, fixed figures in time and space. "There's always a lighthouse. There's always a man. There's always a city," she tells Booker.
It's at this point that it is revealed that Booker sold his daughter Anna to Father Comstock in order to wipe away his past deeds. He tried to get Anna back, but failed to do so, resulting in her losing part of her pinky finger. This is when Booker learns that Elizabeth and Anna are one in the same.
Not only that, but Booker is actually Comstock, who chose he chooses to be born again as a new person. It is unclear if the Booker the player controls is the Booker that becomes Comstock or if that was a different Booker in a different reality. At this point, multiple versions of Elizabeth drown Booker, all in an effort to undo all of his terrible actions as Comstock. All but one version of Elizabeth fades away, implying that the cross-reality problems caused by Booker/Comstock have finally been resolved.
The Lutece 'Twins'
The ending also reveals the truth about the Lutece "twins," who appear to Booker throughout the game's story. The twins, Robert and Rosalind, are actually the same person from different dimensions. The Luteces are the ones who invented the machine that allows for tears in realities to be created, which allows for Comstock to snag Anna from one dimension and take her to a different one. Rosalind Lutece helps Comstock because he is one of the few people willing to fund a female scientist. As fans have surmised, Comstock later has someone destroy the Lutece's machine, resulting in them gaining the ability to exist outside space and time.
As pointed out by Reddit user u/Space_Cowboy98, the Luteces have attempted to have Booker save Elizabeth/Anna to fix the broken realities over 120 times. The idea is that if Booker can get Anna back and they can make it so that Booker never becomes Comstock, everything will be reset, since Comstock is the one that asks the Luteces to get a child from another reality in the first place. Non-linear time and dimension-hopping sure gets confusing, doesn't it?
What Happens to Elizabeth/Anna?
The end of the game sees Elizabeth create a new constant using her reality-bending powers. Over on Reddit, u/Crimision wrote, "In the original ending I thought Elizabeth used all her god-like power to change a variable to a constant. That being if Booker chooses to be baptized then he will drown and not have a chance of becoming Comstock."
After Elizabeth's actions, it appears as though the alternate versions of Elizabeth are merged into a single being, seemingly making herself a constant as well. Of course, Crimision added that the game's "Burial at Sea" DLC complicates the story a bit, as Elizabeth needs to track down and kill one more version of Comstock that occurs in Rapture.
While trying to kill the final Comstock, Elizabeth also ends up getting involved with the set-up to the original "BioShock." During the story, she becomes aware of the final results of that game, and realizes she must die in order to set that game's twist-filled plot into motion.