Rosalind: Or Tails?
The game is making fun of the "Illusion of Choice" that a lot of games give you now the point being there are no branching paths in the game you only 'think' you did something different in the story.
So what does this have to do with Rozencrantz and Guildenstern are Dead? Well a lot actually. This play/film has a lot to do with Existentialism and how it doesn't matter what they do or even if they saw their death a "head" of time they still were powerless to stop it from ineligibly happening. Bioshock Infinite is a game all about Fatalism and at the end of the game, no matter what Booker dies just like Rozencrantz and Guildenstern. The marks on the twins board is every time Booker has came through.
In the beginning of the you find your way to the floating city and get baptized before going and exploring the city this is also a connect with the recurring Fatalism. I suppose the ultimate act of fatalism performed by the game is that the absolutely key choice of Booker’s baptism, one of two choices upon which the whole of BioShock Infinite hinges, is a choice which has already been made (and not made) for you before the title even begins. Your main goal, it turns out, is to prevent a choice from ever happening.
Even though I’m not completely satisfied with how Infinite ends up being a video game about choice that’s also linear, it does get an awful lot right. I have a love for titles which play around with the idea of “what it means (maaan)” to be a game, and there’s plenty of that on show here.
As much as I could dig up about this game and its connection themes to the play I talked about earlier this is all I could really bring up with out just going on a rant about the two beliefs being very connected but I'll leave with some examples of the twins from Bioshock Infinite and all their high-jinx.