rrspamrr :
What is the cheapest possible build (not including the OS) to play crysis 3 on max settings 1080p 1920 x 1080?
It depends on what you're trying to accomplish, you can build a 500$ system and start crysis and set everything to max @1080p. Though chances are you will be running it ~5fps, so essentially are you trying to get something to run crysis at a playable 60~fps maxed out?
Here is a toms review of the 780ti and its performance along with a few other GPUs with crysis 3 http://www.tomshardware.com/reviews/geforce-gtx-780-ti-review-benchmarks,3663-7.html