Does a 4k projector for gaming exist?

[Millhouse_5]

So here's a little backstory.  I'm in a new house and building a home theater in my basement and want to be able to watch movies but also hook up a computer so I can play steam games and a few console games as well.

Since the screen is going to be at least 100 inches, 4k seems like the way to go to keep everything crisp at that size.  (I'll only be about 10 feet away from the screen).

 

But here's the question. Is there a 4k projector that runs at 60hz that has low enough input lag to game on and doesn't cost over 2k. 

[TheFlyingTraut]

You're going to have a tough time finding something worth your $ for what you're wanting at that price honestly. How dark/bright is the room?

[Ross Siggers]

24 minutes ago, TheFlyingTraut said:

How dark/bright is the room?

I mean...it's a basement. You can have it as dark or as bright as you want  

[Millhouse_5]

Basement lighting is very easily controlled.  There's one window in the room in question with a blackout blind over it and dimmer switches on my lights.

 

If there isn't an option that's even vaguely affordable then how does 1080 work on a screen that size.  I would imagine that it gets a little pixilated at that size.

[beavo451]

According to Projector Central, the Benq TK800 and Viewsonic PX747-4K have the least input lag at ~44ms.

[NickPickerWI]

Oof...44ms...

 

But then again it is a projector.