How long would 3 780 Tis be sufficient for gaming?

Solution
This is a very difficult question to answer precisely, but as of now one 780 ti will run most games on max settings at well over 100 fps, which suggests that 3 would probably yield 250 fps+ (assuming you had a cpu that could keep up, which would be difficult if not impossible to find). If we assume that by "support gaming on max settings" you mean a single 1080p monitor at a minimum of 60 fps in the most demanding games, I would imagine that that would be possible for at least 5 years, and probably closer to 7 or 8, perhaps even more.
This is a very difficult question to answer precisely, but as of now one 780 ti will run most games on max settings at well over 100 fps, which suggests that 3 would probably yield 250 fps+ (assuming you had a cpu that could keep up, which would be difficult if not impossible to find). If we assume that by "support gaming on max settings" you mean a single 1080p monitor at a minimum of 60 fps in the most demanding games, I would imagine that that would be possible for at least 5 years, and probably closer to 7 or 8, perhaps even more.
 
Solution
as above, but it would seem pointless buying 3 now just so you can run games in 5 years time, because they'll be under utilised at huge cost for the next 3-5 years, by which time, there will be a single GPU at much lower cost that will trash them.

Unless you are going for 3 x 4k monitors now, which I would if buying 3 x 780 ti's
 
The law of diminishing returns affects graphics cards after the 300 dollar price range and since 60 fps is achievable now with the card on most games a single 780 ti maybe a waste money wise. essentially you will have a much less efficient system in terms of power heat and space compared to new cards in the next generation of graphics cards.