There are 24 games to 1 full page. There are, in total, 75 full pages of games, plus 1 page that contains 18 games.
24x75 + 18 = 1818 games. Why am I getting a vastly-smaller number than Ian? Either the number of games listed is acting up or something fishy's going on....
Technically there will be an infinite amount of games on Armor Games as long as the site keeps running. When the site shuts down (if that every happens) then there will be zero games available on Armor Games.