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personal recommendations:
FPS:
counter strike source or g.o.- perhaps needless to say; also has other types of gameplay than the default arena rounds, at least zombie mod)
arma 3 (= Operation Flashpoint 4) - also perhaps needless to say, realistic military FPS, freely scriptable with ingenious gamemodes (e.g. 16 players, each with a free selection of AI soldiers & vehicles, fighting for villages on 20x10 km with RTS unit production); large maps; scenarios of this are origin of DayZ and Battle Royale
natural selection 2 - arena fps aliens vs humans with RTS commander, 16+ players
gta V online - many players, modded maps with partly spaced-out race and stunt tracks
-if older games and few player sessions without central relay servers also count: -
warzone 2100 - one of the first 3D computer RTS games, huge tech tree and customizable vehicles, with extensive artillery / indirect fire
age of empires 1&2, empire earth 1&2 - perhaps needless to say, roughly similar games, RTS with technology age progression (empire earth 1&2 extend the ages up to and beyond the modern age, which can result in even more unusual lopsided (combat) encounters)
old FPS/RTS hybrids:
machines - old 3D RTS with awesome looking robots and the rare possibility to take first person control of the units (and not crappy like in earth 2175)
battlezone 98 - difficult first person RTS with hovertanks on the planets of the solar system
(urban assault - difficult first person RTS with both a fixed player unit and taking remote control of any other; might not run right away on modern computers, but there are people who found out how and put it online, potentially with patches)