The developers of two multi-player bot opponents have happened upon the right formula, managing to convince human players they were playing against actual people rather than computer controlled chunks of code.
This gaming equivalent of the Turing Test was passed by multi-player bots UT^2 and MirrorBot, which gained "humanness" rating percentages of 52.2 per cent and 51.9 per cent respectively, in multi-player matches. Humans usually only get humanness rating scores in the 40s, so they convinced players they were more human than... actual humans.
The UT^2 bot has been made publicly available if you'd like to face off against it and own a copy of Unreal Tournament 2004, with the coders sticking it up on their site for all to enjoy and get irrationally angry with. [BotPrize via The Register]