I don't think a full Culture Mind is present but he outstrips his spacecraft's ability to help him with preparation in later stages of the competition. I clearly remember this.
Indeed. (spoiler following) The plot basically revolves around SC manipulating both Gurgeh and the Empire of Azad in an ever bigger and complex game than the one in the book. Given how Banks describes the Minds in other books it would be extremely curious if they wouldn't crush any biological player in any normal game the same way chess computers crush humans these days. But, it is possible that a more limited mind like the security drone could be outstripped by Gurgeh. In one of the other books they do mention that "smaller" machines like environmental suits and small drones get more limited minds than full starships as it would be cruel to put a fully capable Mind in such a limited body.
The last page of the book gives it away: (MASSIVE SPOILER OBV) The security drone who came with Gurgeh to Azad was the same drone he meets during the introduction chapters who was "rejected" from SC and offers to let him cheat (though it was wearing a disguise at the time). Then, after he cheats he basically gets blackmailed into going to Azad and conveniently this "non-SC" drone comes with him in a very "non-SC" ship that claims to have its weapons removed but doesn't. At some crucial points the security drone influences Gurgeh to play the best he can, such as when he takes him on a tour of the slums and the Culture-educated Gurgeh gets so furious at the mistreatment he witnesses that he absolutely crushes his opponent in the next match.
They mention in one of the final chapters that the minds wanted the Azad empire to become a better place since it was really shitty to its citizens. However, they couldn't just invade and impose laws because they're the Culture, and the Azad empire kept claiming moral superiority because they had this one thing (the Game) that they thought the Culture couldn't match. The Minds knew Gurgeh was talented enough to get far enough in the tournament that the Azad Empire would be seriously shaken, because if this single foreigner can beat so many of the best and brightest in the Empire at the thing it claims to do best then what could the entire Culture do? This turns out to have been correct, at the end of the book the Azad empire starts to collapse because they no longer trust their leadership, who have been proven to be incompetent at the very thing they claim to do best. Beaten by a human btw, not even by one of the god-machines that the Culture also has. Having predicted that this would happen, the Minds set out to manipulate Gurgeh into going to Azad to play the Game and by doing so bring about regime change. The Minds and/or SC were playing a much higher level game than Gurgeh all along, he was merely one of the pieces they used to play.
