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Second Game by Charles V deVet
I remember rambling about this book sometime during the discussion of Player of Games - well, I finally tracked down a reasonably-priced second hand copy and read it again for the first time since my late teens 
The basic principle of Second Game is that a human explorer / spy / negotiator tries to infiltrate an enemy society which is threatening interstellar war with the large number of loosely affiliated human planets (think Federation or Ekumen rather than Galactic Empire). He masquerades as a player of the local game, with the challenge "I'll win the second game". He uses the first game (which he may or may not win) to identify his opponent's weakness and goes on to exploit the weakness and win the second game.
Superficially, at least in my memory of it, the basic idea and plot were not all that different from the rather later Player of Games, but in fact the overall sweep, and the feelings you are left with, are very different. Second Game is much shorter, for one thing, and focuses more on the particular direction of the plotline rather than meandering from side to side as Player of Games does. Iain Banks is also, IMHO, a better writer, and was also writing after quite a lot more development of how SF tends to be written. Second Game comes over as rather dated in parts, which is fair enough since the original version was published in 1962 - however it's still an interesting idea and I am glad to have refound it.
Comments
Interesting! I remember you talking about this at the time. I would not be surprised if Banks had read this and at least had it in the back of his mind - like Harrison and My Sweet Lord.