OIN is an anagram of 'No I,' which not very satisfyingly satisfies the clue, (that's not *much* worse than saying 'less and more.')
I think 'You're in second place' means the second letter is the 'red' one, so it could also mean that several dwarves (although 'any' would be hyperbolic) would fit the bill ... well, Oin, Bifur, Fili and Kili in this case, since Gimli isn't in the particular *sub-gaggle* of Erebor dwarves who went on the actual Quest of Erebor.