Last semester I took a course on Game Theory, and within that course we went through both classical and combinatorial game theory. While it was very fun to study combinatorial game theory specifically, I have yet to encounter an actual application of the theory, be it in real life or in any other part of mathematics, technology or the sciences.
As far as I know, the theory of impartial games (Sprague-Grundy in particular) is somehow of interest to theoretical computer science (and you are very welcome to explain that or correct me if I'm wrong), but other than that, I have no idea how/where I could apply my knowledge of surreal numbers, thermography, ups and downs, et cetera.
Not even the (quite) common type of mathematical proof technique denoted "adversarial games" have I seen analyzed with these tools, which I find odd.
I should also mention that I am aware that Go players use terminology stemming from combinatorial game theory, but as I am not a Go player myself, someone might be able to give me an explanation.
So, the question is: Are there any applications of combinatorial game theory worth mentioning?
You can assume that I have read (at least some of) all four volumes of "Winning Ways", "On Numbers and Games", as well as the newer "Lessons in Play" when answering.
