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.

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    $\begingroup$ Similar question on another se site: cstheory.stackexchange.com/questions/31884/… $\endgroup$ – Gerry Myerson Nov 11 '15 at 12:18
  • $\begingroup$ Thank you, @Gerry Myerson, this is exactly the kind of stuff I was looking for. $\endgroup$ – MonadBoy Nov 11 '15 at 12:20
  • $\begingroup$ …if anyone else has something to bring to the table, you're still very welcome to do so. $\endgroup$ – MonadBoy Nov 11 '15 at 21:31
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    $\begingroup$ Just found this: math.stackexchange.com/questions/415638/… , so nobody has to point that one out. $\endgroup$ – MonadBoy Nov 11 '15 at 21:33
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    $\begingroup$ You might be interested in "The Rat game and the Mouse game" by Fraenkel which appears to be related to connections between combinatorial game theory to combinatorial number theory. $\endgroup$ – Mark S. Nov 22 '15 at 21:24

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