Well, they are full-length books (Ok, SN is shortish). There aren't many books that can be presented as a single lecture as is. The surreal numbers (as you kn

Well, they are full-length books (Ok, SN is shortish). There aren't many books that can be presented as a single lecture as is. The surreal numbers (as you know, I'm sure) are fairly subtle, and people don't have much intuition for how they should behave. Even non-technical people have lots of intuition for real numbers (even if some of it is wrong); they know that they can add them, multiply them, compare them, etc, and they even know algorithms to do so. When confronted with the surreal numbers, it's not at all obvious that you can perform those operations, much less how to do so, so there's an enormous weight of basics to build up before you can really do anything interesting (much like how the first week or two of an introductory linear algebra course can be pretty dull). Games are perhaps easier to motivate and make interesting (in my experience), as you can get to the point of analyzing and reducing simple positions and establishing the addition operation pretty quickly, without getting bogged down in "wait, why would I use this horribly complex approach to what seems at first to be not terribly unlike the real numbers except maybe I can't even do all the operations I know and love". Unfortunately, multiplication of games doesn't really make terribly much sense, so you need to restrict to numbers reasonably quickly to continue developing "conventional" mathematical structures. TL;DR: for a single lecture format, motivating and defining games and showing that there's a reasonable embedding the natural (or dyadic rational) numbers isn't a bad introduction in my experience.