Recently, while watching a tennis match, I was chatting with a friend of mine, my first poker teacher. Back in 2006, after following his online poker play for a semester, my understanding of the game increased dramatically. I had a breakthrough that I imagine most other beginning poker players have at some point, during which they rapidly realize their previous approach to the game needs to be completely scrapped. My simplistic method could not accommodate the depth of poker, and so I rebuilt my strategies within a new framework and became much better at the game. If you're reading, thanks man.
So while we watched Federer demolish some early round opponent at the Australian Open or Dubai, I tried to catch up on my poker gossip, asking about the results of recent tournaments. Quite naturally, we started comparing what we were talking about (poker) to what we were watching (tennis). To my surprise, the comparison was quite fruitful: many characteristics of one game had an analogous feature in the other game. Now, before we get to this likeness of games, I'd like to introduce the theoretical framework which will serve as the language of the comparison: category theory.