Hah! Phil: read the relevant chapter of Winning Ways. There can be no better introduction. I think Carroll is having a little joke—the wetpaint file was written by me to explain some of the subtler points in Berlekamp's book, which you might want to read after Winning Ways. I would suspect that a lot of what I wrote in that wetpaint file would be incomprehensible to someone who hasn't read Berlekamp or WW.
As for online literature, the big lacuna is that no-one, it seems, has written an online explanation of the application of Nim to dots and boxes. In short, a “typical” game of dots and boxes ends up with a few long “chains” of boxes which snake around the board. There is a natural and obvious way to play such a position—open the shortest chain first, let your opponent take all of the boxes in it, and then they open the next shortest chain, which you take all the boxes of, etc etc. This is typically totally the wrong way to play the endgame; there's a trick called the all-but-two trick, which you can read about on ilanpi's site. Once you realise this you instantly deduce that most games of dots and boxes are about parity—you don't want to open the first long chain. So now consider the following game, strongly related to dots and boxes: the rules are just the same, but you don't count who gets how many boxes, you just say that the last person to complete a legal move has won the game. This game is in fact surprisingly similar to dots and boxes, and the Conway-Berlekamp-Guy theory of games applies to it now because it satisfies the “normal play” rule. Winning Ways explains the practical consequences of this observation, and if you have understood these then you're already a fine dots and boxes player.
wcc
