This game was featured on the USACO US OPEN this year.

Seems like an interesting article, though I didn't follow all the details. I don't think it mentioned the beautiful connection to http://en.wikipedia.org/wiki/Beatty_sequence (but the example on that wikipedia page does allude to Wythoff's game)

There's an interesting connection between Wythoff's game and this year's USAJMO, #4. In the problem, we define a sequence of words . Here are the first few words and , where is written backwards:


Every word is the first part of the next word , so each word can be considered the first part of an infinitely long word . The question is, for a positive integer , how can you tell if the th letter in is or ?

AMAZING GAME!! SOO COOL. Analyzing this, here is what I have so far:
In these situations this is what will happen, given both players make their best moves:
x and x: Won game; just take everything.
x and x+1: Won game; leave 2 on one side, 1 on the other. Note that the exception to this is 1 and 2.
x and x+2: Still working on it...