There is a real difference between impartial and partisan games. I don't just mean that analysis is different, or that impartial games will always evaluate to Nimbers. I'm referring to something more basic:
People generally like playing Partisan games.
I can best present evidence by looking at the vast array of published partisan board games. It is hard to find published impartial games! Instead, published games are able to support some sort of mantra. I have my pieces and you have yours. I will build up my position and at some points there may even be a lack of interaction with whatever you're doing. We will race towards some winning condition. I will be able to see my strategy materialize, whether or not it is a good one.
All of these are aspects of partisan games that are missing in impartial-land. In that mystical place, every move forcibly interacts with your opponent. Your board strength is tied precisely into who is the current player and not in some separate position that you can see. Instead of racing towards a finish line, both players are the same racer, just worried about which leg will be forward when the ribbon is snapped.
I think it's natural that we don't like these sort of games. I'm looking forward to playing a World War 2 simulation game with my dad this thanksgiving, but I wouldn't be looking forward to it if after each turn we swapped teams!
In the past few years, I've made some off-hand comments (not here, in "real life") about people being bad logical machines, but instead good emotional machines. We often allow our emotions to make decisions for us instead of precisely reasoning through all the logical details. Sometimes this causes bad decisions to be made, but sometimes it lets us get to the heart of the matter and make decisions quickly. I'm in no way a psychologist, so I won't attempt to back this up with any data and keep blundering ahead.
Partisan games really clue into this emotional capability. "Well, at this point, there are lots of my tanks on the board and not many of the opposing tanks... I must be winning." We hope to be able to evaluate the strength of our board position and we can at least approximate this by taking a look at the game state. "Is it better to go first in Hex? Yes, it's better to have more of your pieces on the board." That is the basic response, and it turns out to be true, though an actual proof is somewhat more involved.
This is more difficult with impartial games. Near the beginning of a long game of Kayles on a complicated graph, I am not sure whether I'm winning or losing unless I check all the possible moves. Oof! That is a logical problem my brain doesn't want to have to work through. (At least, not on it's own.)
I may continue challenging my students to impartial games, but soon they're going to get sick and ask me to break out a Hex board.
P.S. Enjoy the greatest rivalry in sports this weekend!
A Domino-Covering Problem
5 weeks ago