- Conway's game of Life
- Eight queens puzzle
- Game theory
- Magic squares
- Graphs, directed acycylic graphs, trees
- Rubik's cube
- Towers of Hanoi
Why is this relevant? Because I think I like games that are based on this sort of maths. Games such as Trias, Domaine, and Rheinlander have a simple finite underlying model which the players manipulate to try to score the most points. In these games there is overt conflict, but you're only susceptible to conflict because you didn't manipulate the model to defend yourself properly - you chose different moves which left you vulnerable.
The GIPF Project, and many other abstract strategy games (Gobblet, Quoridor), are very simple finite systems (except TAMSK which has that annoying continuous time thing happening), so I can get my head around them and love to play.
Word games like Scrabble and Milleranagrams and Lexicon I think scratch some entirely different itch, but deduction games like Mystery of the Abbey, Coda, Code 777, Black Vienna, are all about optimally narrowing down a finite set of possibilities. Hare and Tortoise is blatantly mathematical, which makes it difficult to find opponents!
What about games that suck? CyberKev (who this blog is NOT about) swears that Cosmic Encounters is analytical, but I find it to be mostly political so I don't really get the fun bit. Mall of Horror is the same game with better components. Even Fish Eat Fish, although it looks like an abstract, turns out to be a political game.
Other games that suck are ones that aren't finite, where there aren't even discrete spaces for you to move on, like Warhammer 40K, De Bellis Antiquitatis, Mech Warrior, and so on. Maybe they're decent excuses to play with toys, but I don't find them very interesting as games. Even games with large maps like Heroscape don't work for me, because there are too many possibilities and I don't feel like I'm manipulating a system.
And party games! Don't get me started on party games! Oh hang on... it's my blog, I can say what I like. Taboo, Pictionary, Cranium, all absolutely suck. You can't even get people to agree on the rules so the games are decided by screaming matches between the drunken participants. They turn out to be political games where the politics isn't even part of the rules. By the way, I find playing word games without a dictionary to be a political game as well - if there's any chance of arguing about whether something's a word or not the game ceases to be a game and becomes an argument. You've gotta have the dictionary to make sure there are no arguments. Scattergories! VOMIT!
So I think this is the best characterisation of my favourite sort of games that I've been able to come up with so far. Others that suit me are Puerto Rico, Vinci, Tikal, Torres... with so many good games, there's no time to play bad ones.