First, thanks to people who suggested I add rows to the game table page. Please suggest more games to add for rows!
In the past two weeks, I have gotten more chances to play games with Wittenberg students over lunch. This turns out to be one of the best ways to try out new games! Exploring them with other newbies is very helpful and the right attitude can add a non-competitive spin to the discovery of good strategies. Unfortunately, since these students have not been studying combinatorial games, I usually wind up with an unfair advantage. Not always, though. This is the best: getting beaten by missing a great strategy that gets pointed out by someone else! Seeing the realization of that great move in a student as they make it is wonderful!
Unfortunately, next I have to admit that I had never played Domineering before. Domineering is the guiding example for many basic combinatorial game aspects, yet I had never pulled out the dominoes and checkerboard before with another player. Actually, I don't even own dominoes; I had to borrow the set from our Math lounge.
Domineering is a partisan game between two players where each turn a domino is placed over two adjacent (share a side, not a corner) squares. The Left player must place dominoes vertically while Right must place them horizontally. You may not place dominoes on squares already occupied by a domino. Assuming normal play, the first player who cannot place a domino loses.
Domineering is a wonderful example for combinatorial games and game positions. It is used as the first guiding example in Lessons in Play, mostly because simple game values can be easily found. Good moves are sometimes very easy to spot, even long before the game ends. Perhaps most important, as the game continues, it clearly decomposes into smaller subgames that add together.
Still, while playing with students lately, one of them quickly became bored. "I wish we could play the pieces either way," she said (or something like that).
"That game's called Cram," I said. "I've also never played that one. Wanna give it a go?"
We played Cram, then quickly analyzed end game scenarios. We played it a bunch more times, allowing backtracking near the end and generally figuring out how a lot of the game worked. The next time, we skipped the Domineering and went straight to Cram.
This contradicted my assumption that many people prefer proper partisan games over impartial games. Is there a general consensus between these two games?
The Best Writing on Mathematics 2016
18 hours ago