Friday, March 26, 2010

Game Description: Toppling Dominoes

I did a "tour" of classes the past few weeks, advertising my board game course next semester. While doing this, I brought my copy of "Lessons In Play" to show off. On the cover is the addition of a Konane game with a Toppling Dominoes game that equals an Amazons game.

I point out that it's pretty cool that we can express games this way. Unfortunately, I realized that I didn't really know anything about "that dominoes game". Hmmm...

It turns out the rules to this game are very simple! Here's how it works.

With a supply of dominoes, each colored green, blue or red, set some of them up in one row. Then the Blue and Red players alternate turns, each knocking one of their own colored dominoes (or any green domino) to the right or left, thus knocking down all the other dominoes on that side.

Notice that this game, just like normal Nim, is not terribly interesting alone. In just one row, any player who has a domino of their color (or green) on one of the edges of row can just topple that one, knock down all the other dominoes, and win as there are no more plays. In fact, in the case with only blue and red dominoes, if both ends are in your color, your opponent has no way to prevent you from winning.

With more than one game, however, this gets more interesting and it becomes important to find the actual value of each game to play best.

I don't know the complexity of analyzing this game, though.

2 comments:

1. I hope it's not rude to ask a general question in the comments of a post on a specific topic. I'm probably not part of the intended audience of this blog and as such there are some embarassingly simple concepts that I'm not confident about.

For example, when you talk about the complexity of a game, are you talking about the computational complexity of determining whether (or does it mean determining how) you can win a game.

Is this a concept that, as Wikipedia notes, only apply to games that have been generalised so they can be made arbitrarily large?

2. Oh, wow, I thought I had responded to this days ago!

Commentium, it is definitely not rude at all! There are many simple concepts I am also embarrassed not to know!

When I talk about the complexity of a game, I am referring to the computational complexity of determining which player has a winning strategy, yes.

This does only apply to games that can be generalized to any size. For some games, such as Hex, this is very natural, while with others---Chess, for example---this is a bit more contrived.

This is often the question I am most interested in in this field, but I am learning to appreciate other game qualities! :)