A recent post on Less Wrong, Levels of Action, reminded me of a game I created whose dynamics I wanted to explore. I still have not explored the dynamics to a great level of depth, but I thought it would be interesting to the nerdy community that reads my blog.

The idea came after playing Castle Wars 2. In that game you try to build your castle as tall as possible while keeping your opponents castle as short as possible. The basic game dynamic is an action/meta-action trade off: (oversimplifying) you can play a card to gain 10 bricks, or you can play a card to gain one brick per turn for the rest of the game. I was surprised by the amount of subtlety derived from such a simple dynamic, and I recommend the game to anyone wanting to kill an hour. It’s not the best game ever, but it’s not as trivial as it at first seems.

I wondered what would happen if I removed the cards, the weapons, the defense from that game and replaced them with more levels of this same dynamic. Here’s what I came up with.

You can play it with a chessboard and poker chips (my old game design standby). You don’t need 6 of the rows of the board. Each player plays on a side of the board, and has eight squares which we will label, from left to right, 1 to 8. Each square can have up to eight chips in it. The goal of the game is to get eight chips in the eighth square. Here is how play proceeds:

On your turn, place a single chip in any of your squares. Your opponent does the same. Before each turn, “cancel out” any chips that both players have on corresponding squares. That is, if you have 4 chips on the 5th square, and your opponent has 5 chips on the 5th square, remove 4 chips from both, so that you have none and your opponent has one. Then (still before your turn) duplicate each square to the next higher position and truncate down to 8. So before this action if your eight squares had these values:

0 0 1 4 5 2 0 3

Then after this action, the state of your board will be:

0 0 1 5 8 7 2 3

Another way to think about it is that you slide a copy of your board one position to the right and add (then truncate).

Then place your new chip, and your opponent takes his turn. That’s it. The first player to eight in the eighth square wins.

Despite this game’s simplicity, I have been unable to devise a good strategy for it. The strategy for the game seems to revolve around estimating the length of the game. If you know how many turns the game will last, it is fairly easy to determine how to play optimally. But knowing how long the game will last is not so easy to determine.

Try it out, think about it. Let me know if you discover anything.