Sunday, April 08, 2007

Red vs. Blue

No, this is not about the 2008 Presidential Election. It is a little Firefox entension game called Red vs. Blue.

This is a very simple game which you can either master or concede defeat to in less than 30 minutes. Warning: it is a bit maddening. I think air traffic controllers, hockey goaltenders, and parents with four or more kids would probably fare well in this game.

As always, below are my high scores (Normal level) if you want to try to beat them (Firefox only).

One interesting thing about this game is that it will terminate play with a dialog box as soon as a winning position is achieved (i.e. all of the red balls on the left, and all of the blue balls on the right). An interesting thought that occurred to me is whether the game would ultimately win "by itself" due to essentially random brownian motion in the field of play.

There are 20 balls in the game, that can each be in one of two positions. So it seems clear to me that there are 2^20 = 1,048,576 total possible positions. There are 604,800 seconds in a week. So assuming a ball is transferred from one side to the other on average roughly once per second, it would take about 12 days to go through a million permutations. I suspect that, for various reasons, it might take longer (maybe a month) on average to reach a winning position. This is because some balls seem to travel faster than others, and because I suspect that the successive positions are too highly correlated with one another.

Anyhow, if someone is interested in leaving Firefox open for a few weeks, it might be interesting to see if a winning position is ever achieved.


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