Comments on: Tetris http://www.withoutatraceroute.com/2009/06/tetris/ Time to live. Thu, 03 Dec 2009 05:42:46 +0000 http://wordpress.org/?v=2.9.1 hourly 1 By: Nathan http://www.withoutatraceroute.com/2009/06/tetris/comment-page-1/#comment-3888 Nathan Fri, 19 Jun 2009 03:44:07 +0000 http://www.withoutatraceroute.com/?p=2431#comment-3888 Saying it's "mathematically" impossible to win at Tetris is a bit of an odd way to put it; I'd say it's <i>defined</i> to be impossible, since there's no winning condition (but that's not very interesting mathematically - it's just that the game always keeps adding more blocks). Still, the fact that there are fatal sequences of blocks is interesting. I wonder if someone has estimated the expected time to lose given perfect play. I wouldn't be surprised if it's longer than the period of most PRNGs (that 70,000-block sequence of S and Z must be horrifically unlikely). If that's the case, on a real computer the sequence of blocks might repeat after some tremendous amount of time, and so it <i>would</i> be possible for a perfect player to continue forever, sometimes - as long as the repeating sequence they got didn't happen to contain a fatal sequence. By the way, that last link seems to be broken - it just goes back to this page. Saying it’s “mathematically” impossible to win at Tetris is a bit of an odd way to put it; I’d say it’s defined to be impossible, since there’s no winning condition (but that’s not very interesting mathematically – it’s just that the game always keeps adding more blocks). Still, the fact that there are fatal sequences of blocks is interesting. I wonder if someone has estimated the expected time to lose given perfect play. I wouldn’t be surprised if it’s longer than the period of most PRNGs (that 70,000-block sequence of S and Z must be horrifically unlikely). If that’s the case, on a real computer the sequence of blocks might repeat after some tremendous amount of time, and so it would be possible for a perfect player to continue forever, sometimes – as long as the repeating sequence they got didn’t happen to contain a fatal sequence.

By the way, that last link seems to be broken – it just goes back to this page.

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