20 — A Closer Look at Tetris: Analysis of a Variant Game

Following in the vein of the single-author publication pattern from a few days ago, here’s work by Kaitlyn M. Tsuruda — in fact, her dissertation — which I wouldn’t usually consider a paper in the same sense as the other reading I’ve been doing except this was a really fun thing to read:

It addresses the winnability of Tetris (where “winning” means being able to play forever, which is arguably not ideal but I digress), and poses some mathematical strategies for designing “workshops” in which to experiment with block constructions. The main construct presented is the “variant well”, which is a well with an oddly shaped, uneven floor (such as a funnel), around which one can design proofs for winnability. But first, the winnability of vanilla Tetris:

Some of the statements presented here are intuitive: You can’t win in an odd-number-of-columns well using only squares, for instance.

Some of the statements take some thinking, at least for me (and I had to draw out a few):

“It’s not hard to see that if every lane is smooth then at least one lane is empty. Moreover, there is never more than one bumpy lane, since playing a bumpy piece in the lowest smooth lane requires playing it in an empty lane.”

(Here, a “lane” is a group of two sequential columns.)

From the theorems proved in this section, Tsuruda demonstrates that Tetris in its original form is unwinnable. She then designs a system for testing variant wells toward building a winnable Tetris-derivative.

I don’t think this work necessarily relates directly to much I encounter in my work, but it’s a very entertaining way of approaching a system of complex problems. (Notably, Tsuruda works in cancer research now, as far as I can tell via Google. So that’s neat!)

This dissertation also introduced me to the concept of a Young tableau, and a mathematical way of representing a tetronimo, or a “4-edge-connected unit-cell.”