After building Fuse and Palette from the ideas of others, I was on a run where I sparred with the question, “What does a Toby game look like?” Without getting into a list of all the SRPGs I have ever played, or how I 100%’d Balatro, I thought about some of the more esoteric games I have played.
Stephen’s Sausage Roll came to mind. The best way I can explain it is as a topological puzzle game where you help Stephen grill sausages.
This reminded me that once upon a time, I had been assigned the task of writing Tic-Tac-Toe in MATLAB, and I decided to extend the concept further, and built it to support different topological surfaces: namely a torus and a Klein bottle.
If you are curious, here is a web rendering of my MATLAB Tic-Tac-Toe. I did things manually at the time… I hand coded each board state for each surface that resulted in a win, and the version I have today is missing five of the Klein bottle’s 22 winning states.
To get a little into the nerdy math…
A Möbius strip is a two-dimensional surface where you have the magical ability to return to your starting place while walking in a straight line AND the space is twisted over on itself. To make a Möbius strip, take a strip of paper, twist it, and glue the ends together. Now imagine you are an ant walking along the paper.
Extending this beyond a strip, we first must start with a joke. How many holes are there in a coffee cup? One, the same as my donut. In topology, two things are homeomorphic if there is a continuous mapping between them that is bijective and whose inverse is also continuous. Notably, this continuous deformation cannot fill ‘holes’, or tear new ones.
This brings us to three surfaces relevant for bend: a torus, a Klein bottle and a projective plane. A torus is a donut, in simplest terms. It wraps around and connects.
Like our Möbius strip, to illustrate this, imagine we have a flat board and glued its edges to each other, but this time in both directions and without a twist. I can go top to bottom continuously, and right to left continuously, and in both cases continue to return to my starting point.
Now imagine we try to play a game on the surface: how does this change the game, if at all? It does. On a flat board there are 8 ways to get three in a row. On a torus there are 12, because the diagonals wrap too, and every square sits on four of them. This makes each square as strong as the center.
Now, going up a notch, what happens if I twist one pair of the edges? This is a Klein bottle. A Klein bottle is a surface that cannot even exist in three-dimensional space without passing through itself! Similar to how a Möbius strip cannot exist in two, the Klein bottle ‘folds into itself’, and our ant friend walking along its surface can not only return to its starting point by walking along a row or a column, the space itself folds over like that of a Möbius strip.
Given the math, I thought, what games could I play on a Klein bottle? I had proven Tic-Tac-Toe could be played, and while different, it is not much more engaging once the novelty wears off.
So I wondered, what about solitaire Scrabble? If that was to work, what should the board size be? Still on my run, I settled on the idea of a 5x5 board with core mechanics close to Scrabble: a 7-tile rack, and words must be formed left-to-right and top-to-bottom for each way the tiles connect. A full wrap or bend looks at each possible rotation of the letters and works if any is a word.
On my run, 5x5 seemed large enough to be interesting for a daily game, and would support words up to 10 letters long. A core constraint on it being a daily game is it needs to not take forever to play. It was mostly a gut sense that it was big enough to be too interesting, but not too large for a daily game. It also means the ‘interesting’ tiles have a high density of the board, as the board gets larger, the seams take less space.
The next idea to solve was the scoring mechanic. For this I thought it would be relatively easy. I should heavily incentivize making use of the Klein bottle geometry. A word across a bend scores 3x, and across a wrap 2x. Fill a full bent loop 50 more points (10 letters on the 5x5 board) and playing all seven tiles at once also earns an additional 50.
The last components I needed to think through were: how do I ensure the game will be playable, how should the mechanic work to ditch unwanted tiles, how should the difficulty flow, and what do I call this?
The playability is a check and a contract. The initial set of tiles (randomly determined each day) must always yield a few playable words: at least four two- or three-letter words on Monday, three on most days, and two on Friday. I also decided each tileset should be random, with rules for how the letters get selected: how many vowels there are, and how often the difficult letters (J, K, Q, X, Z, V, W, F, H and Y) show up.
Ditching unwanted tiles became the trash. After a bit of thinking and experimentation, I landed on trashes are earned for every 20 points.
The difficulty itself took a pattern from what I had already done in Fuse and Palette:
- Monday: Easiest entry, fewest difficult tiles, and a starter word already in your hand
- Tuesday: Fewer vowels, a few more difficult tiles
- Wednesday: Fewer vowels again
- Thursday: Twice the difficult tiles, with one guaranteed early
- Friday: Most difficult tiles, fewest vowels and the smallest bag
- Saturday: Same tile difficulty as Thursday, and on a projective plane… Double Twist
- Sunday: 7x7, difficulty same as Wednesday
The projective plane. For Saturday, I decided we needed to do something weird: introduce a second twist. What this means is that words can bend in both directions, and opposite corners touch each other twice, once across and once down. So those corner spaces need to be able to form two-letter words with each other both ways. One pair even flips: ON across reads NO down.
All that left was a name, I wanted a name and presentation that was somewhat austere, but also absurd, nearly a Comic sans aesthetic. Like, who would think to make this? That’s where I landed on the name and mark bend. In lowercase, and made that permeate throughout. Similar to Stephen’s Sausage Roll, playing bend requires you to bend your thinking around topological concepts.
That yielded the first build of bend. The strange thing to really understand is that the words still flow left-to-right and top-to-bottom. A word that runs off the right edge comes back on the left, on the mirrored row, and keeps reading the same way.
across the bend · off the right edge, back on the mirrored row
down the wrap · off the bottom, back in at the top
Pick a tile, then a square. Submit both boards to compare.
Shockingly, the game is without a shadow of a doubt fun, to me at least. The daily has become the last thing I do each night, or one of the first things in the morning! Unlike similar games, by being solitaire it is a planning game. I start by building the smallest word I can, and plan for what words I could build upon it. The scoring seems comparable to bowling: 100 is a solid beginner game, with practice and skill 200 is a very good running average, and 300+ is a ‘perfect’ game!
One thing I might have changed, the game has no form of undo, even if you make a mistake like trashing the wrong letter. I did make there be no punishment for guessing, but every once-in-awhile I get punished by greedily waiting for a letter that never comes, or get impatient and then the letter I needed was next. It is unforgiving, and I have learned it makes the game, but these experiences tempt me to create an undo.
There are a lot more things for me to say about bend, including its accessibility options, what else I thought about in the visual presentation, how I stopped the temptation to cheat, and even how I extended it to feature correspondence multiplayer, but I will leave it here for now.