The Incomplete Strategy Guide

About This Guide

Until recently, I mostly played Transmutations rather aimlessly--without ever feeling like I had quite a grasp on what I was doing. I've known since making the game that some strategy must exist, theoretically, but it would to take a bit of math to figure out.

This guide is a first swing a hashing out some of that strategy. I call it "incomplete" because it certainly doesn't cover every situation, but also because it isn't necessarily the best case strategy either--it's just the best I've come up with so far.

How Transmutations Works

Transmutations is built on cellular automata. Each game, a new automaton is created, which determines how different tiles (or empty spaces) transmute. This means that the actual combinations that produce each Element will be different each game. However, we can learn a little about the automata that Transmutations uses and build a generalized approach off of that. (If you're lost at the notion of cellular automata, don't worry--I'll try to explain the parts you'll need to know.)

Formally, the automata in Transmutations are outer totalistic cellular automata, which is a fancy way of saying that each element has a value, and every tile transmutes based on the sum of the values around it. There's a diagram of this in the in-game guide. The in-game guide also explains that 2 Earths = 1 Iron and 2 Iron = 1 Gold, but for this guide I'm going to use more directly mathematical language.

Here are the automata values of each tile in Transmutations:

• Empty Cell: 0
• Earth: 1
• Iron: 2
• Gold: 4
• Elixir: 0 (Note: Don't leave Elixirs on the board! They are equivalent to an empty space, but you lose the Elixir!)

Every time you hit transmute, each square on the board looks at the squares next to it (including diagonally), takes the values from the list above, and adds them all together. The sum tells it what element it is going to transmute into, according to the rules created for this round.

Each tile (or empty space) has a different set of rules for transmuting, so the other factor worth noting is the tile itself. I've been combining these to form a little short-hand. For instance: E3 represents an Earth tile with a sum of 3 around it (that could be 3 other Earths or 1 Iron and 1 Earth). If we discover that E3 transmutes to Iron, we could say E3 → I.

I'll be using these letters to indicate the different tiles:

• V - Empty Square (void)
• E - Earth
• I - Iron
• G - Gold
• X - Elixir (Though we won't actually worry about any Elixir contexts, since you shouldn't be transmuting Elixirs!)

So we might talk about V0, G4, or I18. We'll call each of these pairs a context. How many contexts are possible in Transmutations? Quite a few. Each square can have a value up to 4, and with up to 8 squares surrounding a tile, we can have sums up to 32. Combine that with each of the 4 letters (V, E, I, and G) and we get 128 different contexts! Yikes.

[Technically, we can disregard a couple: V0 will never produce anything but another empty square, and no combination of tiles can produce a sum of 31 (we'd need a value 3 for that). But that still leaves us with 123 contexts to worry about.]

Transmutations Theory

So our goal is to produce the most Elixir. To do this, first we have to find out how to even make Elixir, and then we need to figure out how to make as much of it as possible. Lets call these two facets of the game Tests and Production. For Tests, we need to explore as many different possibilities on a single board; for Production, we need to get as many squares as possible to have the context want.

Both Tests and Production boards are going to vary somewhat based on the round we're playing, but there are some things we can generalize across each round.

For Testing, it works well to memorize specific board layouts that test several contexts in a group that you want to focus on. If you know the pattern you just played, you'll be able to figure out which contexts produced something useful. I'll share a few of the Test Boards I've designed below. They only cover a portion of the 123 contexts, but often they are enough to discover the recipe for Elixir.

Production boards vary a lot more, since we're trying to maximize a specific context, rather than create a broad variety. Theoretically, there could be a different optimal layout for each context, perhaps even more when things like cost come into play. But there are still some general techniques which are useful--though you may need to tweak them depending on the specific context you're working with.

Test Boards

One consistency in Transmutations is the first round: we always start off knowing nothing about the rules, with an empty board and no arcana. Because we have no arcana, the only element we can place on the first round is Earth, so the only contexts we can test are Void and Earth contexts. Furthermore, since Earth only has a value of 1, we can only test sums up to 8. So on the first round, we're limited to the range { V[0-8], E[0-8] }.

What we need to do on the first round is test out as many contexts as possible in the above range. I've come up with a layout that tests all but 3. I call it Moonlight, since it looks like a moonlit scene (and I needed a name):

Play this board on your first turn and see what turns up. If you get an Elixir, you might be ready to switch to production!

If you get Iron or Gold, it may be time to do some Test boards using those new elements (or you might have to run a production board on one of them to get arcana first). In the rare case that you play Moonlight and still get nothing but Earth and empty squares, you'll need to test out those last 3 contexts: V6, V7, and E6. It's pretty easy to fit all three of these on one board, so I'll let you come up with a layout that you like. Just make sure you remember what was where!

Once you've gotten Iron or Gold, you can farm arcana to make whatever elements you need. You still need to track down a recipe for Elixir, but now you're looking across all the contexts (minus the ones you've already tested).

Here are a few boards that test selections of the Iron and Gold contexts. I haven't designed boards for every context (after all, this is an Incomplete guide), and it's likely there are better options out there, too!

Of course, these Test Boards only cover a handful of the situations, but they're a good start. There's likely a board that covers more ground in the Gold contexts than Gold Wedge does, but I haven't gotten that far yet...

If you have to improvise with tests, the important thing is to be able to remember how you had things before you Transmuted. If you make an Elixir in an unexpected spot, you'll need to be able to figure out how you did it!

Production

Once your test board produces the element that you need, you'll need to take note of the specific context for that tile. Unless you've memorized which contexts are where, you'll need to recall the original tile and figure up the sum that was around it. Once you know the context, it's time to figure out how to produce as much as possible.

In a production board, you're likely to have squares that you're planning to transmute, as well as some squares that are just to help create the right sums for the context you need. Let's call these target squares and helper squares.

Here are just a few quick tips for how to make a good production board:

• Place helper tiles in spots where they are adjacent to as many target squares as possible (without bumping them into target squares that already have the correct sum!).
• Try to turn helper squares into target squares! For example, if you need I3 to make Elixir, you could place Iron tiles with 3 Earths, but it might be smart to use an Iron and an Earth instead. That way, you can make pairs of Irons with a shared Earth, and you'll be getting two Elixirs instead of one!
• Similarly, it's often good to use fewer helper tiles when possible. If you can switch in an Iron in place of 2 Earths, or a Gold in place of 4 Earths, you'll clear up a lot of space on the board to try and make more of whatever you're producing. The flip side of this is cost, though, since higher-value Elements also cost more arcana.
• Squash things together--but carefully! A good production board is very compact, but be mindful that any extra tiles will throw off the context. That includes your target tiles, if you put them next to one another. For instance, if you need E4, you might want to cluster a bunch of Earths around a single Gold--but that isn't going to work! If the Earths are within range of each other, they'll be added to each other's sums and throw off the context. At that point, you might need to switch your Gold for an Iron and position the Earths so that each one has 2 other Earth neighbors.
• Use the edges and corners! Edges have 5 neighbor squares; corners have only 3. In some instances, this is too few to achieve the context that you need, which might make them a good place to put helper tiles. In other cases, they work well as target tiles, since it's easier to keep track of what their neighbors are.