Cold Take #36 - Bounding the Strategic Triangle

Strategic freedom is a fragile thing, yet the feeling of devising your own plans is something that many games try to instil. The issue is that, as players explore and refine their strategies, the space of viable strategies can narrow down to a few options. This is usually seen as a problem with competitive multiplayer, but singleplayer games are not immune. Any game that offers strategic exploration and mastery risks revealing itself to have only a single best approach, and if the challenges become great enough, players will resort to it. This problem is never fully solved, only managed, but there is still quite a bit in the managing.

This post is on some concepts that help tackle the problem above: strategic RPS (rock-paper-scissors) and the strategic triangle.

Strategic RPS is a simple model of strategy that reduces decision making to one of three approaches: offence, defence, and economy. These approaches form a natural counter relationship where offence beats economy, economy beats defence, and defence beats offence. Many players have an intuitive understanding of strategic RPS, as it is common knowledge that defensive play is beaten by investing in economy and eventually overwhelming the defences.

The power of strategic RPS is its generality, at least if we define it broadly enough. This requires a brief detour into the idea of economy. The standard economy of RTS involves extracting resources such as metal, ore, or minerals, then spending it on units and more economy. But the economy part of strategic RPS encompasses more than that. To start with, it is useful to think of construction capacity (buildpower in Zero-K) as a form of local, unstockpileable, resource. We can go further though, as the cost of anything can be converted into the time taken to assemble its prerequisites, which suggests treating travel time as a kind of cost as well. Many games have resources in the most general sense, but what sets strategy games apart is the ability to make choices that dramatically increase your resource income.

We will call income-increasing decisions "economic investment", and the term encompasses all ways to reduce your strength now for the promise of greater strength later. This covers building metal extractors and power plants, but also covers actions such as research and increasing your tech level. An upgraded unit is a more efficient unit, so upgrades are roughly equivalent to generating extra income that can only be spent on unit production. Local actions can be economic investment too, such as moving a constructor to a better location. The constructor trades the work it could be doing now for the ability to do work in a more advantageous position later. It takes more time to "produce" a constructor far from your factory.

It is worth taking a closer look at the relationships between the three aspects of strategic RPS. In doing so I want to demonstrate the strategic RPS is something intrinsic to strategy games. Once you have economic investment, you have strategic RPS, and it takes extra work to downplay or remove. It all hinges on economic investment, so we will start there.

Offence beats economy because economic investment leaves the investor vulnerable to attack. RTS needs offence because otherwise there would be nothing to stop players funnelling all their income into more and more economy. Strictly speaking, a game with absolutely no offence would lack a win condition, as even the most economically focused strategy needs to turn its overwhelming resource advantage into a way to kill the enemy. This is how economy beats defence: if both sides leave each other alone for a while, the side with more economy will overwhelm the other. With the economy interactions of strategic RPS figured out, the relationship between offence and defence can only go one way.

"The best defence is a good offence", or so the adage goes, but this is not the case in strategic RPS. Offence already beats economy, so for offence to not be the dominant strategy it had better lose to defence. Strategic depth in RTS requires that there be ways to spend resources defensively, and defences have to be good enough to fend off a greater investment in offence. Note that this does not mean all games need turrets. Producing defence-oriented units counts as defence, as does building in a more defensive way, at the cost of some economy. Starcraft provides an example with ramp walling, since it takes workers longer to reach structures when they are built further away.

Strategic RPS is a decent model, but it is a bit unrealistic as players rarely go all-in on offence, defence, or economy. Back in the day we would use the term as a shorthand for related ideas. For our purposes we had better park the term here and start on the strategic triangle.

The strategic triangle is a map of strategy space, where strategy space can be imagined as a nebulous cloud that represents every approach players could take in a game. The strategic triangle adds structure by scoring each approach by how offensive, defensive, and economic it is. The space is then stretched and flattened into a triangular shape so that the most extreme strategies sit at the vertices of the triangle, while everything else exists somewhere in the middle. To simplify things we also discard the pointless strategies, such as that of blowing up your commander at the start of the game. If you want to get technical you could consider the triangle to be the Pareto frontier of the projection of strategy space onto three dimensions.

In other words, the strategic triangle is the nuanced version of strategic RPS. Players can do a mix of offence, defence, and economy. The strategic RPS relationships still hold though: we expect a strategy that focuses mostly on economy to lose to one that focuses more on offence.

The first thing to notice about the strategic triangle is that it is inherently unbalanced. Remember "the best defence is a good offence"? That turns out to be good advice, in a roundabout way. The most general type of RTS strategy advice often boils down to making as much economy as possible while investing in as little defence as you can get away with. Offence is often an effective way to tie your opponent in knots and trick them into making more defence than they need, reducing their expenditure on offence and economy, hence the adage. Economy is the best way to get a long-term advantage, and economy beats defence, so whoever builds the most defence loses. This bias in RTS is probably due to the focus on armies and quick combat, compared to other genres of strategy game.

The strategic triangle helps us create a sense of strategic freedom because, as a map of strategy space, its size reflects the range of options available to players. But its main purpose is to highlight and avoid strategic RPS. As you may have guessed from its somewhat pejorative name, players tend to complain about strategic RPS when it becomes too apparent. A satisfying game involves jockeying for position on the strategic triangle, trying to counter whatever the enemy is up to via scouting and intuition.

There is tension here: strategic freedom demands a large strategy space, while an aversion to too much strategic RPS demands that it remain small. The solution, used by Zero-K and many other games, is pretty simple: start battles with a small triangle and grow it as the match progresses. This is why there are relatively few options early in the game, with relative soft counters. It is only later that the hard stuff comes out, such as nukes and bombers. But how do we dial in the size of the strategy space, or in other words, how do we bound the strategic triangle?

The trick to bounding the strategic triangle lies in the realisation that most actions achieve a mix of offence, defence, and economic growth. So, for example, if we wanted to prevent players spending more than 60% of their resources on offence, we would just have to avoid giving them any options that are more than "60% offensive". These numbers are just made up, remember that the triangle is conceptual rather than calculable, so it is time for some examples.

Take the very first unit of the game: the commander. Its laser and high health pool give players a baseline level of defence, while its income and ability to construct constitute economy. This starts players in the defence-economy area of the triangle, and there is a limit to how fast their decisions can them in other directions, limiting the extent to a player can go all-in on offence. At one point we experimented with starting players with an ordinary constructor, but the lack of the commander as "strategic ballast" resulted in too much strategic RPS.

Here is another example: constructors can build turrets, which makes sending a constructor out to build metal extractors a partially defensive action. Constructors can even end up taking on an offence role when they move close enough to the enemy base. So even the most greedy economic opening has built-in defence. Just imagine how swingy a Zero-K with dedicated economy-constructors and defence-constructors would feel. The cost of metal extractors has also gone up over time, limiting just how quickly a greedy opening can shore up its weaknesses.

Most units perform all three roles. A riot that sweeps raiders from a potential expansion site is performing an economy duty. Alternately it could defend existing metal extractors or trundle towards the enemy expansion. The most generic view of resources considers units to be resources that are spent by placing them in different parts of the map, since they can only be in one place at a time. This flexibility of deployment smooths over a lot of potential excess strategic RPS, as it means that decisions are not just made when a unit is built.

Our attempts to bound the strategic triangle often butt up against other design principles. Atomic unit design prevents individual units from performing too many distinct roles, and Quant's Rule is always pushing everything to the outskirts of the triangle, where strategic RPS is the strongest. We have, at times, considered giving factories an inbuilt turret to boost their inherent defence, but ultimately felt that such a thing would feel too arbitrary. Similarly, we avoided adding armed metal extractors because we wanted to retain the feasibility of pure economic expansion, with no defensive aspect, at least once the constructor has walked away.

The strategic triangle is most useful for thinking about the early stages of the game. This is fine, as every game has a beginning, and this part of the game is often the trickiest to get right. However, it does limit its applicability in large team games, as they quickly become too complex to analyse. The ideas are broadly applicable as, for example, a team that captures ground and invests in economy will beat one that does not, but these are rarely the decisions of individual players. Luckily for us, these games rarely have a problem with strategic RPS, so the strategic triangle can stick to doing what it does best.

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