Minimize calculation (in games worth playing)

This is a short follow-up to my article, “Uncapped Look-Ahead and the Information Horizon“, in which I proposed the concept of an information horizon: the distance between the current turn, and the point at which information becomes known to a player (usually, but not always, this means that it has become “public information”).

A simpler way to word it is, “how much time do players have to react to new information?” In the case of rolling a die to hit, you have zero time to respond, so in this case the “information horizon” would be right up in the player’s face. Alternatively, drawing cards to a public market or revealing new terrain via fog of war tends to lend the player a few turns / some time to respond to that new information before it affects the gamestate.

I also discussed the issue in Episode 6 of the 3 Minute Game Design YouTube series.

This concept is important because one of my guidelines for strategy game design is that, as I talk about in the video, if the information horizon is too close, the line of causality and the final outcome quickly starts being disassociated with that of the player’s performance—which is what we’re trying to measure in a strategy game, after all. If the information horizon is too far away, we get a “look-ahead contest” situation where it largely comes down to who calculated (solved) more of the available game state. This is mostly a brief review of things I’ve talked about the above linked articles/videos.

The new thing I want to suggest today is: Assuming a reasonable degree of goal feedback efficiency, we should strive for as little calculation as possible. To phrase it another way, in any game that’s good enough to be worth playing, you should try to minimize the amount of calculation that’s possible.

A reasonable degree of goal feedback efficiency

When we look at a game, “goal feedback efficiency” is a rough approximation that we can make that describes how accurate the end state of the game is with regards to player performance. A game with perfect goal feedback efficiency would give a win to the player who made stronger inputs 100% of the time. A game with good goal feedback efficiency would give a win to the player who made stronger inputs somewhere about 90% of the time.

Every game needs to have a pretty high degree of this, without exception. I’m not sure what the number exactly is, but I would say if it gets much lower than, say, 85-ish%, it starts becoming hard to “trust” a game. If you have less efficiency than that, it becomes hard to defend playing the game.

I would not play a 75% efficiency game. Why? Because a quarter of my matches are sending me false signals about my performance. That might not sound like too big a deal, but it becomes a very big deal when the player has no way of really knowing which matches are the false signals and which aren’t.

The classic answer to this problem is that figuring out which matches to believe and which to chalk up to randomness is part of the skill of the game. First, this strikes me as an attempt to make excuses for what exists, rather than an actual suggestion about what makes for good game design.

But beyond that, I don’t think that this is possible in an unsolved game. It’s hard for me to believe that a person could play a complex game, barely cling to enough understanding to pull off a win, and then also, on top of that, have enough additional systemic understanding to determine that this win was because of random effects and not their own agency. In other words: if you have a balanced game, players will be understanding the system just well enough to win or lose – they will be playing at their maximum capacity. So it’s unreasonable to expect players to be able to also interpret their win/loss as to whether it’s just based on randomness or not.

Ideally, games would have a 95+% efficiency rating, and I actually don’t think that that’s too hard to pull off. It doesn’t mean you can’t have some random variance; it just means that the random variance should be sufficiently input variance so that players can account for it, and to the extent that there is some output variance, they’re small enough in impact and there are enough of them so that they mostly average out. Hundreds of small (+-10%) random damage variance over the course of a match is probably OK, but a couple of critical card-draw failures throughout a match probably isn’t.

This is actually a pretty practical concern. Having a low efficiency rating means it will simply take the player too long to explore your system. In the finite number of hours they’re going to give your game, the amount of “effective depth” (depth the player can access) drops quickly after 95% and then plummets when you go much lower.

Of course, today’s game players who are used to playing stuff like Hearthstone will probably do it anyway, but for game designers who want to potentially someday make something better than Hearthstone, it is critical that we understand and internalize this idea.


…As little calculation as possible

So, if you’ve got this roughly 95% efficiency rating (which you should!), then we can ask the question: how much calculation should your game allow for? Or put another way: where should your information horizon be? Quick definitions:

Quickly, a couple of terms: Calculation, for the purposes of this article, means solving. It means literally following logical courses of action to their deterministically guaranteed outcomes. When one does “look-ahead” in games, they are typically doing calculation. Sifting through public, deterministic game states in Connect Four is a great example of calculation.

Analysis, on the other hand, is a word I use for the kind of “thinking” in games that doesn’t fall in that category. When you can’t calculate, you use a looser, heuristic estimation process, and I call that analysis.

So back to my claim:

Assuming a reasonable degree of goal feedback efficiency, we should strive for as little calculation as possible.

Obviously we can create a game with zero calculation – perhaps something like the card game War, or maybe (a single match of) Rock, Paper, Scissors. In these, we’ve brought the information horizon to “right up in your face” – once the other player has played Rock, you can’t do anything about that. But we’ve also destroyed our goal feedback efficiency. Wins have nothing to do with player performance.

The point is, you do need some degree of determinism in games; some “causal line” that goes from the player’s input and stretches out into the system to some extent. But by using input randomness smartly and carefully selecting the position of the information horizon, you can (and should) reduce the calculate-able (solvable) parts of your game down to a reasonable level.

This isn’t just a matter of “balancing” goal feedback efficiency and calculation. It’s much more like, goal feedback efficiency has a floor that it really just can’t go below (95, mayyyybe 90%) no matter what, whereas calculation is much more flexible.

This is because the downside to too much calculation is that the game is a little too solvable, but still totally skill based. In short, it’s a little bit too much like Chess. It’s kind of OK for games to lean into being a little bit Chess-like.


The downside to too little goal-feedback-efficient is that the game becomes indistinguishable from noise, and totally unplayable to anyone who’s alert to this kind of problem. Granted, there are a lot of people who will happily play this kind of game anyway, as so many popular games fall into this category these days, but my writing has never been about “game design guidelines that help you make games people won’t know better than to play”. My game design guidelines are about helping you make good games.

If you build a strong system, with a well-placed information horizon, this new guideline is going to be met somewhat naturally. But it’s another way to test a system you’re already working with and to understand the information horizon concept.

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  • Jereshroom

    What are you saying here that you haven’t already said in previous articles and the video you linked to? You haven’t given any advice on *how* to minimize calculation, just repeated your (valid) reasons for disliking games like Chess or Hearthstone.

  • I think before this article, I hadn’t made the distinction between the two sides of the information horizon balancing act. In this article, I’m trying to explain how one of those two sides is more flexible than the other.

    Calculation is minimized by bringing the information horizon closer.

  • I liked the article :). But I can see why he might have missed the point. What do you think about putting the guideline in a block quote to highlight it, or maybe spell it out at the beginning and end of the article? I understood the guideline to be you need to find a balance between moving the information horizon further away to avoid the problems with randomness and moving the information horizon closer to avoid having to do to much calculation/look-a-head. Thanks for the article Keith, keep them coming 🙂

  • Pelle Nilsson

    I think talking about dice from this pov only is unfair as the strength (from a strategy game design pov) of dice is in what comes before the die roll, the setting up of the best possible conditions so that you will win almost no matter how bad you roll. A good player has several turns of planning with full information about the possible outcomes. That is why a game like Advanced Squad Leader can have hundreds of die rolls in a game, yet probably close to or above 95 ℅ feedback efficiency. Input vs output and your information horizon are valid ways of analyzing a design, but not the complete story.

  • MichaelSinsbeck

    Nice article. I am glad you are addressing “calculations”. As a fan of the game go, I am very much interested in this topic.
    Could you explain more specifically, what you mean by “analysis”? In this article you only give a negative definition: Thinking in games, that is not “calculation”. Can you give a positive definition of what you exactly mean?

    This is how I understand your definitions. Is that what you mean?
    Calculation: By means of calculation, I make predictions of possible future states of the game. These predictions are based on my understanding of the rules and require me to intellectually explore the consequences of combining the individual rules. Calculations allow me to play a game well, even if I haven’t played it before (this is actually one way, people practice go: they solve go problems, instead of playing the game).
    Analysis: Analysis seems to work differently. Instead of using my understanding of the rules, I use the feedback the game provides. After playing the game a couple of times, I have a catalogue of wins and losses. From these I derive heuristics that allow me to get better at the game. The process of forming these heuristics is analysis. By this definition, I can only do “analysis”, if I play the game often, because each round only gives me one data point.

    Would you agree with these definitions? Or are there other nuances to it?

  • Some guy

    I’m glad to see this brought up on this blog, I think minimizing the ability for the player to calculate future states is very important to making a good game. However, I don’t think the way you describe it is really useful; its better to think of this in terms of randomness and possibility-space, not the position of the information horizon.

    For a purely deterministic game the possibility-space a certain number of turns in the future is always precisely 1. In other words, to predict the state of the game t steps into the future you only need to put in some amount of effort directly proportional to t. However, if a game involves non-determinism, or an “information horizon” as you put it, the size of the possibility space in the future is exponential with respect to how far into the future you try to predict. e.g. If each turn in a game the player’s action has a chance of either failing or succeeding, then to predict the exact state of the game t steps into the future, the size of the possibility-space is directly proportional to 2^t.

    This is an important part of what makes games like XCOM so great. You are generally controlling 4-6 soldiers, and often there are a similar amount of enemies on the screen, and every one of them can either miss, hit, or critical hit every turn. The possibility-space is absolutely massive. Calculating the entire possibility-space of a single turn is daunting, and calculating the possibility-space two or three turns down the road is something that would literally require days of effort. This is the reason that, despite the fact that XCOM shows you the probability of each shot landing, there is almost no calculation involved in playing it. The game involves essentially 100% analysis, even at very high levels of play.