Uncapped Look-Ahead and the Information Horizon


I write a lot about how bad output randomness is for games, but today I want to write about a problem common in many deterministic games – specifically ones that lack hidden information.

Why doesn’t everyone just play chess, if it’s so great? The answer is that chess, or other ancient abstracts like Go and shogi, or even modern abstracts like the Gipf games, Through the Desert or Hive – these games really aren’t that great. They are all largely “look-ahead contests”, and people pick up on this, consciously or subconsciously, and it makes them all kind of annoying to play.



Here’s the process of look-ahead in action: what will happen if I make move X? Once move X is made, what will happen if the opponent makes moves A, B or C? If he should make move A, then I can make moves D, E or F… and so on. It’s literally scanning through every possible (or reasonably valid-seeming) move that you can. Games of chess, at least at novice and intermediate levels of play, tend to come down to simply who does more of this. One way to put it is that it’s a matter of quantity, not quality.

As with any exponentially-expanding possibility tree, no one can really scan the entire possibility space, or even come close with super-complex games like chess and go. So we do have to make some heuristic loose choices based on loose patterns – the kind of thing that we expect to be doing in a strategy game. Not “blind guesses”, but not “the solution”, either.

But no one can deny that if you sit there for a long time mapping out more and more and more of the actual possibility space, you’re going to just be making better moves. Not because you had a creative idea or showed ingenuity, but because you simply explored more of the possibility space.

Of course, these kinds of games – when played seriously – are almost always played with a timer for this reason (as well as others). However, this does not solve the problem. That simply changes it to “how much of the decision-tree can you explore in 30 seconds?” You still have, to some extent, a look-ahead contest.

The problem is that look-ahead is uncapped in chess. The entire state is there for you to calculate out, and this is not only something that can undermine the kind of strategic decision-making we want to foster, but it also is oppressive to people. Knowing that the answer (or at least a strong answer) is there –  you just have to sit there doing a hundred easy problems in the next 30 seconds in order to get it – feels crappy.



7fcd4ca8a4cc149f3c04b202f6908bee_largeA recent example of a very interesting game with no randomness and no hidden information is the successfully Kickstarted Prismata.

When I first read the rules, I could see that, similar to chess, there really isn’t a lot of interaction between game elements. Basically, things can absorb damage, deal damage, or give you a resource. Despite being a complex game that’s difficult to solve, I could tell almost immediately that the method for playing the game would be to simply sit there and do a bunch of easy math problems very quickly, because that’s all that’s going on. There is nothing else in the range of actions you can do, despite the fact that you can theoretically read ahead to the end of the game.

Some of the most high-level players in the game have confirmed my suspicions. For instance, this Dinofarm Forum post, where a high-level player named Captain says similar things. As a result – sure, maybe it’s a good “game of pure strategy”, but as Captain says, “Prismata is a bad game at being fun to play”.

Even the designers appear to be at least somewhat aware of this problem, as they’ve been pushing for severely short timers and adding tons of content in order to try to “loosen up” a system which is inherently a “simple math problem contest” (again, quite like Chess).

The first half of solving this problem is by carefully introducing hidden information.


Hidden Information

What we should be doing with our deterministic games is giving players just enough deterministic space in front of them so that they both cannot solve it and also hopefully have numerous attractive-looking options. There should be just enough complexity here to allow for real, creative problem solving.

… And no more. Beyond a certain point, things should be hidden – we can call this point the “information horizon”. Fog of war is a decent example of how some games already do this – one can imagine a StarCraft without fog of war and what a nightmare that would be.

Up front – having hidden information at all necessarily makes your game more random. However, if you’re careful, it can be a very slight increase in randomness that is certainly preferable to the oppressive look-ahead that is the alternative.

It’s a very difficult balancing act. If the information horizon is even a little bit too close, the game becomes too random. If it’s too far out, you risk having a look-ahead contest problem. You must find the right balance, and have a system that is rich and interesting enough to allow for creative play within a restricted space.

Of course, you can’t just take a game like Prismata and slap some hidden information on it and expect it to work. Prismata’s elemental bits are just very simple and very direct, and so reducing the known area is a bit like having people play chess on a 3×3 board or something – the game will get totally solved almost instantly.

In order to have a relatively near information horizon, your game’s rules have to be deep.



play-store-screen-3I don’t often like to use my own games as examples of my design principles, but in this case, Auro: A Monster-Bumping Adventure is one of the best examples of this principle in action. If you’re unfamiliar with the game, watch this video or read the manual to learn the basics.

Essentially, it’s a turn-based tactics game, where you’re a single actor (Auro) on a hexagonal grid. You can push monsters back a tile, move, or cast spells that cause other effects. As you’ll see in the video below (played by Ludite Sam) the amount of complexity gets very high.

Click here to watch on Twitch.

In Auro you’re only able to see a 5×5 hex grid of tiles – that’s the information horizon of the game. Regardless, the amount of skill there is to the game is massive. Testers have already been playing this game for years and they continue to dive deeper into the game. There are players who are significantly better than me at the game, and there are players who are significantly better than those players.

How is it accomplished? It comes back to something I’ve talked about before – the clockwork design pattern (I’ve also got a book about it). Auro has a strong core mechanism and supporting mechanisms, laid out in an elegant, intentional way. Because of its elegance, it’s able to achieve huge depth despite having a pretty restrictive information horizon.

If you compare Auro to chess, Auro is like a dozen interesting problems, and chess is like a million rote tasks. The kinds of combinations you can make in Auro are numerous – things interact with each other on many, many different levels. In chess, things are basically in each others way, threatening to kill, or killing each other. Those are the only interactions that exist in the game. You can’t really do anything in chess, except just make sure your units are killing their units. The same goes for something like Starcraft – or really, most games, which as I mentioned in my 3 Minute Game Design episode on depth vs. width, are wide games, not deep ones. They have tons and tons of shallow interactions.

I mentioned Through the Desert at the top – it’s worth noting that this game has a bit more of a “clockwork design” and is a bit more elegant than most perfect information abstract games. In fact, many designer Euro games are pretty good on this front – games like Puerto Rico or Agricola do a decent job at maintaining this balance (even if they have other problems).


In Conclusion

As a side note, this issue of carefully placing your information horizon presents a real problem for physical game designers. On a computer, it’s easy to hide whatever information you want, with things like fog of war or other hidden variables. With board games, it’s very difficult to get the kind of nuanced control over hidden information that you can with digital games. In board games, it’s pretty easy to make everything hidden or everything open, and a few other arrangements are easy, but something similar to “fog of war”, for instance, has always been a notorious challenge for board game designers.

With that said, you basically have three options:

1. Create a perfect information, deterministic look ahead contest, like chess or go

2. Create a random game, like Hearthstone

3. Utilize elegance and consciously limit your information horizon.

So, if you can’t do this without a computer – start developing computer games. While option #1 is certainly a lot harder than option #2, option #3 is by far the hardest to accomplish. However, they also are the most enjoyable, deep, efficient and rewarding games to play.


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  • Thomas Bartscher

    I’m not sure I agree. While limited look-ahead might make for a better contest (and thus raise the enjoyability) I am not sure it makes it a better game.
    For people who enjoy doing mathematics unlimited lookahead shouldn’t be a problem, really. I like to play chess (and randomly determined chess variants) against people and analyze the game while it is still going on – I don’t care whether they win because I explained what I was doing to them, the point is to understand what is going on.

  • I think the article’s point is that limited look-ahead makes for a WORSE contest (and a better game), because you have to rely LESS on mathematics, and more on decision-making.
    our second paragraph actually supports that. Yes, if you’re looking for a calculation contest, deterministic games with unlimited look-ahead are fine. If you’re looking for a strategy game, with actual creative decisions, though, they’re not.

  • Ben

    You can do the exact same look-ahead in games with hidden information as you can in games with perfect information. You just substitute potential decisions by the other player with potential combinations of hidden information. If anything, hidden information makes the look-ahead more tedious due to the fact that you have to multiply the quantity of look-ahead by the number of potential game state variations.

  • MichaelSinsbeck

    Interesting train of thoughts.

    I have a question though: How is hidden information different from randomness?
    By hidden information, of course, I mean such information that the player cannot possibly know (and not information that the player theoretically could have, but simply forgot).

    In my view each action in a game needs one (or more) of these three qualities: execution, thinking, luck. (And in “thinking” I include calculations and strategic decisions.) In this context, decision-making is “thinking” so the designer should eliminate “execution” and “luck” as far as possible. Now, you are saying that the designer should include “luck”. Or do I get it wrong? Or am I missing a 4th quality besides execution, thinking and luck?

  • Eric

    There’s an assumption here that look-ahead is not an interesting or fun challenge. This may be true for the author, but is certainly not true for all gamers. Also, doing more look-ahead – dismissed as “merely doing more, not better” – does require several sorts of skill, not all of it quantitative. (At least in Chess and similar games. I can’t speak to Prismata.) Part of it is certainly looking at many possibilities rapidly. But another part of it is working memory, and a huge part of it is the very heuristics the author feels you need limited information to encourage.

    No living human can actually consider all possible 15-moves-ahead chess positions – or even 10, or probably 5. Heuristics are necessary even while doing look-ahead. There’s *always* an information horizon – it’s just that with perfect information the information horizon is dictated by the limits of the player’s brain.

    In fairness, this can certainly result in the sort of AP the author references, because players try to stretch that limit as far as they can manage. When there’s hidden information, it both makes the possibility-space so much larger that there may be a clearer cutoff for “not worth looking anymore”, and it can give the player an excuse to not run through all the possibilities.

  • It’s not different from randomness, as I say in the article – it does increase the randomness of your game. The point is to just carefully manage the information horizon so as to not allow the game to be a look ahead contest, but also not to allow it to be highly random.

  • Guest

    “you have to rely LESS on mathematics, and more on decision-making”

    Come again? Aren’t calculations in chess influencing your decision-making? So what’s influencing your decision-making in other games? “Creativity?” I’m not sure what that means. People make moves in chess that are described as creative/brilliant all the time.

  • Guest

    It seems like the underlying point is that hidden information creates so many variations that it’s pointless to calculate any further, thereby eliminating any mental burdens the player might have to suffer. The author refers to this as an information horizon, but a more cynical name for it is artificial stupidity.

    Prismata’s rationale for having unlimited lookahead is that with modern matchmaking systems, you can easily match players against other players at the same skill level, so it’s not really oppressive at all (unless you’re challenging someone significantly higher-rated than you, in which case, yeah, you’re probably going to lose because they’re better than you). I’m inclined to agree with this.

  • Guest

    “One can imagine a StarCraft without fog of war and what a nightmare that would be.”

    Citation needed.

    As a high-ranking Zerg player, my FAVOURITE situation in Zerg vs Zerg was close positions on a map like Python, where the two players effectively had full vision of one another due to overlord scouting. It made the game more interesting and actually increased the number of viable strategies by decreasing the usefulness of rush builds that generally made tech-based (evo before lair) or econ based (early 3rd hatch) builds too likely to be countered. This may be more the fault of ZvZ having a pretty boring nash equilibrium at high levels of play, but the point is that removing fog of war doesn’t necessarily make the game worse.

  • Using randomness as a tool to cap the information horizon is a great insight. The preferred distance of the information horizon (or, the amount of randomness in the game) clearly comes down to taste though. It seems that most players would rather keep the information horizon fairly short (MTG, Dominion, Poker, Blood Bowl).

  • Actually I would say the popularity of those games does not necessarily reflect the “tastes of most players”. Instead I would say that almost all games are made that way because it’s much easier to make highly random games than it is to make more-deterministic games. So players just have to pick their poison between what exists, and it’s almost all highly random.

  • ZoltanTheHun

    Sorry to say that Keith, but I truly think you make wrong assumptions with many of your articles. First, the question ‘Why doesn’t everyone just play chess, if it’s so great? ‘ is similar to questioning why not everyone listens to the Beatles. Second, chess is not a look ahead contest, it is a position evaluation contest. If it was about the look-ahead, computers would have been winning for a long time. Human can look ahead of a few steps at a time in comparison to game length. I think the problem is that you don’t see that Chess is truly that great. Chess is not a simple math problem as you state. Even more, as of today it is still not solved from a mathematical perspective.
    The reason why not everyone is playing Chess in reality is, that most people play with games because of the feeling not because of the mechanics. Most people cannot understand chess. Actually most people do not understand any game they play on a strategic level. And if they do, what you do not recognize is that the player itself is the information horizon. Therefore Chess does not need hidden information and it would not make it any better.

  • gerryq

    Consider a chess-like game in which the rules would change significantly in one of a thousand ways, four moves from now. Clearly you would analyse four moves ahead, to see if you could gain a big advantage in that time – but past that you would use heuristics based on your knowledge of the possible changes, but without doing a huge amount of direct calculation. The window for tactical calculation is reduced compared to chess.

    As for the argument about match-making, I’m not sure I agree with you. It may be that for many players it is a problem that long tactical lookahead is the optimum strategy for success, regardless of whether they are as good as or better than their opponents. Working out more fluid heuristic criteria may simply be more enjoyable for many people. I think that is how I feel, even though I am – or used to be – a good chess player.

  • SwiftSpear

    Hidden information isn’t the same as randomness. If you need to keep track of the state of the invisible elements because they might effect the state of the on board elements, they are hidden information. If they do not affect the state of the on board elements they are random (as far as the player is concerned).

    If you encounter another empire in civilization which feels far weaker than your own empire, you might infer that somewhere on their boarder which you cannot see they are in conflict with a third empire. Where as you may know the approximate likelyhood of a blue candy to drop in candy crush, but nothing currently on the board makes the blue candy more or less likely. You can’t gain meaningful information about which candy might drop next by observing the current state of the board.

    There’s also such a thing where you have some sort of AI that decides to spawn content randomly weighted by the current state of the visible board. This is a version of random information, but it’s probably usually useful to identify that as a separate thing as well, because there’s hidden information that the player will unravel over time (the way the AI content generator works), so it’s not an information black hole in the same way unweighted random content is.

  • Peter Siecienski

    I’m sorry that this is a year later response, but computers do beat people at Chess.