Designing Strategy: The Random Factor

by Shannon Appelcline

February 6, 2003 - Strategic games rest on the balance of two ideals. On the one side you have decisions — the ability for players to take their own destiny into their hands — which I covered at some length last week. And, on the other side you have chance, when destiny takes control of things, and has her own way with the game. And that's going to my topic this week — randomness (or chance), with a quick stop first at its godparent, unpredictability.

Types of Unpredictability

You can have lots of different types of unpredictability in a game. For a start chance, my core topic for this week, can be broken into two general, overlapping categories:

Randomness: At its heart random chance tends to be a die — typically a six-sided die that's numbered 1 to 6. Some games have spinners and others have weirdly shaped dice or dice with weird pictures on them, but in each case you have a fairly simple chance event drawn fairly equally from a small set of options. Examples: a die rolled to move in Monopoly or attack in Risk.

Arbitrariness: At its heart arbitrary chance tends to be a card — typically drawn from a large set of cards. In many cases each card has a unique result (e.g., 9 of clubs) but in some cases multiple arbitrary results might be a part of an complete card set (e.g., 20 knights, 10 victory point cards, 3 monopolies, and 7 unique cards). Examples: a card drawn in Poker or a tile drawn in Scrabble.

However, these chance unpredictabilities are only half of the story. There's also a large amount of unpredictability that comes from opposition, which is to say what other players do. Some categories of opposition include:

Chaos: At its heart chaos tends to be a total unpredictably that arises when other players in a game are faced with sufficient choices that you can never quite know what they're going to do, and thus really can't determine the future state of the game. Examples: any game where each player has an at-least medium-wide decision set, such as what to build in The Settlers of Catan or where to place a tile in Carcassonne.

Uncertainty: At its heart uncertainty tends to be hidden information — typically known by other players but not by you. It's usually a card held in a hand, but could also be any number of items held behind a player screen. Examples: the location of your ships in Battleship or the value of your pieces in Stratego.

Though I'm not currently planning an article on them, the types of opposition are probably worth a whole discussion of their own. For example, hidden information can often be much improved in a web game where the computer does moderation. As another example, chaos is often purposefully designed by game designers in such a way as to give extra choices to players who are behind in order to help balance a game.

For now, just be aware that opposition unpredictability exists, because this week I'm going to stay on those topics most closely related to chance — randomness and arbitrariness — mainly because they're the most frequently used type of unpredictability in games.

Types of Chance

Given that you have chance in your game, what form does it take exactly? As is the case for most things, chance is a spectrum. Following are some of the most frequent types of Chance that appear in games:

No Chance: The most basic type of chance is the total lack thereof. Everything within the game is based solely on the wits of the opponents and how they might interact with each other. Nothing is drawn, rolled, spun, selected, or otherwise randomized. If these games need unpredictability, they usually achieve it through chaos, or less frequently uncertainty. Examples: Battleship, Checkers, Chess, Othello.

Unweighted Distribution: Chance is based on a simple, easy to understand singular roll of one die or spin of one spinner. Every result is equal in probability. This type of chance forms our most basic understanding of "random chance". Examples: rolling 1 six-sided die to move in Trivial Pursuit.

Weighted Distribution: Chance is based on a simple, easy to understand singular random selection, but rather than each selection having a different outcome, instead multiple selections might all lead to the same outcome. Although sometimes achieved with dice and tables, weighted distributions most often appear as "arbitrary chance", which is to say cards or tiles. Examples: a spinner where the different slices are different sizes, or an air strike in Naval War where a six-sided die is rolled with the results: 1: ship is sunk; 2-6: no effect, or a tile drawn in Scrabble.

Curved Distribution: Chance is based on a probability curve. This is usually produced by adding together multiple dice which forms a bell curve and results in the middle of the curve being more likely and the edges being less likely. More complex curves are possible; they can be formed by taking the maximum of all the dice rolled or the minimum or by engaging in some more archaic dice consultation. This is again usually seen as "random chance", because dice are almost always used. Examples: The Settlers of Catan makes, perhaps, the best use of a bell curve distribution in any game by allowing players to roll two six-sided dice and clearly showing the different probabilities from the unlikely "2"s and "12"s to the common "6"s and "8"s.

With that all laid out, which of those types of chance is the best?

If you want a very simple method that introduces just a tiny bit of unpredictability into your game, you might as well go with an unweighted distribution. However, if you're trying to do something interesting, and want to offer a wide variety of random results, a weighted distribution or a curved distribution is what you want. Generally I think that curved distributions work the best in tabletop games because you can create them with a couple of dice, while weighted distributions are at least a serious contender in web games because you can have computers do all the table lookups.

Why to Have Chance

With all that said, the obvious question is: why would I want chance in my game? As with my discussion of decision spaces last week, I think the answer is, you might not. However I believe that games with a random factor are more likely to be fun to play and are more likely to be accessible to casual gamers. Unless you're trying to create a very serious, thoughtful, intelligent game where each turn is carefully scrutinized, some element of chance is a plus.

Here's some more specific reasons:

Reduces Ego. If there's a chance element, players will be able to remove a bit of their ego from the game. Whether they win or lose is no longer solely a result of their own intelligence and skill. Instead, a bad game can be attributed to bad luck — whether that's true or not. In my experience this just tends to make the game more fun.

Reduces Predictability. A non-random game can be a very staid thing because you can predict exactly what will happen turn after turn. Chance introduces unpredictability into that equation. And, that can also get your adrenaline pumping, when you make an attack that only has a small chance of succeeding... and pull it off. Games without die rolling or tile drawing just don't seem to have the same raw excitement and joy that chance can bring. An excellent example of chance being fun comes from slot machines. How many people would play them if they had a regular return of $.97 every time they put in a dollar? It's the lack of predictability that keeps people pumping Susan B. Anthonys into those one-armed bandits.

Reduces Lookahead. This is another aspect to that same lessened amount of predictability. As I mentioned last week, by reducing lookahead you also reduce the width of decision sets by not allowing them to span turns and turns into the future. And thus, you make the game more playable.

Balances Games. Finally, if designed well, chance can act as a balancer in games. Because random events (dice) tend toward the mean (especially if you're building curved distributions), they can give people who are behind a chance to catch up and people who are ahead the chance to fall behind. Arbitrary events (cards) are even more effective at this, because there's a set distribution that will eventually all be revealed. The Settlers of Catan is a game that uses dice to figure out what lands produces resources. A variant called The Settlers of Nurnberg replaces those dice with cards, and thus reduces the chance for a really bad run of luck to occur — because that bad run isn't built into the arbitrary cards.

Why Not to Have Chance

On the other hand, I can't count the number of times I've heard someone say that a game was "too random". Chance definitely has its bad side as well:

Removes Choices. If used poorly, chance can replace player choices with random events, and ultimately make decisions meaningless because the chance element plays so much more importance in ultimate victory.

Decreases Strategy. Closely related, if chance is allowed to become more important than strategy, then ultimately the core basis of strategy games is undermined. Chutes & Ladders is an example of a game where the chance factor total subsumes the game: you can't make a decision, you just flick the random spinner turn after turn; thus, Chutes & Ladders really doesn't even meet my definition of a strategy game.

Balancing Chance

When all's said and done, I think the art of including chance in a game is a careful balancing act, intended to ensure that its level is acceptable to your players. Here's my general outline for creating that balance.

1. Decide Upon Your Audience

You need to start off knowing who you're trying to appeal to. The kids that play Chutes & Ladders probably rarely complain "it's too random", and that's because the game is aimed at an age group that isn't yet chomping for strategic games.

Generally you can go from there, decreasing the amount of chance as you increase the "seriousness" (read: obsessiveness or hard-coredness) of your game players. A family game like Monopoly can still be very random, a European couples game like The Settlers of Catan can still be moderately random, a hardcore strategic game like Tigris & Euphrates should have a low random component, and a very cerebral game, like Chess, should have none.

2. Moderate Your Chance Elements

Unless you're purposefully making a family or kids' game with lots of chance elements you should make sure that that the chance implicit in the game is carefully moderated by your other elements. Another way to put this is: make sure player decisions count.

Many random (dice) based games of chance do this in such a way that the dice are rolled so many times that it tends toward the mean. For example in Risk if you make a large enough attack you'll roll the dice enough times that you should lose almost exactly the expected number of pieces. Likewise in common trivia/racetrack games like Trivial Pursuit the dice rolling that the players do to move themselves forward tends to equalize by the end of the game, and thus the final race results are ultimately dependent upon the other element — in this case answering the questions.

Other games accomplish moderation by making the random variance a fraction of the "set" values in the game for various tokens. For example in Skotos' Galactic Emperor: Hegemony whenever a fleet attacks an enemy their total score is (randomly) multiplied by somewhere between 80% and 110%. Thus, there is chance, but it's only about 30% of the total (and, because there tend to be many battles in one game, this is another case where the total result tends toward the mean).

3. Consider Alternative Uses for Chance

The most common use of chance is to determine the outcome of a specific event — usually some type of conflict — in a game. This is generally an acceptable tactic, but it's also the one most likely to lead to complaints, because players can feel, often with justification, that the chance elements cost them a game (or won them the game, but they're less likely to complain about this).

A way to get around this is to let players decide to randomize. In this situation you present a choice that will lead to a chance outcome, and let the players decide whether to select it or not. The Starfarers of Catan makes use of a somewhat similar technique: on event cards you're presented with a choice (e.g., whether to use a wormhole or not); if you go with the choice, understanding that it might be dangerous, you're then presented with a somewhat random outcome (e.g., your ship jumping across the galaxy, just a few spaces, or disappearing entirely).

Another option is to use randomization as a constraint rather than a result. Almost any game which uses arbitrary (card-based) unpredictability actually does this. Based on the cards you draw, you'll be able to do some things, and not others. However, this technique could easily be adapted to any random situation. E.g., you might roll a die and only be able to engage in combat on turns where you roll a 3-6.

4. Clearly State Your Level of Randomness

Once you've selected your audience, made your decisions about chance, and either moderated or varied the chance elements, you should then be very careful to be honest and upfront about how big of a factor that chance plays in your game.

As I've already said, many different levels of chance are acceptable. The idea is just to let your players know what that level will be, before they select your game, so that they're not disappointed down the road.

Conclusion

Very smart people have spent a lot of time talking about chance. I'm not going to try and go into that type of depth, but I hope that I have touched upon the generalities for a strategic game. You need to know what options you have for both unpredictable and chance elements, and then to figure out what level your audience will tolerate. Once you've done that it's merely a matter of carefully balancing things, so that the chance and decision elements both play appropriate levels of importance in your game.

And that's it.

As always thanks to my regular triplet: Saul Bottcher offered some great thoughts on randomness a couple of weeks ago that led to many topics in this article; and Quigg and Christopher Allen offered some feedback on stuff to add after I prepared my first draft.

Next week I want to look in-depth at the design of one game, to try and figure out what makes it good, and thus approach many of the abstract topics I've covered thus far in a much more hands-on way.

The victim? Klaus Teuber's The Settlers of Catan.

I'll see you in 7.

Recent Discussions on Trials, Triumphs & Trivialities: