FUNDAMENTALS OF GAME DESIGN, SECOND EDITION

Dominant Strategies in Video Games

Video games seldom permit players to use strategies so strongly dominant that they absolutely guarantee victory, although some, whether PvP or PvE games, allow powerful strategies that give the player little reason to use any other. By far the best-known dominant strategy in any PvP video game is the tank rush in Westwood's Command & Conquer: Red Alert. An experienced player playing as the Soviet side can devote all of his energies to producing a large force of tanks in the early part of the game, then use those tanks to attack the nascent enemy base en masse. Against an unprepared opponent, this almost always produces a victory; an experienced opponent can prepare for the onslaught, but the tank rush remains so effective that it takes the fun out of the game. Many players add an additional rule to the game—no tank rushes allowed—just to balance this problem.

Several editions of Madden NFL included unstoppable offensive plays that guaran­teed success against an AI-controlled opponent. Fighting games, too, are especially prone to dominant strategies. In both fighting games and football games, the large numbers of possible combinations of offensive and defensive actions makes it diffi­cult to test them all. Badly designed characters can also result in dominant strategies; in Super Street Fighter II Turbo, the secret character Akuma's unbeatable attack, the air fireball, leaves the rest of the characters with no chance. Tournament matches ban the use of Akuma to ensure fair play.

The next few sections discuss ways that dominant strategies can emerge in a video game and how to avoid them or remove them by using balancing methods.

TRANSITIVE RELATIONSHIPS AMONG PLAYER OPTIONS

The term transitive describes a relationship among three or more entities so that if A stands in a certain relationship to B, and B stands in the same relationship to C, then A stands in the same relationship to C also. If you may correctly draw this conclusion, the relationship displays a property called transitivity. Greater than in arithmetic provides an example of a transitive relationship: If A is greater than B, and B is greater than C, then A is greater than C.

If a transitive relationship exists among a player's strategic options, then option A is better than option B, and option B is better than option C. Why, then, would a player ever use option C? Selecting option A becomes a dominant strategy. To use a con­crete example, if you design a game so that an aggressive strategy is always better than a defensive one and a defensive strategy is always better than a stealthy one, a smart player always chooses the aggressive strategy—it is superior to all the others.

To correct this imbalance, you may impose direct costs on using each strategy, costs that counteract the superiority of the stronger strategies and so give players a rea­son to consider the (formerly) weaker strategies as well. To draw an analogy, a lot of kids who would like to ride horses have to ride bikes instead because, even though horses are more fun to ride, they cost a lot of money.

Suppose you build a road-racing game in which players vie to earn the most prize money available over a series of races. You offer the player the chance to buy one of three cars made by three different manufacturers, such as Ford, Dodge, and Chevrolet. To make this a meaningful choice, you decide to create some variety among the cars so that the Ford is faster than the Dodge, and the Dodge is faster than the Chevrolet. If they all cost the same amount and their performance is iden­tical in other ways, choosing the Ford constitutes a dominant strategy. However, if you price each car in proportion to its advantage so that the Ford costs the most and the Chevrolet costs the least, the game regains balance. Because the players' goal is to earn money, not merely to win races, the financial disadvantage of the faster car offsets its speed advantage if you set the costs correctly.

Setting up direct costs that exactly counter the advantages of certain choices does balance the game, but such a clear and obvious balancing mechanism produces a game that seems rather bland. The player can see that there's no real difference among the choices. To create a more interesting choice for the player, you can instead impose shadow costs. Shadow cost, a term from economic theory, refers to secondary, or hidden, costs that lie behind the apparent costs of goods or services. For our purposes, a shadow cost is one that the designer creates but doesn't warn the player about explicitly. It serves to balance the game without being blatant about the mechanisms. For instance, giving the Ford a smaller fuel tank that requires the car to stop to refuel more often in the road race could counter its speed advantage. The smaller fuel tank serves as a shadow cost that the player becomes aware of through repeated play.

You can hide a shadow cost completely by building it into the mechanics and not documenting it in the game's manual—for instance, not telling the players how big the fuel tanks in the cars are so they have to find it out through trial and error. More often, a shadow cost is available to the player but not obvious. Continuing the same example, the player might be able to learn the sizes of the fuel tanks by comparing the numbers on the fuel gauges in each car, but the instructions for the game don't draw attention to it. Another classic example is a weapon that does a great deal of damage but has a slow rate of fire. The slow rate of fire is a shadow cost that the player only discovers once she starts to use the weapon.

Players of PvE games often feel that entirely hidden shadow costs are unfair because the player cannot know what costs lurk behind the scenes or learn to com­pensate for them. For example, if a game reduces a character's accuracy at throwing a javelin in proportion to the weight of the character's backpack (on the theory that throwing a javelin while wearing a heavy backpack is bound to be rather uncertain) but never explains this to the player in the manual or anywhere else, the player can't learn to compensate for it. He finds that his accuracy worsens at times, but he can't understand why. If he does figure it out, he will probably cry foul and post a warning on an Internet gaming forum for the benefit of other play­ers. A number of game publishers deliberately hide shadow costs from the players
but reveal the costs in printed strategy guides that the player must pay extra for. This is an abusive practice.

In practice, designers most often use transitive relationships to upgrade a player's powers during her progress through the game. The player begins with a single option, the weakest, and works her way up to better ones. In other words, she starts with the Chevrolet, then receives the Dodge as a reward for good performance, and later still receives the Ford. This creates positive feedback, which is covered in a later section. If you also make it possible for a player to lose her upgrade due to poor performance—going back to the Dodge after a bad performance in the Ford—you can create an interesting progression/regression dynamic that can lead to some taut and suspenseful gameplay. Take care to ensure that the player can reestablish her previous level once she does well again.

INTRANSITIVE RELATIONSHIPS (ROCK-PAPER-SCISSORS)

If the relationship between strategies or other player options is intransitive, then just because A beats B and B beats C, you can't assume that A also beats C. Game professionals use intransitive relationship to mean not merely a lack of transitivity but an explicit loop in which option A beats option B, B beats C, and C beats A (see Figure 11.1). The game rock-paper-scissors (also called scissors-paper-stone and Rochambeau) works that way: Paper beats rock, rock beats scissors, scissors beat paper. This results in a balanced, three-way intransitive relationship (although intransitive relationships are not confined to systems of only three entities).

The rock-paper-scissors (or RPS) mechanism is a classic design technique for avoid­ing dominant strategies and forms the basis for balancing player strategies in many games. Designer David Sirlin pointed out in his article "Rock, Paper and Scissors in Strategy Games" that Virtua Fighter 3 includes RPS relationships among general types of moves available to the player: Attacking moves beat throwing moves, throwing moves beat blocking moves, and blocking moves beat attacking moves (Sirlin, 2000). The Ancient Art of War, an early example of a video game that includes an RPS relationship, offers players three unit types: knights, archers, and barbarians. Knights have an advantage over barbarians, barbarians over archers, and archers over knights.

As Chapter 14, "Strategy Games," explains further, a direct implementation of the RPS model without any modifications fails to meet the needs of modern war games due to its simplicity. It doesn't offer any interesting choices—there's no reason to choose any one unit or strategy over any of the others. However, as Sirlin points out, you can adjust the system to produce different benefits. If you give the player different amounts of money for winning with rock, paper, or scissors, players have to think not only about which object their opponent might choose but which choice earns the most money.

Now imagine a system in which instead of just allowing each choice to beat another in all circumstances, as in rock-paper-scissors, one choice is marginally better than others in some circumstances but not in others. You can make this adjustment in the core mechanics of your game, and it need not be a war game. For example, suppose you set up a race between a lizard, a frog, and a mouse. The liz­ard does best on rocky ground; the frog does best in swamps; and the mouse does best on grassy ground. If you design the mechanics such that these advantages remain slight rather than overwhelming, it will take a while for the players to learn about the system of advantages. Make the race course a complex mixture of rocks, grassland, and swamps, and give players partial but not total freedom over the routes they take. Add some shadow costs: The frog is generally slower than the oth­ers overall; the mouse has to stop for air every 15 seconds while swimming; and the lizard slows down sharply at transitions between types of ground. If you set these values carefully, your game remains balanced, and players will have some interest­ing decisions to make about which creature they would rather play with.

ORTHOGONAL UNIT DIFFERENTIATION

In his lecture at the 2003 Game Developers' Conference, "Orthogonal Unit Differentiation," game designer Harvey Smith argued that each type of unit a player can control in a game (a car, a soldier, an RPG character, or anything else the player can command) should be orthogonally different from all the others (Smith, 2003). By orthogonal, he meant that each kind of unit should be unlike the others in a different dimension, not simply more or less powerful when measuring in one dimension. The example of the Ford, Dodge, and Chevy in the preceding section
differentiates between them in the same dimension—speed—so they are not orthogonally different.

To make the player's choice of units more interesting and to offer her a larger vari­ety of strategies, Smith suggests that units should not only differ in the magnitude of their power at performing one task, as the Fords and Dodges did, but also should display entirely different qualities. Ideally, every type of unit should possess capa­bilities that no other unit has, and this gives each type a distinct role to play in the game. Otherwise, there's little point in including a weaker unit in the game except as part of an upgrade path to a stronger one.

The more diverse the types of challenges in your game, the easier you will find it to create orthogonally differentiated unit types. In a realistic car racing game, all the cars face the same challenge and must be constructed to similar standards, which makes racing games a poor field for examples of orthogonal differentiation. Player success depends more on driving skill than on the attributes of their cars, which is appropriate for a racing game. In a war game, however, opportunities to create orthogonally differentiated units abound. Some units may fly or travel on water, whereas others may not; some may transport other units; some may possess ranged weapons and others only hand-to-hand weapons; and so on. You cannot directly compare the advantages of a unit that wields hand-to-hand weapons with the advantages of one that heals the wounded: These qualities make the player's choices more interesting, and success in the game consists of deploying the appro­priate combination of units to defeat the enemy's forces.

Orthogonally differentiated units also help to prevent dominant strategies from arising if you define the victory condition in such a way that the player must use a variety of different units in order to win the game. Many inexperienced chess play­ers rely on using the queen aggressively, wrongly believing this a dominant strategy because she is the most powerful piece on the board. In fact, however, each type of chess piece plays a role and they work cooperatively. The queen cannot control the board alone; she needs the help of the other pieces. The types of pieces exhibit enough diversity to keep games interesting and prevent dominant strategies.