Design: Fighting Zombies

In this post I look at the design of combat against zombies. I’ll leave the issue of fighting other players to a later post.

The zombie battle should contribute towards several parts of the target experience:

  1. To force the players to coordinate against a common threat.
  2. To increase dissent between players over how to respond to the threat.
  3. To give a short-term a dramatic arc to the game as the tides of battle rise and fall.

There are two important perspectives to look upon zombie battles: as a team and as self-interested individuals.

Team perspective

From the team perspective, the most important task is to eliminate the zombies with as little damage to the team as possible. This is a strategic tradeoff between attacking, to do damage, and defending, to avoid taking damage. Consider a simplified example, in four players face three zombies. We’ll assume every player is armed with a 1 damage melee weapon and defending avoids all damage. We’ll also ignore the ‘call’ action for the time being. All three zombies start with zombies have 3 health.

The obvious strategy is for everyone to attack until there is only one zombie left. Then some players should defend:

  1. All attack for 4 damage. 3 zombies attack with 80% chance damage. 1 zombie dies.
  2. All attack for 4 damage. 2 zombies attack with 80% chance damage. 1 zombie dies.
  3. 1 attack for 1 damage. 1 zombie attacks with 20% chance damage. 1 zombie dies

The expected damage is 3 * 0.8 + 2 * 0.8 + 1 * 0.2 = 4.2 health points. A better plan is:

  1. 3 attack for 3 damage. 3 zombies attack with 60% chance damage. 1 zombie dies.
  2. 3 attack for 3 damage. 2 zombies attack with 60% chance damage. 1 zombie dies.
  3. 3 attack for 3 damage. 1 zombie attacks with 60% chance damage. 1 zombie dies

With an expected damage of 6 * 0.6 = 3.6 health points.

The key idea is to defer attacks that do not reduce the number of zombies. Attacking when there are fewer zombies means less chance of getting hurt. It is only worth having everyone attack if there are 4 or more zombies.

This strategy is made more complex with the addition of ranged combat. Ranged attacks can kill an opponent before it has the chance to retaliate. They have a cost however, either they use ammunition (guns) or the player drops their weapon (knives). Consider the above scenarion again, but with the option of throwing the weapon as a ranged attack. The best strategy becomes:

  1. 3 attack for 3 damage. 3 zombies attack with 60% chance damage. 1 zombie dies.
  2. 2 attack for 2 damage. 2 zombies attack with 40% chance damage.
  3. 4 ranged attack for 4 damage. 2 zombies die.

The expected damage is only 2.6 health points.

This is not as strategically complex as I’d like. It seems it is always best to defer ranged attacks to the end, even if the players have other weapons as back up. I’m still looking for a mechanic which creates more diverse strategies without adding too much extra complexity. Then again, I don’t want strategy to be the main focus of the experience. The game is fundamentally about the inter-player politics. I don’t want it to turn into a heavy number-crunching strategy game.

Individual perspective

Zombie combat is deliberately designed as a free-rider problem. As we saw above, it is often useful for some players to attack while others defend, but attacking is more dangerous than defending. Every player has an incentive to see the fight finished, but would prefer to be the one who gets the “free ride” while everyone else takes the risk. Because moves are simultaneous, there is no way to force other players to act. The game effectively becomes one of Chicken:

Player 2
Player 1 Attack Defend
Attack 3,3 2,4
Defend 4,2 1,1

Outcomes are listed as preferences for Player 1 then Player 2, with 4 being the most strongly preferred outcome and 1 being the least. Mathematically it is a fairly simple game with three Nash equilibria (2 pure, 1 mixed). But psychologically it is more interesting, especially when played repeatedly. There is the real possibility of a stalemate in which the players refuse to attack and stare each other down.

This simple game is made more interesting by a couple of factors. The first is cheap talk. Players are allowed to make whatever threats or promises they like during the battle, but none of them are binding. Promises are unreliable, especially since no trading is allowed until combat is over, at which time they may not be kept. Threats are also risky. Carrying out a threat can be costly to the player making it. For example, attacking a player if they don’t comply is costly to the parties overall health and thus everyone’s survival chances. Furthermore, announcing your intention to attack is giving the other player forewarning and the opportunity to defend or attack you in return.

The second factor is unequal conditions. When players have different levels of health the outcomes of the battle matter differently. A player with only 2 health will fear an attack more than a player with 5 health. Different attack strengths also affect the game. When one player has a better weapon than the others, the party might look upon them to attack more often. This makes sense in terms of overall cooperation and it reduces the total expected health cost of the fight, but health is not transferrable and the attacking player may begin to resent taking all the risk. There is, of course, the option of swapping weapons, but players are usually reluctant to give away a powerful weapon in case it is used against them in the future.

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Published in: on December 17, 2012 at 3:36 pm  Leave a Comment  

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