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.

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

Design: The Zombie deck

The distribution of cards in the Zombie deck is designed to add dramatic tension to the game. It contains three kinds of cards: 10 “Safe”, 10 “Zombie” and 5 “Draw 2”. The weights were chosen so that the average number of zombies per card draw is 2/3. This can be seen by considering the equation

z = 2/5 * 1 + 1/5 * 2 * z

‘z’ is the expected number of zombies draw as a result of drawing a single card. There is a 2/5 chance of it being a Zombie card, resulting in 1 zombie, and a 1/5 card of it chance of it being a Draw 2, which will return in 2*z zombies. Solving for z gives 2/3.

This equation is not quite accurate. It assumes cards are drawn with replacement, which is not the case. Cards drawn are not replaced until the deck is empty, so the probabilities are biased depending on recent history. If you have encountered a greater than average number of zombies recently, the expected number will be lower. If you have encountered fewer, the deck will be full of undrawn zombies and the probability of drawing them will be higher. Thus the deck creates a simple self-balancing long-term experience which would not be the case, for example, if dice were used instead. This gives the designer more control over the experience.

The Draw 2 cards are added to give an additional sense of drama to the draw. When you see 3 face-down cards at a location it is easy to estimate that there are probably 2 Zombies. When the cards are revealed as a Zombie and two Draw 2 cards, the tension increases. As additional cards are drawn one by one there can be a sense rising tension or relief. It might turn out to be no threat at all. Or it might turn into a much larger fight than first expected.

Calculating the theoretical probabilities of different numbers of zombies is rather difficult, so I wrote a simulator to generate ten thousand draws from the same deck and collate the number of zombies that appear. I repeated this for draws of up to eight cards (the most cards that might be drawn for a location). The results are graphed below.

Probability of different numbers of zombies

The mean value remains at 2/3 per card, as expected, but as more cards are drawn the peak broadens. This makes large draws more unpredictable. They could be very large or surprisingly small. This is an interesting issue for the final battle: sometimes it is overwhelmingly huge, sometimes it is surprisingly easy. This works in my favour. The Road is not a game that you should expect to win. A sense of capricious fate is one of the design goals of the game. This deck design allows us to string the players along with occasional surprises and then throw an ending at them which may make them question the value of all their preparations.

Published in: on December 9, 2012 at 1:16 pm  Leave a Comment  

Design: Health vs Food

The main design element of the game is the health vs food vs strength tradeoff. Let us first consider food and health.

Every player starts with 5 or 6 health points, 2 or 3 pieces of food.

Health and food are closely related. Each day a player must consume a piece of food or starve and lose a health point. More food is gained by scavenging which usually means fighting zombies. Getting in a fight means running the risk of lose health, so there is a risk-reward tradeoff. Fight and there is a chance you will lose health, perhaps a large amount if things go unexpectedly badly. Or else run away and face the certainty of eventual starvation.

There is also an interesting tension between health and food. The starvation mechanic seems to set a 1:1 equivalence between the two, but food and health are not equal. Food is transferrable, health is not. A player with 2 health and 3 food has more power than a player with 5 health. They have more options for trade and negotiation in the party. However they are also in more danger. Low health is risky and invites attacks.

Health and food are both tuned to be on a steady decline. There are only two opportunities in the game to regain lost health (the Hospital and the First Aid Kit). The are rare and often do not appear at all. If they do appear the players have to decide when to use them. Too early and they may be used on a player who does not need them. Too late and players may die before they have the chance.

The rates of health and food loss are deliberated tuned so that four players are likely to hit zero after about 9 days, depending on the distribution of cards. The road deck is tuned to take somewhere between 8 and 12 days to reach the airfield. Three players can survive longer – they have less fighting power but they consume less food. The gain in food usually outweigh the loss in strength, assuming no-one is hurt in the process. Of course, most parties will not consider this option until the food supplies are already too low for it to matter.

Then there is the cannibalism option. The party can exchange total health (and strength) for temporary food by letting one of their number die in combat (or deliberately killing them). This is the only way that health can be transferred, and it is deliberately drastic. Players who starve to death cannot be eaten. While this may be unrealistic, it forces the party to make a deliberate decision to kill their teammate, rather than just letting them die by “natural forces”.

Published in: on December 6, 2012 at 11:18 pm  Leave a Comment  

Stories from The Road

I’m designing a zombie-survival card game with the working title The Road. It’s a semi-cooperative game. Your chances of surviving alone are small but the zombies are not the only threat on the road. Food is short and your fellow travellers are eyeing you dangerously.

The thing I like best about the game is the stories it generates. I’m playtesting at the moment and recording the stories on a new blog Stories from The Road. Check out that site for updates about the game.

I’m also looking for an illustrator to work on designs for the cards. I’m looking for a gritty, semi-realistic comic-book style like The Walking Dead or Y: The Last Man comics. If anyone is interested, let me know.

Published in: on December 5, 2012 at 7:45 am  Leave a Comment  

The Block of Granite – A Parable

[A little parable I wrote today. Nothing to do with games but I thought I’d share it anyway.]

The Block of Granite – A Parable

Once there was a huge outcropping of granite in the middle of our village. The elders called it Wisdom. They would sit on it and meditate, or rest under its shade from the summer’s sun. It was large, solid and dependable.

However the town grew and the boulder, for all it’s solidity, was impractical. (more…)

Published in: on November 6, 2012 at 12:19 am  Leave a Comment  

That Ball Game – A Game for Teaching Game Design

[This is the full text of a paper I presented at FDG 2013. A PDF copy can be downloaded here.]

For the past six years I have been teaching a game design class to a diverse group of programmers, artists, media theorists and designers. I have found that traditional academic model of teaching, as the handing down of established knowledge from expert to novice, fail badly in such a young and dynamic discipline. Instead I have embraced a more interactive model of learning, accepting students as fellow knowledge-creators and working together to find the ideas to help us better understand our design practice.

In this paper I present a ball game I use as an opener in the very first class. I describe the rules of the game in full and discuss how I employ as a teaching tool. I have used it every year and it has grown in importance as a way to break down the barriers between lecturer and student and between students of different backgrounds. It also serves as an thought-provoking example to help students think more carefully about some of the most obvious and yet troublesome ideas in the field: ‘fun’, ‘rules’, ‘play’ and ‘game’.

Published in: on September 25, 2012 at 5:31 am  Leave a Comment  

Book: Evolutionary Games and Replicator Dynamics

Evolutionary Games and Population Dynamics, by Josef Hofbauer and Karl Sigmund.

I won’t lie to you. This is a dense mathematical work full of theorems, proofs and exercises. I only understood about a third of it. After the first seven chapters I got lost and could only scan page after page of formulae. But what little I understood was very interesting and work sharing.

Published in: on July 24, 2012 at 1:39 am  Leave a Comment  
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Ira Glass on Storytelling

Talking about creativity, you’ve probably already seen this doing the rounds, but there is a lovely quote from Ira Glass on the difficulty one faces as a new artist, when your taste exceeds your capacity to create:


Published in: on July 20, 2012 at 6:27 am  Leave a Comment  
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Books: Steal Like an Artist

Steal Like an Artist: 10 Things Nobody Told You About Being Creative, by Austin Kleon.

Austin Kleon’s Steal Like An Artist is a must-read for any aspiring creative, whether in writing, music, visual arts or game design. It contains a brief but profound manifesto:


Published in: on July 20, 2012 at 6:09 am  Comments (1)  

Books: Danger

Danger: Our Quest for Excitement
by Michael J. Apter.

Why do people enjoy dangerous sports like mountaineering or running with the bulls? Why do civillians enjoy playing soldiers and why do ex-soldiers sometimes talk about the dangers and even the suffering of war with nostalgia? Why do we enjoy other’s suffering in stories or movies or the evening news?

Published in: on July 18, 2012 at 7:09 am  Leave a Comment  
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