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.
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.