Quantifying Strategy

Will I draw an epidemic card in Pandemic?

(and more) When an epidemic card is drawn in the cooperative game Pandemic, it ramps up the difficulty of the game. Knowing when this occurs, or when it could occur, is useful to players to achieve victory. Here, one question ends up leading to additional questions. As we know more about a problem, the horizon of our ignorance often expands, rather than contracts.

What if we're in the middle of the game?

The single probability that we calculated is limited, though, as it doesn't match the amount of information that we have for much of the game. Once we draw cards, we know more about some of the remaining turns. We can compute the conditional probabilities, the probabilities given the knowledge we have from either drawing or not drawing epidemic cards on previous turns.

How many turns are there between epidemic cards?

This leads us to question the distribution of the number of turns between epidemic cards, as this can impact the game in notable ways. Do we get new heavily infected cities back to back, or a long gap to take care of the current situation.

What is the probability of drawing the newly infected city after an epidemic card?

One of the things that can happen after an epidemic card is drawn is that the newly infected city is drawn from the infection deck. The probability of this occurring is a function of how many cards are in the discard pile of the infection deck, which in turn depends on how many turns are between epidemic cards (or since the beginning of the game).