!Board Game
!!''A priori'' optimal placement of research stations in vanilla ''Pandemic''
When playing the Operations Expert, it is paramount to place new research stations in such a way as to minimize overall travel times for all players. Luckily, we can solve that conundrum with some combinatorics and some graph theory. First, we define the overall fitness of a particular station placement as the average length of the shortest path between two random cities on the map, given said stations' placement (the shorter, the better). The marginal utility of putting a station in a particular city then equals the difference between the overall fitness before and after the placement. A building plan is a sequence of six cities where stations are to be built, in order, with the last one replacing the initial free one in Atlanta. Two approaches to finding the best building plan can be distinguished:

# The '''greedy search''' (GS) approach is to only consider the next station's marginal utility, building it in the city that would immediately improve the overall fitness of the map by the largest amount. This approach favors short-term gains over long-term performance. It is unclear whether it will converge on the global optimum if we keep building new stations by replacing new ones.
# The '''exhaustive search''' (ES) approach is to compute the fitness of all 12 million possible placements of 6 stations across 48 cities to find the best one. The building order is then calculated by maximizing immediate marginal utility, similar to the GS. While the ES returns the best end result, its immediate fitness gains are lagging behind GS until the fifth station is placed.

The following table shows the two resulting building orders (both start out with the Atlanta station already on the board and the overall fitness of 4.21):

|| '''GS: City''' || '''GS: Fitness''' || '''ES: City''' || '''ES: Fitness''' || '''ES adv.''' ||
||Cairo || 3.96||Istanbul || 3.96|| −0.02%||
||Hong Kong || 3.50||Shanghai || 3.56|| −1.62%||
||Mexico City || 3.31||Chennai || 3.35|| −1.26%||
||Paris || 3.14||Mexico City || 3.15|| −0.37%||
||Delhi || 2.97||Kinshasa || 2.95|| +0.72%||
||Washington || 2.93||New York || 2.87|| +2.09%||

We observe that although the cities are largely different (except for Mexico city), most are actually direct neighbors within specific high-priority regions: Middle East (Cairo-Istanbul), China (Hong Kong-Shanghai), India (Delhi-Chennai), and the US East Coast (Washington-New York). The shift from Paris to Kinshasa is a result of both the Middle East and the East Coast stations shifting northwards, making Europe much more accessible, but necessitating a dedicated station in Sub-Saharan Africa.
----