science of board games

Power Grid is one of my favorite games: the point is to build your power plants in cities and power them, while minimizing connecting costs, prices of new power plants, cost of resources, etc. It has an evil handicapping system, where the person in first is given fairly stiff penalties.

During the initial part of the game, players must select which city they wish to start building in. This can be a critical choice, but it is difficult to see how some regions are truly better than others. To answer this question, I turned to Ruby.

To win the game, the player needs to build in 17 cities (or 15, or less, depending on the number of players and the board). So, which city can get to 17 cities the cheapest? The following table lists all of the costs to build 17 cities for the US Map (only connecting costs, not the actual city costs, which are a minimum of 170):

Cost	City
59	Jacksonville
59	Miami
59	Savannah
62	Tampa
64	Buffalo
64	Memphis
64	New Orleans
64	New York
64	Pittsburgh
68	Kansas City
68	Knoxville
68	Omaha
68	St. Louis
70	Atlanta
70	Chicago
70	Duluth
70	Fargo
70	Houston
70	Minneapolis
71	Birmingham
71	Boston
71	Cincinatti
71	Detroit
71	Norfolk
71	Philadelphia
71	Raleigh
71	Washington
73	Dallas
73	Oklahoma City
106	Billings
106	Boise
106	Cheyenne
106	Denver
106	Portland
106	Salt Lake City
106	Santa Fe
106	Seattle
132	Las Vegas
132	Los Angeles
132	Phoenix
132	San Diego
132	San Francisco

Edited 8/17/2008. This should be more correct now. I had a piece of code commented out in my function that skewed the numbers by quite a bit.

This confirms the obvious: the east coast is cheaper, by half as much as most of the west coast cities. Of course, having competition in an area will drive up prices (at the very least by driving up the 170 fixed cost of building all of the cities).

This also tells us that it takes a minimum of 170 + 59 = 229 elektro (money) to end the game, although much more to actually win (including powering them all), since the person who then ended the game would lose to anyone who still had elektro left, or anyone who could power even a single city. The cheapest set of power plants that will power 17 cities costs 81 elektro (for example, the 20, 30, and 31 power plants can supply enough power), so we are up to 310 elektro.

From there, we start getting into a lot of variables. I'm still working on tweaking my Ruby code to come up with some interesting numbers, so stay tuned.