What is generalized geography? How does it differ from the original geography game?
Kushal article lead paragraph
Geography is a child's game in which players take turns naming cities from anywhere in the world. Each city must begin with the same letter that ended the previous city's name. Players are not allowed to repeat a city name that has appeared before in the same game. The game starts with a designated starting city and ends when a player loses because they are unable to continue. For example, if the game starts in Manhattan, the next player could say New Orleans, followed by San Diego, Oakland, and so on.
Kushal article paragraph
We take all the cities that we consider legal for our game. We model a directed graph from the problem space with each city being a node in the graph. We draw a directed edge or an arrow from one node (city) to another if the last letter of the name of the former is the same as the first letter of the name of the latter. For example, the last letter of Oakland is D and the first letter of Dallas is D as well. Therefore, a directed edge exists from Oakland to Dallas.
You can think of generalized geography as an abstraction of geography game. Consider the graph above. Now, replace all the names by unique symbols (for example, integers 1, 2, ... ). In generalized geography, we take an arbitrary directed graph with a designated start node instead of a graph associated with actual cities. For example, consider the graph in Figure 1: Directed graph where each node has its in degree and out degree as its label.
Let us say the designated start node is (1, 1). Let us also say that there are two players in this game. Player one must move from (1, 1) to (2, 2). Player two moves from (2,2) to (2, 0). Player one is now stuck. Player two wins.
As you can see, the game changes if you change the start state. If (0,2) is the start state, player one will choose to go to (2,0) so that player two now gets stuck. Thus player one has a winning strategy. Note that player one could have gone to (2,2). However, this leads to player two going to (2,0) which means player one is stuck. A winning strategy doesn't mean player one will win in every case. A player has a winning strategy for a game if that player wins when both sides play optimally.
http://mcny.duckdns.org/article/generalized-geography