An abstract strategy game is a board, card or other game with perfect information, no chance or physical skill, and (usually) two players or teams. Some board games which do not involve the removal of taken pieces can be played as pen-and-paper games.
n-in-a-row games involve placing and/or moving pieces on a game board attempting to create a layout of n of your pieces in a straight line (often n=3, but not always). Positional games involve only playing pieces, with no movement or captures afterwards. Many of these positional games can also be played as paper and pencil games, and these are marked †. (Generally, 3D games are difficult to play on paper.)
Blockade games primarily involve moving your pieces, following the game rules, so as to block your opponent from having any move they can make. In symmetric blockade games, both players have the same number of pieces with the same movement capabilities. In asymmetric blockade games, players have different numbers of pieces with different movement capabilities - usually one player having a single piece of greater movement range and the other player having multiple pieces of lesser movement capabilities.
A connection game is a type of abstract strategy game in which players attempt to complete a specific type of connection with their pieces. This could involve forming a path between two or more goals, completing a closed loop, or connecting all of one's pieces so they are adjacent to each other. Those marked † can also be played as paper and pencil games.
Those marked † can also be played as paper and pencil games.