Pencil and paper games: Blocking

Another theme is pencil and paper games is blocking, i.e., as the game advances, less and less squares are available, until the stalemated player loses the game.

A well-known example is 1970's Snort by Simon Norton, aka Cats & Dogs. 

The rules: on an 8x8 grid, players take turns marking an empty square, provided that the square is not orthogonally adjacent to an adversary mark. The first player unable to move, loses the game.

To prevent mirror strategies, in the beginning the first player should play in the central 2x2 area, and the second player must play outside that area.

There's also a faster variant, called Obstruction, that includes diagonal adjacencies as illegal moves.

Slimetrail, designed by Bill Taylor in 1993, is also a pencil and paper game with a blocking theme. To recap, in Slimetrail each player has a home, each one staying in opposite corners. The snail mark starts at the middle of the board. Each player, on his turn, shades the snail mark, and places/marks the snail on an adjacent empty square. Wins the player that moves the snail into his home or stalemates the adversary.

Domineering (aka Stop-Gate, Crosscram) is another example. Designed by John Conway in 1976, the game is also played on a square grid, where each player marks two adjacent empty squares with a domino. One player marks vertical dominoes, while the other player marks horizontal dominoes. The first player to be stalemated loses (i.e., the last player to move wins).

Cram is a variant where both players can mark dominoes horizontally or vertically. It is what's called an impartial game in Combinatorial Game Theory. This means that Cram is just the game of Nim with other clothes (I mean, rules).

Chomp is another example. The game is played on a rectangular grid. Each player on his turn selects an empty square, and shades all squares that form a rectangle between itself and the grid's bottom-right corner. The player that moves last loses the game.

Blue lost the match after move 11

Another example comes from JeuMok Plus. There are 24 shared 1x2x4 blocks. The game comes with a rulebook containing five different games (one is a NIM game, another is a Jenga), where the main game rules that players drop blocks in empty squares on a board, and each tile must be adjacent to at least another already on board. The board center cannot be used. The player that moves last wins the game.