Fibonacci
Fibonacci is a fast and furious two-player tactical game, and unlike a large proportion of the strategy games on the market, I am pleased to say that this is NOT a chess variant. In fact, Fibonacci has little relationship to any other strategy game I have played...
I should point out that there is a variation of Fibonacci which involves the use of cards, and which introduces an element of luck into the game. Although the cards are supplied with Fibonacci, I must confess that I haven't played this version of the game, and I will say no more about it.
The board is hexagonal, divided up into hexagonal spaces (forgive me if I occasionally laps into calling them 'squares'). Each player starts the game with 13 pieces; one centrepiece, six attacking ('strike') pieces, and six neutral ('support') pieces. The objective of the game is to completely surround your opponent's centrepiece with your attacking pieces.
The centrepiece cannot move itself, but can be moved by other pieces of either side. All other pieces move in exactly the same way... a piece can either move to any adjacent hexagon, or it can move to any hexagon adjacent to another piece to which it is connected. This is best seen with the help of the following diagram...
_/ \_/x\_/ \_/ \_ / \_/x\_/x\_/ \_/ \ \_/x\_/2\_/x\_/ \_/ / \_/1\_/3\_/4\_/ \ \_/x\_/x\_/x\_/ \_/ \_/x\_/x\_/ \_/ \_/ \_/ \_/
If a player has pieces in positions 1, 2, 3, 4, then a piece at position 1 can move to any of the positions marked with an 'x', since 1, 2, 3 are connected.
If a piece moves to a square... er... hex which is already occupied, then the two pieces exchange places. This occurs regardless of who owns the piece on the destination hex.
One final twist... a player gets to move several pieces during their turn. The first player makes one move, the second player two, the first player then moves three... until the dizzying total of six moves is reached. After that, each player takes six moves each turn. However, a player loses one move for each of their opponent's attacking pieces which is in contact with their centrepiece.
The movement rules make this game very fast-moving, with pieces flowing backwards and forwards across the board, there is plenty of scope for lightening strikes, eg building a ladder to the enemy centrepiece, and transporting it to the opposite end of the board.
The sheer number of possibilities, however, reduces the value of long-term planning; on an average turn, each piece would be next to about 5 other pieces, giving about 14 possible positions for each piece. If you multiply this by the number of pieces able to move (12), then you have 168 possible moves. Assuming that you have four moves in an average turn, this gives 168 x 168 x 168 x 168 = about 800,000,000 possible moves per turn. Compare this to about 39 moves from an average position in a game of chess!
I would say that this game is a must for any serious strategy game player, and the pace of the game and movement of the pieces should appeal to casual boardgamers too.