L game
The L game (or "L" for short) is a board game developed by Edward de Bono that uses a minimum of rules without being trivial. It was first presented in 1968 in his book The five day course in thinking (German translation: Learn to think in 15 days ).
Rules of the game
The game is played on a 4x4 board . Each player has a four-square, L-shaped piece (the L-piece ), plus two neutral pieces the size of a square.
At the beginning the two L-stones are placed next to each other so that they cover the middle 4x2 fields of the game board. The two neutral stones are placed in front of the short legs of the L-stones in the corners of the game board.
The two players take turns drawing. In each turn a player has to place his L-stone in any new position, whereby it can also be lifted and turned. Then the player can either place one of the two neutral stones in a free position or do without it.
The game is over as soon as a player has no more free positions for his L-stone.
To develop the game
De Bono says he developed the game because he likes to play but doesn't want to focus on too many pieces. Its development criteria were:
- as few pieces as possible
- the smallest possible game board
- As few rules as possible so that it is easy to learn and play
- the game should still be interesting for experienced players
analysis
The L game is simple enough to analyze completely. There are a total of 18,368 possible arrangements of the four stones, which can be reduced to 2,296 fundamentally different arrangements if reflections or rotations are not considered separately and the two neutral stones are viewed as interchangeable. Each of the positions can be derived from another, so that all arrangements have to be considered for a winning strategy .
Winning strategy
15 of the 2296 arrangements each represent a winning position and a further 14 positions lead to one of these winning positions in the next few moves. From the remaining 2267 positions, two perfect players can play an endless game. For these arrangements there are between 13 and 221 moves per player. The average is around 90.
A player cannot lose if he chooses his next moves in such a way that the opponent cannot get into one of the 15 winning or the 14 winning positions. It is important to recognize these arrangements. In every winning position there is at least one neutral stone on one of the eight killer positions , these are the edge fields of the game board. In addition, the loser's L-stone always covers one of the corner squares.
The L game on the computer
Since the complete analysis is relatively simple and the number of arrangements and winning positions is low, the L game is often set as a programming task. After the preparatory analysis, it is the programmer's task to algorithmically implement the path to the winning positions . Then there is the creation of an appealing graphical user interface .
