# L game

The L- match (or " L") is a system developed by Edward de Bono board game that requires a minimum of rules, without trivially simple. First introduced it in 1968 in his book The five day course in thinking ( German translation: in 15 days learn thinking ).

## Game rules

The game is played on a 4x4 game board large fields. Each player has a four fields large, L- shaped tile ( the L stone), and two neutral stones of the size of the field come.

At the beginning of the two L-blocks are placed together, they cover the middle of the game board 4x2 fields. The two neutral stones are placed in front of the short leg of the L-blocks in the corners of the board.

The two players take turns. A player must place his L- stone into any new position per turn, this may also be lifted and turned. Then the player can still put one of the two neutral stones on a free position, or without it.

The game is over when one player has no more free position for its L stone available.

## For the development of the game

De Bono has developed the game by its own account, because although he likes to play, but do not want to focus on too many pieces. His criteria in the development were:

- As few pieces as possible
- The smallest possible board
- As few rules, so it is easy to learn and play
- The game should be even more interesting for experienced players
- It should not be deterministic

## Analysis

The L- game is simple enough to analyze it completely. There are a total of 18368 possible arrangements of the four stones, which can be reduced to 2296 fundamentally different arrangements, if reflections or rotations are not considered separately and the two neutral stones are regarded as interchangeable. Each of the positions can be derived from another, so that a winning strategy for all arrangements must be considered.

## Winning strategy

In each case, 15 of the 2296 arrangements represent a winning position and another 14 positions within the next trains lead to one of those winning positions. From the remaining 2267 positions two perfect players can unsubscribe an endless game. For these arrangements, there are per player 13-221 possible moves. On average, there are about 90

A player can not lose if he so chooses his next moves that the opponent can not get into one of the 15 profit, or 14 leading to the winning positions. These arrangements must be recognized. An analysis of the winning positions, one can see that at least one of the two neutral stones stands on one of the eight killer positions, these are the surrounding areas of the game board. In addition, the L- stone covered the loser always one of the corner squares.

## The L- play on the computer

Since the complete analysis is relatively simple and the number of packages and the winning positions is low, the L- game is often provided as a programming task. After the preliminary analysis, it is the responsibility of the programmer to implement algorithmically the way to the winning positions. Added to this is still making a successful graphical user interface.