KEFREN

Copyright (c) 2001 João Pedro Neto

After seeing Epaminondas, I associate the stone movements with the idea of 2D shifting. There are another two related operations, namely, rotation and scaling. I took the latter and created SCALUS. Now, after some time, I made KEFREN based on rotation (the original Twirl concept is due to Claude Chaunier inspired in turn by SCALUS). All 3 games have names based on Classical History, and I tend to see my two games as an homage to Epaminondas, forming a kind of 'Classical Trilogy' on abstract games. 

KEFREN is played a board with 19x9 intersections. Each player has 18 stones. The initial setup follows:

TURNS - Black starts playing. Players may not pass. GOAL - Wins the player, that at the end of a turn (i.e., after both players had moved), has the greater number of stones on his last rank; or is able to stalemate the opponent! MOVE -  Stones move by twirling. Twirl is a pivot move. This is achieved on the following steps: Select a friendly stone on a straight line (diagonal or orthogonal) as the Pivot (say, at a distance of N cells). The stone can move to another cell on a straight line (diagonal or orthogonal) at a distance of N cells from the pivot and from the original cell; There must be no stones in-between the three lines defined by the Pivot, the source cell and the destiny cell (there is no restriction inside the area of the triangle defined by those three cells). CAPTURE - If the stone moves to a cell with an enemy stone, this one is captured. Capture is mandatory. After the first capture, the moved stone must continue to capture other stones, if possible. The player can decide, after each partial capture, between two or more capturing options (so, maximal capture is not mandatory). Only one stone can capture on each turn (even if there are other capturing moves with other stones). Stones never capture backwards, only forward or lateral captures are valid.

 

note: A Twirl is a move by triangulation. The origin, the pivot and the destiny form a triangle, where all cells between the edges are empty. It seems difficult to see Twirls, but after the first game, the idea becomes quite familiar.

Pivot Moves

Some basic samples Stone G10 can move to E10 using E8 as a Pivot, since both stones are separated by a distance of one cell, and E10 also has a distance of 1 cell both to H10 and to E8. However G10 cannot move to G8, because of stone F8. Stone C2 can move to G2 using C6 (or C6 can move to G2), but cannot move G6 due to E6. Both C6 and E6 can capture E8 using the other as the Pivot.

Keep Walking A single stone cannot move or capture. KEFREN needs team work to achieve any goal. The easier way to move is using two stones. The Black  walk could go like: B6-B7, C6-C7, B7-B8, C7-C8,... The White walk is three times faster: D10-D7, G10-G7,  D7-D4, G7-G4, .... As expected, as further apart the stones are, the faster is the walk. However, the easier is to prevent that walk from happening (just place some stone between them!)

Some basic tactics

Mandatory Capturing Black moves F3-E4. White must capture. If he moves D4:E4, then C3:E5, and E4 is helpless. If White moves E5:E4, then C5:G9, advancing 4 rows, and D4 cannot move until some other friend comes to the rescue.

	Capture multiple stones Black moves F4-E4. White must capture C4:E4 or C6:E4. Then Black captures two stones with movement F3:E4:E7.
	Leave First Row? The simple strategy of do not moving the first row of stones does not work! That would mean only half the stones in the center battle, which means that after a while, there will be the remaining enemy army ready to attack that first row, without any reasonable line of defense. In this sample, Black cannot stop the multiple A1, C1 and E1 attack!