  We present here the new insight or revisiting the algorithm for playing in
Chess with incomplete information (which can be recognized by its newly
short-name as Phoenix-Chess strategy). The only difference with respect to the
classical variant of Chess-game is that each rook after its having been
captured by enemy chess piece in the proccess of gaming is not to be eliminated
from the current game, but this rook is assumed being under virtual repairing
during next N-steps (the required number of N is discussed in the current
research). Then afterwards, such rook will be introduced in game again during
maximal N-steps if only the chessboard square (on which it was captured
previously) has not been occupied at previous step. In this case, Phoenix-Chess
can be classified as game without predictable horizon of planning, so this kind
of game should be considered as Chess-like games with incomplete information.
