Handicap Achievement for Squares

Given a polyomino \( P \) with \( n \) cells, two players \( A \) and \( B \) alternately color the cells of the square tessellation of the plane. In the case of \( A \)-achievement, player \( A \) tries to achieve a copy of \( P \) in his color and player \( B \) tries to prevent \( A \) from achieving a copy of \( P \). The handicap number \( h(P) \) denotes the minimum number of cells such that a winning strategy exists for player \( A \). For all polyominoes that form a square of \( n = s^2 \) square cells, the handicap number will be determined to be \( s^2 – 1 \).