Player 1 (P1) eats the cookie just one row above and one column to the right of the poissoned one, leaving two "legs". P2 picks to eat one cookie of one of the two legs, leaving say m cookies above (or to the right) of the poissoned one. P1 eats the corresponding cookie of the other leg, leaving the same m cookies on this leg: in this way symmetry is preserved. This evolves untill P2 leaves no cookies on a leg. P1 wins!