Player.java

class Player {
    public boolean first;
    public boolean second;

    Player(boolean first, boolean second) {
        this.first = first;
        this.second = second;
    }

    @Override
    public boolean equals(Object o) {
        if (this == o) return true;
        if (o == null || getClass() != o.getClass()) return false;
        Player player = (Player) o;
        return first == player.first &&
                second == player.second;
    }

    @Override
    public int hashCode() {
        return Objects.hash(first, second);
    }
}

Scratch.java

class Scratch {
    public static void main(String[] args) {
        testAgainst(true, true);
        testAgainst(true, false);
        testAgainst(false, true);
        testAgainst(false, false);
    }

    static void testAgainst(boolean originalForce, boolean originalUsing) {
        Player mock1 = new Player(originalForce, originalUsing);
        Player mock2 = new Player(originalForce, originalUsing);
        Player mock3 = new Player(originalForce, originalUsing);

        boolean result1 = original(mock1);
        boolean result2 = clive(mock2);
        boolean result3 = solution(mock3);

        boolean equalResult = result1 == result2;
        boolean equalMutation = mock1.equals(mock2);
        System.out.println(String.format("TEST[%s,%s] SAME RETURN[%s] SAME MUTATION[%s]", originalForce, originalUsing, equalResult, equalMutation));
    }

    public static boolean clive(Player player) {
        if (player.second) {
            player.first = false;
            return true;
        }
        player.first = false;
        player.second = true;
        return false;
    }

    public static boolean original(Player player) {
        if (player.first && player.second) {
            player.first = false;
            return true;
        }
        if (player.second) {
            return true;
        }
        player.first = false;
        player.second = true;
        return false;
    }

    public static boolean solution(Player player) {
        player.first = false;
        if (player.second)
            return true;

        player.second = true;
        return false;
    }
}