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                                                                    Exhibit 3.4

                            CERTIFICATE OF AMENDMENT

                                       TO

                       CERTIFICATE OF LIMITED PARTNERSHIP

                                       OF

                       AMERICAN REAL ESTATE PARTNERS, L.P.



It is hereby certified that:

         FIRST: The name of the limited partnership (hereinafter called the
"Partnership") is American Real Estate Partners, L.P.

         SECOND: Pursuant to provisions of Section 17-202, Title 6, Delaware
Code, the Certificate of Limited Partnership is hereby amended by adding the
following paragraph 4:

         "4. This Agreement will be deemed to include all provisions required by
         the New Jersey Casino Control Act and the regulations thereunder and to
         the extent that anything contained in this Agreement is inconsistent
         with the Casino Control Act, the provisions of the Casino Control Act
         shall govern. All provisions of the Casino Control Act, to the extent
         required by law, to be included in this Agreement, or incorporated
         herein by references are fully stated in this Agreement.

                  Any securities of the Partnership are held, subject to the
         condition that if a holder thereof is found to be disqualified by the
         Casino Control Commission pursuant to the provisions of the Casino
         Control Act, such holder shall dispose of his interest in the
         Partnership in accordance with the Casino Control Act."

         The undersigned, a general partner of the Partnership, executed this
Certificate of Amendment on May 9, 2002.

                          AMERICAN PROPERTY INVESTORS, INC., its general
                             partner


                          By:           /s/ John P. Saldarelli
                             --------------------------------------------------
                                            Vice President