<Page> 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