Document:

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                                                                    EXHIBIT 4.55

                             SUPPLEMENTAL INDENTURE

         Supplemental Indenture (this "Supplemental Indenture"), dated as of
December 1, 1999, between Horseshoe Gaming Holding Corp., a Delaware corporation
(the "Company"), the successor of Horseshoe Gaming, L.L.C. ("LLC"), to the
Indenture referred to below, and U.S. Trust Company of Texas, N.A. (the
"Trustee").

                               W I T N E S S E T H

         WHEREAS, LLC has heretofore executed and delivered to the Trustee an
indenture (the "Indenture"), dated as of June 15, 1997, among LLC, Robinson
Property Group, Limited Partnership and the Trustee providing for the issuance
of 9_% Senior Subordinated Notes due 2007 (the "Notes");

         WHEREAS, LLC and the Company entered into an Agreement of Merger (the
"Merger"), dated as of December 1, 1999, which provides, among other things, for
the merger of LLC with and into the Company;

         WHEREAS, the Indenture permits the Merger to occur if certain
conditions are met and if the Company and the Trustee enter into this
Supplemental Indenture to which the Company expressly assumes from LLC all of
the Obligations of LLC with respect to the Notes and the Indenture.

         NOW, THEREFORE, in consideration of the foregoing and for other good
and valuable consideration, the receipt of which is hereby acknowledged, the
Company and the Trustee mutually covenant and agree as follows:

         1. Capitalized Terms. Capitalized terms used herein without definition
shall have the meanings assigned to them in the Indenture.

         2. Assumption and Discharge. As of the date hereof, the Company
expressly assumes all of the Obligations of LLC with respect to the Notes and
the Indenture, and the parties release LLC from its obligations under the
Indenture and the Notes except as to any obligations that arise from or result
from the Merger.

         THE TERMS OF ARTICLE V OF THE INDENTURE ARE INCORPORATED HEREIN BY
REFERENCE.

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         3. NEW YORK LAW TO GOVERN. THE INTERNAL LAW OF THE STATE OF NEW YORK
SHALL GOVERN AND BE USED TO CONSTRUE THIS SUPPLEMENTAL INDENTURE, INCLUDING,
WITHOUT LIMITATION, SECTION 5-1401 OF THE NEW YORK GENERAL OBLIGATIONS LAW.

         4. Counterparts. The parties may sign any number of copies of this
Supplemental Indenture. Each signed copy shall be an original, but all of them
together represent the same agreement.

         5. Effect of Headings. The Section headings herein are for convenience
only and shall not affect the construction hereof.

         IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed and attested, all as of the date first above
written.

                                    THE COMPANY:

                                    HORSESHOE GAMING HOLDING CORP.

                                    By:
                                        ------------------------------------
                                        Name: Jack B. Binion
                                        Title:   President

                                    TRUSTEE:

                                    U.S. TRUST COMPANY OF TEXAS, N.A.

                                    By:
                                        ------------------------------------
                                        Name:
                                        Title:

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                                                                    EXHIBIT 4.56

                         HORSESHOE GAMING HOLDING CORP.

                                 FIRST AMENDMENT

                               TO CREDIT AGREEMENT

This FIRST AMENDMENT TO CREDIT AGREEMENT (this "AMENDMENT") is dated as of
November 18, 1999 and entered into by and among HORSESHOE GAMING HOLDING CORP, a
Delaware corporation ("COMPANY"), the financial institutions listed on the
signature pages hereof ("LENDERS"), DLJ CAPITAL FUNDING, INC., as Syndication
Agent (the "Syndication Agent") and CANADIAN IMPERIAL BANK OF COMMERCE, as
Administrative Agent (the "Administrative Agent"), and is made with reference to
that certain Credit Agreement dated as of June 30, 1999 (the "CREDIT
AGREEMENT"), by and among Company, Lender, Syndication Agent and Administrative
Agent. Capitalized terms used herein without definition shall have the same
meanings herein as set forth in the Credit Agreement.

                                    RECITALS

         WHEREAS, Company and Lenders desire to amend the Credit Agreement to
amend the definition of "Subsidiary Guarantor";

         NOW, THEREFORE, in consideration of the premises and the agreements,
provisions and covenants herein contained, the parties hereto agree as follows:

         SECTION 1. AMENDMENTS TO THE CREDIT AGREEMENT

         1.1 AMENDMENTS TO SECTION 1: PROVISIONS RELATING TO DEFINED TERMS

         Subsection 1.1 of the Credit Agreement is hereby amended by deleting
the definition of "Subsidiary Guarantor" therefrom in its entirety and
substituting the following therefor:

         A. "SUBSIDIARY GUARANTOR" means any Domestic Subsidiary of Company that
executes and delivers a counterpart of the Subsidiary Guaranty on the Initial
Funding Date or from time to time thereafter pursuant to subsection 6.8;
provided that any Domestic Subsidiary having both (a) assets valued at less than
one percent (1%) of the value of the

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aggregate consolidated assets of Company and its Subsidiaries and (b) revenues
accounting for less than one percent (1%) of the aggregate consolidated revenues
of Company and its Subsidiaries for the most recently ended four consecutive
Fiscal Quarters shall not be required to be a Subsidiary Guarantor.

         1.2 AMENDMENTS TO SECTION 6: COMPANY'S AFFIRMATIVE COVENANTS

         Subsection 6.8A of the Credit Agreement is hereby amended by adding the
following proviso to the end of such subsection: "provided that any Domestic
Subsidiary not satisfying the definition of "Subsidiary Guarantor" shall not be
subject to this subsection; provided, further that any Domestic Subsidiary that
is no longer excluded from the definition of "Subsidiary Guarantor" shall be
subject to this subsection as any new Domestic Subsidiary would be."

         SECTION 2. COMPANY'S REPRESENTATIONS AND WARRANTIES

         In order to induce Lenders to enter into this Amendment and to amend
the Credit Agreement in the manner provided herein, Company represents and
warrants to each Lender that the following statements are true, correct and
complete:

         A. CORPORATE POWER AND AUTHORITY. Company has all requisite corporate
power and authority to enter into this Amendment and to carry out the
transactions contemplated by, and perform its obligations under, the Credit
Agreement as amended by this Amendment (the "AMENDED AGREEMENT").

         B. AUTHORIZATION OF AGREEMENTS. The execution and delivery of this
Amendment and the performance of the Amended Agreement have been duly authorized
by all necessary corporate action on the part of Company.

         C. BINDING OBLIGATION. This Amendment and the Amended Agreement have
been duly executed and delivered by Company and are the legally valid and
binding obligations of Company, enforceable against Company in accordance with
their respective terms, except as may be limited by bankruptcy, insolvency,
reorganization, moratorium or similar laws relating to or limiting creditors'
rights generally or by equitable principles relating to enforceability.

         D. INCORPORATION OF REPRESENTATIONS AND WARRANTIES FROM CREDIT
AGREEMENT. The representations and warranties contained in Section 5 of the
Credit Agreement are and will be true, correct and complete in all material
respects on and as of the date hereof to the same extent as though made on and
as of that date, except to the extent such representations and warranties
specifically relate to an earlier date, in which case they were true, correct
and complete in all material respects on and as of such earlier date.

         E. ABSENCE OF DEFAULT. No event has occurred and is continuing or will
result from the consummation of the transactions contemplated by this Amendment
that would constitute an Event of Default or a Potential Event of Default.

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         SECTION 3. MISCELLANEOUS

         A. REFERENCE TO AND EFFECT ON THE CREDIT AGREEMENT AND THE OTHER LOAN
DOCUMENTS.

         (i) On and after the effective date hereof, each reference in the
Credit Agreement to "this Agreement", "hereunder", "hereof", "herein" or words
of like import referring to the Credit Agreement, and each reference in the
other Loan Documents to the "Credit Agreement", "thereunder", "thereof" or words
of like import referring to the Credit Agreement shall mean and be a reference
to the Amended Agreement.

         (ii) Except as specifically amended by this Amendment, the Credit
Agreement and the other Loan Documents shall remain in full force and effect and
are hereby ratified and confirmed.

         (iii) The execution, delivery and performance of this Amendment shall
not, except as expressly provided herein, constitute a waiver of any provision
of, or operate as a waiver of any right, power or remedy of Agent or any Lender
under, the Credit Agreement or any of the other Loan Documents.

         B. HEADINGS. Section and subsection headings in this Amendment are
included herein for convenience of reference only and shall not constitute a
part of this Amendment for any other purpose or be given any substantive effect.

         C. APPLICABLE LAW. THIS AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE
PARTIES HEREUNDER SHALL BE GOVERNED BY, AND SHALL BE CONSTRUED AND ENFORCED IN
ACCORDANCE WITH, THE INTERNAL LAWS OF THE STATE NEW YORK (INCLUDING WITHOUT
LIMITATION SECTION 5-1401 OF THE GENERAL OBLIGATIONS LAW OF THE STATE OF NEW
YORK), WITHOUT REGARD TO CONFLICTS OF LAWS PRINCIPLES.

         D. COUNTERPARTS; EFFECTIVENESS. This Amendment may be executed in any
number of counterparts and by different parties hereto in separate counterparts,
each of which when so executed and delivered shall be deemed an original, but
all such counterparts together shall constitute but one and the same instrument;
signature pages may be detached from multiple separate counterparts and attached
to a single counterpart so that all signature pages are physically attached to
the same document. This Amendment shall become effective upon the execution of a
counterpart hereof by Company and Requisite Lenders and receipt by Company and
Agent of written or telephonic notification of such execution and authorization
of delivery thereof.

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         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed and delivered by their respective officers thereunto duly
authorized as of the date first written above.

                                           HORSESHOE GAMING HOLDING CORP.

                                           By:
                                                --------------------------------
                                           Name:
                                           Title:

                                           DLJ CAPITAL FUNDING, INC.,
                                           INDIVIDUALLY AND AS SYNDICATION AGENT

                                           By:
                                                --------------------------------
                                           Name:
                                           Title:

                                           CANADIAN IMPERIAL BANK OF COMMERCE,
                                           INDIVIDUALLY AND AS ADMINISTRATIVE
                                           AGENT

                                           By:
                                                --------------------------------
                                           Name:
                                           Title:

                                           WELLS FARGO BANK, NATIONAL
                                           ASSOCIATION, INDIVIDUALLY AND AS
                                           DOCUMENTATION AGENT

                                           By:
                                                --------------------------------
                                           Name:
                                           Title:

                                           -------------------------------------

                                           ------------------------------------,
                                           AS A LENDER

                                           By:
                                                --------------------------------
                                           Name:
                                           Title:

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