Document:

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                                                                    EXHIBIT 4.57

                         HORSESHOE GAMING HOLDING CORP.

                                SECOND AMENDMENT

                               TO CREDIT AGREEMENT

This SECOND AMENDMENT TO CREDIT AGREEMENT (this "AMENDMENT") is dated as of
November 30, 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 (as amended by the First
Amendment described below, the "CREDIT AGREEMENT"), by and among Company,
Lender, Syndication Agent and Administrative Agent, as amended by that certain
First Amendment to Credit Agreement dated as of November 18, 1999. 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 negative covenant in the Credit Agreement relating to Indebtedness;

         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 AMENDMENT TO SECTION 7: COMPANY'S NEGATIVE COVENANTS

         Subsection 7.1(vi) of the Credit Agreement is hereby amended to read in
its entirety as follows:

         "(vi) After the Signing Date but prior to the earlier of the Empress
Joliet Acquisition Date and the date on which the Tranche B Term Loans must be
paid in full pursuant to subsection 2.4A, Company and its Subsidiaries may
become liable for up to $35,000,000 on terms acceptable to Agents in
Indebtedness relating to the repurchase of Company's capital stock from its
shareholders and membership interests in Horseshoe from

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Horseshoe's members (including no more than $3,000,000 to the Majority
Shareholders), and Company and its Subsidiaries may remain liable for such
Indebtedness;"

         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.

         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.

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         (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.

                  [Remainder of page intentionally left blank]

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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:

                                       4<PAGE>   1

                                                                    EXHIBIT 4.58

                         HORSESHOE GAMING HOLDING CORP.

                                 THIRD AMENDMENT

                               TO CREDIT AGREEMENT

This THIRD AMENDMENT TO CREDIT AGREEMENT (this "AMENDMENT") is dated as of
January 20, 2000 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 (as amended by the First
Amendment and the Second Amendment described below, the "CREDIT AGREEMENT"), by
and among Company, Lender, Syndication Agent and Administrative Agent, as
amended by that certain First Amendment to Credit Agreement dated as of November
18, 1999 and that certain Second Amendment to Credit Agreement dated as of
November 30, 1999. 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 "Ships";

         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 "Ships" therefrom in their entirety and substituting the
following therefor:

         A. "SHIPS" means, collectively, King of the Red (U.S. Coast Guard
Official Number D1061968), Empress (U.S. Coast Guard Official Number 984286),
Empress II (U.S. Coast Guard Official Number 998517), Empress III (U.S. Coast
Guard Official Number 1035754) and the barge located at the Horseshoe Casino and
Hotel, Tunica, all together with

<PAGE>   2

any and all present and future engines, boilers, machinery, components, masts,
boats, anchors, cables, chains, rigging, tackle, apparel, furniture, capstans,
outfit, tools, pumps, gear, furnishings, appliances, fittings, spare and
replacement parts, and any and all appurtenances thereto or belonging to such
ship, whether now or hereafter acquired, and whether on board or not on board,
together with any and all present and future additions, improvements and
replacements therefore, made in or to such ship, or any part or parts thereof;
and all accounts, earned hire, charter payments, freight, earnings, revenues,
income and profits therefrom and additionally all log books, manuals, trip
records, maintenance records, inspection records, seaworthiness certificates and
other historical records or information relating to such ship.

         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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<PAGE>   3

         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.

                  [Remainder of page intentionally left blank]

                                       3
<PAGE>   4

         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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