Document:

<PAGE>   1

                                                                   EXHIBIT 10.51

         THIS NOTE HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
         AMENDED, OR THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE SOLD OR
         OTHERWISE DISPOSED OF EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION
         STATEMENT UNDER SUCH ACT AND APPLICABLE STATE SECURITIES LAWS OR
         PURSUANT TO AN EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF SUCH ACT
         AND SUCH LAWS.

                            HORSESHOE GAMING, L.L.C.

                       PROMISSORY NOTE DUE JANUARY 2, 2004

$422,295.00                                                    November 30, 1999
                                                              New York, New York

                  FOR VALUE RECEIVED, HORSESHOE GAMING, L.L.C., a Delaware
limited liability company (the "Company"), subject to Section 3 hereof, promises
to pay, on or before January 4, 2004 (the "Maturity Date"), to the order of
Nobutaka Motaguchi (the "Holder"), at the Company's offices at 4024 South
Industrial Road, Las Vegas, Nevada 89013, or in accordance with such other
instructions as the Holder (or any other entity entitled to payment hereunder)
may hereafter designate from time to time in writing, the principal sum of FOUR
HUNDRED TWENTY-TWO THOUSAND TWO HUNDRED NINTY-FIVE DOLLARS ($422,295.00) in
lawful money of the United States, with interest on the unpaid principal amount
from the date of this Promissory Note (together with all supplements, amendments
or modifications hereto and replacements or renewals hereof, this "Note") to and
including the date of payment, calculated as provided below.

         I. Purchase Agreement. This Note is issued pursuant to the terms and
conditions of a Purchase Agreement dated as of the date hereof (the "Purchase
Agreement"), between the Company and the Holder, as consideration for the
repurchase by the Company of the Holder's ownership interest in the Company (the
"Ownership Interest"), made in connection with the proposed acquisition by the
Company of Empress Casino Hammond Corporation, an Indiana corporation and
Empress Casino Joliet Corporation, an Illinois corporation, both of which are
subsidiaries of Empress Entertainment, Inc., a Delaware corporation.

         II. Interest. The Company promises to pay simple interest on the
outstanding principal amount of this Note at a rate equal to 10% per annum (the
"Interest Rate") from November 30, 1999 until the maturity date of this Note or
the earlier acceleration of this Note pursuant to Section 6 of this Note, when
all accrued interest shall be immediately due and payable. Interest shall be

<PAGE>   2

computed on the basis of a 360-day year of twelve 30-day months. Subject to the
terms of (i) the Credit Agreement dated as of June 30, 1999 (the "Credit
Agreement"), among Horseshoe Gaming Holding Corp. ("HGHC"), as Borrower, the
lenders listed therein, DLJ Capital Funding, Inc., as Syndication Agent,
Canadian Imperial Bank of Commerce, as Administrative Agent and Wells Fargo
Bank, National Association, as Documentation Agent; (ii) the Indenture dated as
of June 15, 1997 (the "9_% Indenture"), as the same shall have been amended to
date, for the Company's 9_% Senior Subordinated Notes due 2007, among the
Company, Robinson Property Group, Limited Partnership, New Gaming Capital
Partnership, Horseshoe Entertainment, Horseshoe GP, Inc., Bossier City Land
Corporation and Texas Trustee; (iii) the Indenture dated as of May 11, 1999 (the
"8_% Indenture"), for HGHC's 8_% Senior Subordinated Notes due 2009 (the "Senior
Subordinated Notes"), by and between HGHC and U.S. Trust Company, National
Association, as trustee; (iv) the Indenture dated as of June 18, 1998 (the
"Empress Indenture"), for Empress Entertainment, Inc.'s 8_% Senior Subordinated
Notes due 2006, among Empress Entertainment, Inc., Empress River Casino Finance
Corporation, Empress Joliet, Empress Casino Hammond Corporation, Hammond
Residential and U.S. Bank Trust National Association (the documents described in
(i), (ii), (iii) and (iv) above being referred to as the "Financing Documents");
and (v) the various agreements entered into prior to the date hereof to
repurchase the interests of various former employees and members of the Company
which, among other things, do not permit the Company to make principal payments
on the repurchase of the Ownership Interest prior to the repayment in full of
amounts due under the Repurchase Agreements), the Company shall pay accrued
interest semiannually on June 30 and December 31 of each year, beginning on June
30, 2000. To the extent that the Company is not permitted to make interest
payments under the Financing Documents or the Repurchase Agreements, interest
shall accrue and be compounded at the Interest Rate until the earlier of the
date such interest is paid, the maturity date of this Note or the earlier
acceleration of this Note pursuant to Section 6 of this Note.

         III. Payment of Principal. If the Company is not permitted under the
terms of the Financing Documents or the Repurchase Agreements to pay the
principal of this Note in full on the Maturity Date, then the payment of the
portion of the principal on this Note which may not be paid may be delayed until
such date as such principal payments are permitted under the terms of the
Financing Documents and the Repurchase Agreements. However, the portion of this
Note which may be paid on the Maturity Date shall be paid on the Maturity Date
and the balance shall be paid promptly thereafter as permitted by the Financing
Documents and the Repurchase Agreements

         IV. Optional Prepayment. The Company, at its option, may prepay all or
any portion of this Note, at any time, by paying an amount equal to the
outstanding principal amount of this Note, or a portion thereof, together with
interest accrued and unpaid thereon to the date of prepayment and any other
amounts due under this Note, without penalty or premium.

         V. Application of Payments. All mandatory payments under Section 3 of
this Note and all optional prepayments under Section 4 of this Note shall
include payment of accrued interest on the principal amount so paid or prepaid
and all other amounts due under this Note and shall be applied, first to all
reasonable costs, fees, and expenses incurred by the Holder in the exercise of
the Holder's rights hereunder, second to payment of other accrued interest, and
thereafter to principal.

                                       2

<PAGE>   3

         VI. Acceleration. This Note shall accelerate and the outstanding
principal of and all accrued interest on this Note shall automatically become
immediately due and payable, without presentment, demand, protest or notice of
any kind, all of which are expressly waived, if a Change in Control (as defined
in the 8_% Indenture) or an Event of Default (as defined in the 8_% Indenture)
occurs, which Change of Control or Event of Default results in the acceleration
and repayment of all of the Senior Subordinated Notes.

         VII. Replacement Note. Upon receipt of evidence reasonably satisfactory
to the Company of the loss, theft, destruction or mutilation of this Note and of
a letter of indemnity reasonably satisfactory to the Company from the Holder and
upon reimbursement to the Company of all reasonable expenses incident thereto,
and upon surrender or cancellation of this Note, if mutilated, the Company will
make and deliver a new Note of like tenor in lieu of such lost, stolen,
destroyed or mutilated Note.

         VIII. Pari Passu Payments. All payments on this Note will be made pari
passu with payment to holders of similar notes issued on the date hereof in
respect of the repurchase of membership interests in the Company.

         IX. Amendment. Any amendment, supplement or modification of or to any
provision of this Note shall be effective only with the express written consent
of the Company and the Holder.

         X. Covenants Bind Successors and Assigns. All the covenants,
stipulations, promises and agreements in this Note contained by or on behalf of
the Company or the Holder shall bind its successors and assigns, whether so
expressed or not.

         XI. Governing Law. This Note and the rights and obligations of the
Company and the Holder hereunder shall be governed by, and shall be construed
and enforced in accordance with, the internal laws of the State of New York
(including Section 5-1401 of the General Obligations Law of the State of New
York), without regard to conflicts of laws principles.

         XII. Variation in Pronouns. All pronouns and any variations thereof
refer to the masculine, feminine or neuter, singular or plural, as the context
may require.

                                       3

<PAGE>   4

         XIII. Headings. The headings in this Note are for convenience of
reference only and shall not limit or otherwise affect the meaning hereof.

                                     HORSESHOE GAMING, L.L.C.

                                     By: Horseshoe Gaming Holding Corp., Manager

                                     By:
                                         ---------------------------------------
                                         Kirk Saylor, Chief Financial Officer

                                       4
<PAGE>   5

                               PURCHASE AGREEMENT

         PURCHASE AGREEMENT dated and effective as of the 30th day of November,
1999 (this "Agreement"), between Horseshoe Gaming, L.L.C., a Delaware limited
liability company ("Horseshoe"), and Nobutaka Mutaguchi ("Seller").

                                    RECITALS:

Horseshoe is a casino owner/operator with its principal office in Las Vegas,
Nevada.

Seller is the current owner of a .056306% interest in Horseshoe (the "Ownership
Interest").

Horseshoe is the party to an agreement pursuant to which it may acquire (the
"Acquisition") Empress Casino Hammond Corporation, an Indiana corporation and
Empress Casino Joliet Corporation, an Illinois corporation, both of which are
subsidiaries of Empress Entertainment, Inc., a Delaware corporation.

In connection with the Acquisition, Seller desires to sell and Horseshoe
believes it is in its best interest to acquire from Seller the Ownership
Interest.

Horseshoe and Seller have agreed that the fair market value of the Ownership
Interest is FOUR HUNDRED TWENTY-TWO-THOUSAND TWO HUNDRED NINETY-FIVE DOLLARS
($422,295.00).

         NOW, THEREFORE, in consideration of the premises and each act performed
by either party hereto, the parties agree as follows:

Subject to the terms and conditions set forth herein, Seller agrees to sell,
transfer, convey, assign and deliver to Horseshoe, and Horseshoe agrees to
purchase, acquire and accept from Seller, the Ownership Interest, at the price
of $422,295.00 (the "Purchase Price"), payable by a promissory note of
Horseshoe, which is attached hereto (the "Promissory Note").

Seller hereby unconditionally releases and discharges Horseshoe from any and all
claims, known or unknown, directly or indirectly related to or in any way
connected with Seller's ownership of Horseshoe and any and all agreements in any
way connected with or related thereto other than this Agreement and the
Promissory Note. Seller acknowledges and agrees that following the consummation
of the transaction contemplated by this Agreement, Seller shall have no equity
ownership or any other interest in Horseshoe or any of its affiliates or
subsidiaries nor will Seller have rights of any kind to acquire an ownership
interest in Horseshoe or any of its affiliates or subsidiaries; the only rights
Seller shall have will be to enforce the terms of the Promissory Note.

                                       5
<PAGE>   6

Seller represents and warrants that Seller is the lawful record and beneficial
owner of the Ownership Interest, free and clear of any liens, claims,
encumbrances, marital property rights, security agreements, equities, options,
charges or restrictions of any kind.

This Agreement contains the entire agreement of the parties with respect to the
subject matter hereof and may be amended only by a writing signed by each party
hereto.

This Agreement shall be binding upon and inure to the benefit of the parties
hereto and their respective successors and assigns.

This Agreement and the rights and obligations of the Company and the Seller
hereunder shall be governed by, and shall be construed and enforced in
accordance with, the internal laws of the State of New York (including Section
5-1401 of the General Obligations Law of the State of New York), without regard
to conflicts of laws principles.

This Agreement may be executed in one or more counterparts, each of which shall
be deemed an original and all of which together shall constitute one and the
same agreement.

Horseshoe, on the one hand, and Seller, on the other hand, shall pay their
respective fees and expenses incurred by them in connection with the transaction
contemplated herein.

Any term or provision of this Agreement that is invalid or unenforceable in any
jurisdiction shall, as to such jurisdiction, be ineffective to the extent of
such invalidity or unenforceability without rendering invalid or unenforceable
the remaining terms and provisions of this Agreement or affecting the validity
or enforceability of any of the terms and provisions of this Agreement in any
other jurisdiction.

                                       6
<PAGE>   7

         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date first set forth above.

                                     HORSESHOE GAMING, L.L.C.
                                     By: Horseshoe Gaming Holding Corp., Manager

                                     By:
                                         ---------------------------------------
                                         Kirk Saylor, Chief Financial Officer

                                     Seller:

                                     By:
                                         ---------------------------------------

                                       7<PAGE>   1

                                                                   EXHIBIT 10.52

THIS NOTE HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED,
OR THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE SOLD OR OTHERWISE DISPOSED OF
EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER SUCH ACT AND
APPLICABLE STATE SECURITIES LAWS OR PURSUANT TO AN EXEMPTION FROM THE
REGISTRATION REQUIREMENTS OF SUCH ACT AND SUCH LAWS.

                            HORSESHOE GAMING, L.L.C.

                       PROMISSORY NOTE DUE JANUARY 2, 2004

$3,040,515.00                                                  November 30, 1999
                                                              New York, New York

         FOR VALUE RECEIVED, HORSESHOE GAMING, L.L.C., a Delaware limited
liability company (the "Company"), subject to Section 3 hereof, promises to pay,
on or before January 4, 2004 (the "Maturity Date"), to the order of Post
Balanced Fund (the "Holder"), at the Company's offices at 4024 South Industrial
Road, Las Vegas, Nevada 89013, or in accordance with such other instructions as
the Holder (or any other entity entitled to payment hereunder) may hereafter
designate from time to time in writing, the principal sum of THREE MILLION FORTY
THOUSAND FIVE HUNDRED FIFTEEN DOLLARS ($3,040,515.00) in lawful money of the
United States, with interest on the unpaid principal amount from the date of
this Promissory Note (together with all supplements, amendments or modifications
hereto and replacements or renewals hereof, this "Note") to and including the
date of payment, calculated as provided below.

         1. Purchase Agreement. This Note is issued pursuant to the terms and
conditions of a Purchase Agreement dated as of the date hereof (the "Purchase
Agreement"), between the Company and the Holder, as consideration for the
repurchase by the Company of the Holder's ownership interest in the Company (the
"Ownership Interest"), made in connection with the proposed acquisition by the
Company of Empress Casino Hammond Corporation, an Indiana corporation and

<PAGE>   2

Empress Casino Joliet Corporation, an Illinois corporation, both of which are
subsidiaries of Empress Entertainment, Inc., a Delaware corporation.

         2. Interest. The Company promises to pay simple interest on the
outstanding principal amount of this Note at a rate equal to 10% per annum (the
"Interest Rate") from November 30, 1999 until the maturity date of this Note or
the earlier acceleration of this Note pursuant to Section 6 of this Note, when
all accrued interest shall be immediately due and payable. Interest shall be
computed on the basis of a 360-day year of twelve 30-day months. Subject to the
terms of (i) the Credit Agreement dated as of June 30, 1999 (the "Credit
Agreement"), among Horseshoe Gaming Holding Corp. ("HGHC"), as Borrower, the
lenders listed therein, DLJ Capital Funding, Inc., as Syndication Agent,
Canadian Imperial Bank of Commerce, as Administrative Agent and Wells Fargo
Bank, National Association, as Documentation Agent; (ii) the Indenture dated as
of June 15, 1997 (the "9_% Indenture"), as the same shall have been amended to
date, for the Company's 9_% Senior Subordinated Notes due 2007, among the
Company, Robinson Property Group, Limited Partnership, New Gaming Capital
Partnership, Horseshoe Entertainment, Horseshoe GP, Inc., Bossier City Land
Corporation and Texas Trustee; (iii) the Indenture dated as of May 11, 1999 (the
"8_% Indenture"), for HGHC's 8_% Senior Subordinated Notes due 2009 (the "Senior
Subordinated Notes"), by and between HGHC and U.S. Trust Company, National
Association, as trustee; (iv) the Indenture dated as of June 18, 1998 (the
"Empress Indenture"), for Empress Entertainment, Inc.'s 8_% Senior Subordinated
Notes due 2006, among Empress Entertainment, Inc., Empress River Casino Finance
Corporation, Empress Joliet, Empress Casino Hammond Corporation, Hammond
Residential and U.S. Bank Trust National Association (the documents described in
(i), (ii), (iii) and (iv) above being referred to as the "Financing Documents");
and (v) the various agreements entered into prior to the date hereof to
repurchase the interests of various former employees and members of the Company
which, among other things, do not permit the Company to make principal payments
on the repurchase of the Ownership Interest prior to the repayment in full of
amounts due under the Repurchase Agreements), the Company shall pay accrued
interest semiannually on June 30 and December 31 of each year, beginning on June
30, 2000. To the extent that the Company is not permitted to make interest
payments under the Financing Documents or the Repurchase Agreements, interest
shall accrue and be compounded at the Interest Rate until the earlier of the
date such interest is paid, the maturity date of this Note or the earlier
acceleration of this Note pursuant to Section 6 of this Note.

                                       2
<PAGE>   3

         3. Payment of Principal. If the Company is not permitted under the
terms of the Financing Documents or the Repurchase Agreements to pay the
principal of this Note in full on the Maturity Date, then the payment of the
portion of the principal on this Note which may not be paid may be delayed until
such date as such principal payments are permitted under the terms of the
Financing Documents and the Repurchase Agreements. However, the portion of this
Note which may be paid on the Maturity Date shall be paid on the Maturity Date
and the balance shall be paid promptly thereafter as permitted by the Financing
Documents and the Repurchase Agreements

         4. Optional Prepayment. The Company, at its option, may prepay all or
any portion of this Note, at any time, by paying an amount equal to the
outstanding principal amount of this Note, or a portion thereof, together with
interest accrued and unpaid thereon to the date of prepayment and any other
amounts due under this Note, without penalty or premium.

         5. Application of Payments. All mandatory payments under Section 3 of
this Note and all optional prepayments under Section 4 of this Note shall
include payment of accrued interest on the principal amount so paid or prepaid
and all other amounts due under this Note and shall be applied, first to all
reasonable costs, fees, and expenses incurred by the Holder in the exercise of
the Holder's rights hereunder, second to payment of other accrued interest, and
thereafter to principal.

         6. Acceleration. This Note shall accelerate and the outstanding
principal of and all accrued interest on this Note shall automatically become
immediately due and payable, without presentment, demand, protest or notice of
any kind, all of which are expressly waived, if a Change in Control (as defined
in the 8_% Indenture) or an Event of Default (as defined in the 8_% Indenture)
occurs, which Change of Control or Event of Default results in the acceleration
and repayment of all of the Senior Subordinated Notes.

         7. Replacement Note. Upon receipt of evidence reasonably satisfactory
to the Company of the loss, theft, destruction or mutilation of this Note and of
a letter of indemnity reasonably satisfactory to the Company from the Holder and
upon reimbursement to the Company of all reasonable expenses incident thereto,
and upon surrender or cancellation of this Note, if mutilated, the Company will
make and deliver a new Note of like tenor in lieu of such lost, stolen,
destroyed or mutilated Note.

                                       3
<PAGE>   4

         8. Pari Passu Payments. All payments on this Note will be made pari
passu with payment to holders of similar notes issued on the date hereof in
respect of the repurchase of membership interests in the Company.

         9. Amendment. Any amendment, supplement or modification of or to any
provision of this Note shall be effective only with the express written consent
of the Company and the Holder.

         10. Covenants Bind Successors and Assigns. All the covenants,
stipulations, promises and agreements in this Note contained by or on behalf of
the Company or the Holder shall bind its successors and assigns, whether so
expressed or not.

         11. Governing Law. This Note and the rights and obligations of the
Company and the Holder hereunder shall be governed by, and shall be construed
and enforced in accordance with, the internal laws of the State of New York
(including Section 5-1401 of the General Obligations Law of the State of New
York), without regard to conflicts of laws principles.

         12. Variation in Pronouns. All pronouns and any variations thereof
refer to the masculine, feminine or neuter, singular or plural, as the context
may require.

         13. Headings. The headings in this Note are for convenience of
reference only and shall not limit or otherwise affect the meaning hereof

                                    HORSESHOE GAMING, L.L.C.
                                    By:  Horseshoe Gaming Holding Corp., Manager

                                    By:
                                         ---------------------------------------
                                         Kirk Saylor, Chief Financial Officer

                                       4
<PAGE>   5

                               PURCHASE AGREEMENT

         PURCHASE AGREEMENT dated and effective as of the 30th day of November,
1999 (this "Agreement"), between Horseshoe Gaming, L.L.C., a Delaware limited
liability company ("Horseshoe"), and Post Balanced Fund ("Seller").

                                    RECITALS:

         Horseshoe is a casino owner/operator with its principal office in Las
Vegas, Nevada.

         Seller is the current owner of a .405402% interest in Horseshoe (the
"Ownership Interest").

         Horseshoe is the party to an agreement pursuant to which it may acquire
(the "Acquisition") Empress Casino Hammond Corporation, an Indiana corporation
and Empress Casino Joliet Corporation, an Illinois corporation, both of which
are subsidiaries of Empress Entertainment, Inc., a Delaware corporation.

         In connection with the Acquisition, Seller desires to sell and
Horseshoe believes it is in its best interest to acquire from Seller the
Ownership Interest.

         Horseshoe and Seller have agreed that the fair market value of the
Ownership Interest is THREE MILLION FORTY THOUSAND FIVE HUNDRED FIFTEEN DOLLARS
($3,040,515.00).

         NOW, THEREFORE, in consideration of the premises and each act performed
by either party hereto, the parties agree as follows:

         1. Subject to the terms and conditions set forth herein, Seller agrees
to sell, transfer, convey, assign and deliver to Horseshoe, and Horseshoe agrees
to purchase, acquire and accept from Seller, the Ownership Interest, at the
price of $3,040,515.00 (the "Purchase Price"), payable by a promissory note of
Horseshoe, which is attached hereto (the "Promissory Note").

         2. Seller hereby unconditionally releases and discharges Horseshoe from
any and all claims, known or unknown, directly or indirectly related to or in
any way connected with Seller's ownership of Horseshoe and any and all
agreements in any way connected with or related thereto other than this
Agreement and the Promissory Note. Seller acknowledges and agrees that following
the consummation of the transaction contemplated by this Agreement, Seller shall
have no equity ownership or any other interest in Horseshoe or any of its
affiliates or subsidiaries nor will Seller have rights of any kind to acquire an
ownership interest in Horseshoe or any of its affiliates or subsidiaries; the
only rights Seller shall have will be to enforce the terms of the Promissory
Note.

                                       5
<PAGE>   6

         3. Seller represents and warrants that Seller is the lawful record and
beneficial owner of the Ownership Interest, free and clear of any liens, claims,
encumbrances, marital property rights, security agreements, equities, options,
charges or restrictions of any kind.

         4. This Agreement contains the entire agreement of the parties with
respect to the subject matter hereof and may be amended only by a writing signed
by each party hereto.

         5. This Agreement shall be binding upon and inure to the benefit of the
parties hereto and their respective successors and assigns.

         6. This Agreement and the rights and obligations of the Company and the
Seller hereunder shall be governed by, and shall be construed and enforced in
accordance with, the internal laws of the State of New York (including Section
5-1401 of the General Obligations Law of the State of New York), without regard
to conflicts of laws principles.

         7. This Agreement may be executed in one or more counterparts, each of
which shall be deemed an original and all of which together shall constitute one
and the same agreement.

         8. Horseshoe, on the one hand, and Seller, on the other hand, shall pay
their respective fees and expenses incurred by them in connection with the
transaction contemplated herein.

         9. Any term or provision of this Agreement that is invalid or
unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective
to the extent of such invalidity or unenforceability without rendering invalid
or unenforceable the remaining terms and provisions of this Agreement or
affecting the validity or enforceability of any of the terms and provisions of
this Agreement in any other jurisdiction.

                                       6
<PAGE>   7

         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date first set forth above.

                                        HORSESHOE GAMING, L.L.C.
                                        By: Horseshoe Gaming Holding Corp.,
                                            Manager

                                        By:
                                            ------------------------------------
                                            Kirk Saylor, Chief Financial Officer

                                        Seller:

                                        By:
                                            ------------------------------------

                                       7

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