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                                                                   Exhibit 10.31



                                    AGREEMENT

        This Agreement (the "Agreement") is entered into this 21 day of April,
1999, by and among Horseshoe Gaming, L.L.C., Horseshoe Gaming, Inc., Horseshoe
Entertainment, L.P., and New Gaming Capital Partnership (Horseshoe Gaming
L.L.C., Horseshoe Entertainment, L.P., Horseshoe Gaming, Inc., New Gaming
Capital Partnership and all of their affiliates and subsidiary companies are
sometime collectively referred to herein as the "Horseshoe Companies"); Jack B.
Binion ("Binion"); The Robin Group, Inc. ("Group") and August Robin ("Duke").

        RECITALS

        WHEREAS, Horseshoe Entertainment, L.P. owns and operates a gaming and
hotel facility and related operations in Bossier City, Louisiana;

        WHEREAS, Robinson Property Group, L.P. owns and operates a gaming and
hotel facility in Tunica, Mississippi (the "Tunica Facility");

        WHEREAS, New Gaming Capital Partnership, Wendell Piper, Cassandra Piper
and Duke, among others, are partners in Horseshoe Entertainment, L.P.;

        WHEREAS, Horseshoe Gaming, L.L.C., the parent company of New Gaming
Capital Partnership, is in the process of pursuing additional gaming
opportunities and is currently a party to an agreement to acquire additional
casinos and hotel facilities in Hammond, Indiana and Joliet, Illinois (the
"Additional Operations");

        WHEREAS, Horseshoe Gaming, L.L.C. is in the process of a debt offering
pursuant to Rule 144A of the Securities Act of 1933, as amended (the "144A Debt
Offering"); and

        WHEREAS, Group asserts an option to purchase a portion of the profits
and/or losses from the Tunica Facility.

        TERMS AND CONDITIONS

        NOW THEREFORE, for good and valuable consideration, the receipt and
sufficiency of which is hereby acknowledged, the parties agree as follows:

1.      Effective Date; Contingencies. All of the obligations of any party
pursuant to this Agreement shall be effective and enforceable only upon the
execution of this Agreement by all of the parties hereto and the execution by
Wendell Piper, Cassandra Piper and Robert Piper of agreements similar in nature
to this Agreement. The date upon which all of the agreements



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contemplated in this paragraph are fully executed shall be the "Effective Date"
of the Agreement. Neither the transactions contemplated by this Agreement nor
any transactions similar in nature involving the Horseshoe Companies and Wendell
Piper, Cassandra Piper And Robert E. Piper Jr. shall be consummated unless both
such transactions are consummated.

2.      Outstanding Loans. Duke acknowledges that as of March 31, 1999, he owes
Horseshoe Companies $4,950,000 (the "Debt") and that he owes Binion
$2,759,539.73. The amount due Binion shall be forgiven in exchange for Duke's
interest or right to acquire any interest in the profits and losses of the
Tunica Facility including any claim to a capital account balance in the Robinson
Property Group L.P. or any claim to retained earnings of the Robinson Property
Group, L.P. The Debt shall be paid to the Horseshoe Companies through the
forgiveness of a portion of the Debt as provided in the paragraphs of this
Agreement containing covenants not to compete, and the sum of $550,000 which
Duke shall pay to Horseshoe Entertainment L.P. on or before April 15, 2003. All
outstanding promissory notes representing the Debt shall be canceled and Duke
shall execute a new promissory note in the amount of $4,950,000 (the
"Replacement Note"). The Replacement Note shall reflect the terms of this
Agreement and interest shall accrue at a rate of 7% per annum only after the
sums become due and payable pursuant to the terms of the Replacement Note. The
K-1 for 1999 for Duke shall incorporate and reflect an adjustment increasing
Duke's income by the sum of $222,775, plus any distribution made during 1999,
plus all other amounts attributable to Duke as income as required by the
Partnership Agreement of Horseshoe Entertainment L.P.

3.      Grant of Option and Consideration for Grant. In accordance with and
subject to the terms and conditions of this Agreement, Duke and Group hereby
grant to each of the Horseshoe Companies an option (the "Option") to purchase
subject to all necessary regulatory approval, all of his or its ownership,
capital, or equity interests including but not limited to partnership interest,
stock or option to acquire any capital or equity interest, in the Tunica
Facility, Robinson Property Group, L.P., Horseshoe Entertainment, L.P. and
Horseshoe Companies (all such interests being the "Interests"). This Option is
being granted to Horseshoe Companies in exchange for the aggregate sum of
$2,000,000 payable to Duke and Group, which $2,000,000 is non refundable if
Horseshoe Companies fails to exercise the Option. Horseshoe Companies shall pay
the Option Price in two installments. The first installment of $1,000,000 shall
be paid on the Effective Date of this Agreement and the second installment of
$1,000,000 shall be paid on or before December 15, 1999.

4.      Exercise Period. The Option shall expire on December 15, 1999. In the
event Horseshoe Entertainment, L.P. decides to exercise the Option, Horseshoe
Entertainment, L.P. shall transmit, prior to the expiration of the Option, to
Duke an indication of Horseshoe Entertainment, L.P.'s intent to exercise the
Option. Upon transmittal of such notice, the Option shall be deemed to have been
exercised without any further action being necessary.

5.      Exercise Price. The exercise price to be paid by Horseshoe
Entertainment, L.P. to Duke and Group shall be the aggregate sum of $6,000,000
and shall be paid in installments in the



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following manner: (i) $2,080,000 to be paid on December 15, 2000, and (ii)
$3,920,000 to be paid on December 15, 2001.

6.      Participation in Sale By Binion. If, within five years of the date of
this Agreement, the Binion Family Interests collectively sells in excess of a
50% interest in Horseshoe Gaming, LLC, for a purchase price consisting of cash,
debt or publicly traded securities or any combination thereof having a value of
in excess of $5,350,000 per 1% interest sold, then Duke shall receive a cash sum
equal to 2 1/4% of the value of the sale in excess of $5,350,000 per 1% interest
sold (such cash sum equal to 2 1/4% being the "Participation Payment"). For the
purposes of this paragraph, the value of the sale shall be equal to (i) the cash
purchase price, plus (ii) 80% of the value of the publicly traded securities as
determined by the last sales price of such securities at the close of the market
upon which such securities are traded, on the date the Binion Family Interests
receives such securities, plus (iii) 80% of the present value of the debt. For
the purposes of this paragraph, the Binion Family Interests shall mean, Binion
or any entities owned or controlled by Binion, or any member of his family or
any trust for the benefit of any member of his family. In the event that Duke is
entitled to the Participation Payment, all sums due from Duke to Horseshoe
Companies shall be due and payable immediately to the extent of the
Participation Payment.

7.      Payment of Release and Waiver. In exchange for the release and waiver by
Duke described in Paragraph 8, Horseshoe Companies shall deliver, upon the
Effective Date of this Agreement, to Duke the title, free of any liens to the
Horseshoe Entertainment L.P. car in his possession, and on December 15, 1999,
the amount of $500,000.

8.      Release and Waiver. Except for Group, Duke hereby represents and
warrants that he does not now have nor has he ever held any ownership interest
in, or position with any other entity of any kind or nature whatsoever, having
any claim against Horseshoe Companies or Binion or any of their or his current
or former agents, employees, partners, officers, servants, directors, attorneys,
affiliates, successors and assigns. Except for the obligation created or
reaffirmed by virtue of this Agreement, Duke and Group hereby release, discharge
and waive any and all claims, causes of action, and demands of any kind or
nature whatsoever that now exist, whether known or unknown, which he may have
against the Horseshoe Companies or Binion or any of their or his current or
former agents, employees, partners, officers, servants, directors, attorneys,
affiliates, successors and assigns. Except for the obligation created or
reaffirmed by virtue of this Agreement, Horseshoe Companies and Binion hereby
release, discharge and waive any and all claims, causes of action, and demands
of any kind or nature whatsoever that now exist, whether known or unknown, which
each may have against Duke or Group or any of his or its current or former
agents, employees, partners, servants, attorneys, successors and assigns.

9.      Consent to Additional Operations, Pledges or Encumbrances. In
consideration for the sum of $325,000 to be due and payable to Duke on December
15, 1999, Duke hereby consents to any pledge now or at anytime in the future by
the Horseshoe Companies of its direct and indirect



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equity interest in Horseshoe Entertainment, L.P. and Robinson Property Group
L.P., or the granting of a security interest, mortgage, pledge, lien and
encumbrance of any kind upon the assets of Horseshoe Entertainment, L.P. and
Robinson Property Group L.P. and any other assets of the Horseshoe Companies and
any entity acquired by any of the Horseshoe Companies. Duke specifically waives
any objection or claim arising as a result of, or in any way related to the
efforts of Binion or the Horseshoe Companies to purchase or finance additional
gaming or related operation including but not limited to gaming and related
operations in Hammond, Indiana or Joliet, Illinois.

10.     Amendment to Partnership Agreement. Duke hereby agrees to execute
amendments to the Limited Partnership Agreement of Horseshoe Entertainment,
L.P., allowing Horseshoe Entertainment L.P. to pledge, and/or encumber its
assets or guarantee the debt of any of the Horseshoe Companies, such amendment
shall include but shall not be limited to the deletion, from the Limited
Partnership Agreement of Horseshoe Entertainment, L.P. of paragraphs 7.1 and 7.2
in their entirety. Duke hereby designates, authorizes and empowers Binion as his
attorney-in-fact to execute on behalf of Duke the amendment to the Limited
Partnership Agreement of Horseshoe Entertainment, L.P. deleting paragraphs 7.1
and 7.2 from the Limited Partnership Agreement of Horseshoe Entertainment, L.P.
and making all such additional amendments to said Limited Partnership Agreement
as are necessary to effect the spirit and intent of this Agreement.

11.     Representations and Warranties of Duke and Group. As a material
inducement to Horseshoe Companies and Binion to enter into this Agreement, Duke
and Group represent and warrant to Horseshoe Companies and Binion that Duke and
Group have good and marketable title to the Interests, and that the Interests
are free and clear of all adverse claims, liens and encumbrances of any kind,
buy-sell agreements, cross-purchase agreements, shareholder agreements or
restrictions or rights of any kind.

12.     Covenant Not To Compete. Upon the exercise by the Horseshoe Companies of
the Option, as consideration for Horseshoe Companies obligations under this
Agreement and for the sum of $3,000,000 to be due and payable on December 15,
2000, and the forgiveness of a portion of the Debt equal to $2,000,000, Duke
agrees that for a period of two (2) years after the Effective Date of this
Agreement (the "Restricted Period"), he shall not, within the Parishes of Caddo,
Bossier, Webster, DeSoto, Red River, and Sabine, and/or within one hundred and
fifty (150) miles of any facility owned by or where Horseshoe Companies or any
of their affiliates or subsidiaries is engaged in business, be employed by,
provide consulting to or in any way assist any other person or entity during the
Restricted Period, (a) directly or indirectly engage in, be employed or provide
any kind of consulting services or assistance to any entity or person engaged in
any activity or business that is substantially similar to or competitive with
that of the Horseshoe Companies or any of their affiliates or subsidiaries; or
(b) directly or indirectly engage in, own any interest in, manage, operate,
join, control, lend money or other assistance to, or participate in or be
connected with, as an officer, director, employee, partner, shareholder,
consultant, manager, agent, or otherwise, any individual, corporation,
partnership, firm, other company, business organization, or entity that is
engaged in the same or substantially similar



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business as that engaged in by the Horseshoe Companies or any affiliates or
subsidiaries. Upon the request of Horseshoe Companies, Duke shall execute a
separate covenant not to compete. Nothing contained herein shall prevent Duke
from participating in gaming operations in the Parishes of Orleans, St. Bernard,
Jefferson, St. John the Baptist, St. James, Washington, St. Tammany, and
Tangipahoa and the City of New Orleans.

13.     Second Covenant Not to Compete. If Horseshoe Companies exercises the
Option, then within 90 days before the expiration of the Restricted Period, Duke
shall have, at his sole discretion, the option, upon the delivery of written
notice to the Horseshoe Companies prior to the expiration of the Restricted
Period, to extend the Restricted Period for an additional two years in
accordance with the terms and conditions described above. In consideration for
Duke exercising his option to extend the Restricted Period, Duke shall receive
$1,325,000 on December 15, 2001 plus the forgiveness of a portion of the Debt
equal to $2,400,000 of the Debt.

14.     Reasonableness of Covenants Not to Compete. Duke acknowledges that the
restrictions, including the Restricted Period and geographical area, specified
above, are fair and reasonable in all respects. Notwithstanding anything to the
contrary, in the event that these restrictions are found to be overly broad or
unreasonable, Duke and the Horseshoe Companies and Binion agree that such
restrictions shall be severable and enforceable on such modified terms as may be
deemed reasonable and enforceable by court of competent jurisdiction.

15.     Finder's Fee. If Horseshoe Companies exercises the Option, then on
December 15, 1999, Horseshoe Entertainment L.P. shall pay to Duke the sum of
$400,000 as a finder's fee in connection with the acquisition and disposition of
the Chalmotte property, the acquisition of the King of the Red, the
renegotiation of the marine services contract and the development of video poker
opportunities.

16.     Signing Bonus. As a signing bonus, upon the Effective Date Horseshoe
Entertainment, L.P. shall pay to Duke $50,000.

17.     Interest Rate. Upon a sum coming due and payable pursuant to the terms
of this agreement, interest shall accrue on the principal balance outstanding
from the date upon which said amount becomes due and payable at a rate of 7% per
annum, until such sum is paid.

18.     Notices. Any notice or other communication required to be given
hereunder shall be in writing and shall be deemed sufficiently given if
delivered personally or sent by registered or certified mail, postage pre-paid,
in which case such notice shall be deemed to have been served five (5) days
after the mailing thereof, to the address below:



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                                       Horseshoe Gaming, L.L.C.
                                       Attn: Jack Binion
                                       4024 Industrial Road
                                       Las Vegas, NV 89103

                                       August Robin
                                       3 Poydras St., Suite 3C
                                       New Orleans, LA 70130

19.     No Assignment. Except as otherwise provided herein, neither this
Agreement nor any interest hereunder shall be assignable except upon the death
of Duke, or for legitimate and reasonable estate planning purposes and upon
obtaining all necessary regulatory approval, if any. All the allegations and
duties of any kind or nature whatsoever of any of the parties hereto shall be
binding upon their respective successors and assigns.

20.     Governing Law. This Agreement and all transactions contemplated hereby
shall be construed, governed and enforced in accordance with the laws of the
State of Louisiana and shall be treated in all respects as a State of Louisiana
contract without regard to laws related to the conflicts of laws.

21.     Confidentiality. Duke, Horseshoe Companies and Binion agree to use their
best efforts to keep confidential all information provided to them under the
terms and conditions of this Agreement and which is not in the public domain. No
party to this Agreement shall make any public announcement of any action
provided for or contemplated by this Agreement unless the form and substance of
the announcement is mutually agreed upon by all parties, which agreement shall
not be unreasonably withheld or delayed. Nothing contained in this paragraph
shall prohibit any public disclosure or disclosure to any regulatory agency of
any kind or nature whatsoever having jurisdiction over any of the parties hereto
as required by law.

22.     Further Assurances. The parties to this Agreement will each use their
respective best efforts to execute and deliver any additional documents and
instruments, and to do all things necessary, proper, or advisable under the
provision of this Agreement and under any applicable law to make effective any
action contemplated by this Agreement. In addition, Duke shall cooperate with
any proceeding, investigation, licensing process or inquiry of any kind
whatsoever undertaken by any government and/or regulatory body involving any of
the Parties to this Agreement. Such cooperation would include, but not be
limited to, providing testimony, answering questions, appearing before,
providing any documentation and responding to any reasonable request of any such
governmental and/or regulatory body. In light of this Agreement, Duke shall
withdraw any pending request made to any regulatory or governmental agency for
approval to increase his ownership interest in any of the Horseshoe Companies.
All reasonable expenses incurred in connection with such cooperation shall be
the responsibility of the Horseshoe Companies. Duke shall be entitled to receive
copies of all reports for the Horseshoe Companies filed with the Securities and
Exchange Commission and copies of all quarterly and



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annual financial statements for Horseshoe Gaming, LLC and Horseshoe
Entertainment, L.P. Within thirty (30) days of acceptance of a bona fide offer
to purchase in excess of 50% of the ownership of Horseshoe Gaming, LLC,
Horseshoe Gaming, LLC shall provide Duke with a copy of such bona fide offer,
except as prohibited by any confidentiality agreement imposed or required by the
offeree.

23.     No Waiver. No waiver or delay by either party in exercising its right,
power or privilege under this Agreement shall operate as a waiver thereof, nor
shall any single or partial exercise thereof preclude any other or further
exercise of any right, power or privilege hereunder.

24.     Modification. This Agreement may not be amended, modified or altered
except by written instrument duly executed by all of the parties hereto.

25.     Arbitration. All disputes between the parties under this Agreement shall
be submitted to binding arbitration in Louisiana, in accordance with the rules
of the American Arbitration Association (the "Association"). In the event either
party seeks arbitration, the party seeking arbitration shall provide written
notice to the other parties immediately upon seeking such arbitration. The
procedure for arbitration shall be in accordance with the Association's then
existing rules, except that each party may select one arbitrator, and the two
selected arbitrators shall choose a third arbitrator. If either party fails to
select an arbitrator within forty-five (45) days after arbitration is sought, or
the two arbitrators fail to select a third arbitrator within thirty days (30)
after arbitration is sought, the Association shall make the selection. The award
rendered by the arbitrators shall be final and binding on the parties and may be
entered in any court having jurisdiction thereof.

26.     Severability. If a Court of competent jurisdiction makes a final
determination that any provision of this Agreement (or any portion thereof) is
invalid, illegal, or unenforceable for any reason whatsoever and all rights to
appeal determination have been exhausted, or the period of time during which the
appeal or determination may be perfected has expired, the validity, legality and
enforceability of the remaining provisions of this Agreement shall not in any
way be affected or impaired.

27.     Entire Agreement. This Agreement contains the entire Agreement of the
parties thereto with respect to the subject matter hereof and shall be deemed to
supercede all prior or contemporaneous agreements, representations, and
understandings, whether written or oral concerning the subject matter of this
Agreement. This Agreement states any and all payments, debts and obligations of
the Horseshoe Companies owed to Duke and there are no other remaining
obligations. Except as otherwise provided herein, all terms and provisions of
the Partnership Agreement of Horseshoe Entertainment L.P. in effect as of the
execution hereof, shall remain in full force and effect.


                            [Signatures on next page]



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        IN WITNESS WHEREOF, each of the parties has caused this Agreement to be
executed by its duly authorized officer as of the day and year first above
written.

HORSESHOE GAMING, L.L.C.                HORSESHOE ENTERTAINMENT, L.P.

By: Horseshoe Gaming, Inc.,             By: New Gaming Capital Partnership, LP,
    its Manager                             its General Partner

By: S/S                                 By: Horseshoe GP, Inc., its General
--------------------------------            Partner

                                        By: S/S
                                            ------------------------------------
                                            Jack B. Binion
                                            President

HORSESHOE GAMING, INC.                  NEW GAMING CAPITAL PARTNERSHIP

                                        By: Horseshoe GP, Inc., its General
                                            Partner

By: S/S                                 By: S/S
    ----------------------------            ------------------------------------
    Jack B. Binion                          Jack B. Binion
    Chief Executive Officer and             President
    Chairman of the Board


S/S                                     S/S
--------------------------------        ----------------------------------------
Jack B.Binion                           August Robin


THE ROBIN GROUP, INC.


By: S/S
    ----------------------------
    August Robin, its President





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        The undersigned being all of the partners of Horseshoe Entertainment,
L.P. hereby acknowledge and consent that to the extent the terms of this
Agreement are in any way inconsistent with the Horseshoe Entertainment, L.P.
Partnership Agreement as currently in effect, this Agreement shall constitute an
amendment to the Horseshoe Entertainment, L.P.
Partnership Agreement.

                                        NEW GAMING CAPITAL PARTNERSHIP

                                        By: Horseshoe GP, Inc., its General
                                            Partner

                                        By: S/S  
                                        ----------------------------------------
                                            Jack B. Binion
                                            President


                                        S/S
                                        ----------------------------------------
                                        Wendell Piper


                                        S/S                                 
                                        ----------------------------------------
                                        Cassandra Piper


                                        S/S                                 
                                        ----------------------------------------
                                        August Robin







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