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                                                                   EXHIBIT 10.31
 
                         MANAGEMENT AND ADMINISTRATIVE
                              SERVICES AGREEMENT
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     THIS MANAGEMENT AND ADMINISTRATIVE SERVICES AGREEMENT (the "AGREEMENT") is
entered into as of the 1st day of October, 1998, by and between Hollywood
Casino Corporation, a Delaware  corporation ("HCC"), and Greate Bay Casino
Corporation, a Delaware corporation ("GBCC").

                                   RECITALS

   A. HCC owned approximately 80% of GBCC until the spin-off by HCC of its GBCC
      stock ownership to the HCC stockholders on December 31, 1996;

   B. As of the date hereof, (i) HCC is owned approximately 53% by Jack E.
      Pratt, Edward T. Pratt, Jr., William D. Pratt and Edward T. Pratt III and
      certain family trusts and partnerships (collectively, the "PRATT FAMILY")
      and (ii) GBCC is owned approximately 36% by the Pratt Family;

   C. HCC previously provided to New Jersey Management, Inc., a New Jersey
      corporation ("NJMI") which is an indirect 100% owned subsidiary of GBCC,
      the services of personnel of HCC and its subsidiaries at cost pursuant to
      that certain Services Agreement dated as of January 1, 1994 (the "1/1/94
      HCC/NJMI SERVICES AGREEMENT"), between HCC and NJMI, in order to enable
      NJMI to perform its obligations and duties under that certain Management
      Services Agreement dated as of August 19, 1987 (as amended, the "SANDS
      MANAGEMENT CONTRACT"), between NJMI and Greate Bay Hotel and Casino, Inc.,
      a New Jersey corporation ("GBH&C") which is an indirectly owned subsidiary
      of GBCC and owns the Sands Hotel and Casino in Atlantic City, New Jersey;

   D. On January 5, 1998, GBH&C et al filed a petition for bankruptcy (the
      "SANDS BANKRUPTCY") under Chapter 11 of the United States Code in the
      United States Bankruptcy Court for the District of New Jersey, Camden
      Vicinage (the "BANKRUPTCY COURT");

   E. As a result of the grant by the Bankruptcy Court in the Sands Bankruptcy
      of final approval of the motion by GBH&C to reject the Sands Management
      Contract on September 28, 1998, the arrangements contemplated by the Sands
      Management Contract and related 1/1/94 HCC/NJMI Services Agreement (the
      "PRIOR HCC/GBCC SERVICES ARRANGEMENT") are no longer in effect; and

   F. GBCC now desires to enter into a new services arrangement with HCC
      replacing the Prior HCC/GBCC Services Arrangement pursuant to which HCC
      will provide to GBCC and certain of its subsidiaries the services of
      personnel of HCC and its subsidiaries for the consideration and upon the
      other terms and conditions set forth below.

                                  AGREEMENTS

   NOW, THEREFORE, in consideration of the mutual covenants of the parties
contained herein and other good and valuable consideration, the receipt and
sufficiency of which is hereby acknowledged, the parties hereto agree as
follows:
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   1.  DEFINITIONS.  As used herein, the following terms shall have the meanings
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       herein specified:

       "ACSC" means Advanced Casino Systems Corporation, a Delaware corporation.

       "ACSC SERVICES" shall mean the services provided by HCC to ACSC
       hereunder, including, without limitation, in-house legal services
       (including regulatory compliance), accounting services, state tax return
       preparation, insurance procurement and risk management and services
       relating to the participation by ACSC employees in the retirement savings
       plan of HCC.

       "GBCC SERVICES" shall mean the services provided by HCC to GBCC
       hereunder, including, without limitation, executive management functions
       (including the formulation of corporate policy and strategic planning),
       in-house legal services (including regulatory compliance), financial
       reporting services (including internal management reports, SEC and
       regulatory compliance reporting and coordination of annual independent
       audits), budgeting, planning and forecasting, cash management and
       treasury functions, accounting services (including the maintenance of
       books and records and the processing of transactions), federal and state
       tax planning (including tax return preparation), insurance procurement
       and risk management, investor and public relations (including press
       releases, quarterly earning reports, annual stockholder meetings and
       related proxy statements) and services relating to the participation by
       GBCC employees in the retirement savings plan of HCC.

       "GBCC SUBSIDIARIES" mean the subsidiaries of GBCC above the GB Holdings,
       Inc. level.

       "GAMING LAWS" shall mean (i) the New Jersey Casino Control Act and any
       successor statute and any and all rules, regulations, policies, orders
       and resolutions promulgated thereunder, (ii) the Mississippi Gaming
       Control Act and any successor statute and any and all rules, regulations,
       policies, orders and resolutions promulgated thereunder, (iii) the
       Illinois Riverboat Gambling Act and any successor statute and any and all
       rules, regulations, policies, orders and resolutions promulgated
       thereunder, (iv) the Louisiana Riverboat Economic Development and Gaming
       Control Act and any successor statute and any and all rules, regulations,
       policies, orders and resolutions promulgated thereunder, (v) the Indiana
       Riverboat Gambling Act and any successor statute and any and all rules,
       regulations, policies, orders and resolutions promulgated thereunder and
       (vi) any and all other gaming statutes, rules, regulations, policies,
       orders and resolutions, to the extent that such gaming laws apply to HCC
       and/or GBCC.

       "GAMING REGULATORY AUTHORITIES" shall mean (i) the New Jersey Casino
       Control Commission, (ii) the Mississippi Gaming Commission, (iii) the
       Illinois Gaming Board, (iv) the Louisiana Riverboat Gaming Commission,
       (v) the Indiana Gaming Commission and (vi) any other gaming regulatory
       authority, to the extent that any of the foregoing has jurisdiction over
       HCC and/or GBCC.

       "PCC" means Pratt Casino Corporation, a Delaware corporation.

       "PCC SERVICES" shall mean the services provided by HCC to PCC and its
       subsidiaries above the GB Holdings, Inc. level hereunder, including,
       without limitation, accounting and financial reporting services.

                                      -2-
<PAGE>
 
       "SERVICES" shall mean the ACSC Services, the GBCC Services, the PCC
       Services and any and all other services provided by HCC to GBCC and the
       GBCC Subsidiaries hereunder, including, without limitation, the Special
       Services.

       "SPECIAL SERVICES" shall mean certain special services which GBCC or a
       GBCC Subsidiary may specifically request HCC or a subsidiary thereof to
       provide to it in connection with a special project and HCC or such
       subsidiary may agree to provide.

   2.  SERVICES.  During the term of this Agreement, HCC, or at the direction of
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HCC one or more of its subsidiaries, shall perform such services as GBCC may
reasonably request from time to time in connection with the operations of GBCC
and the GBCC Subsidiaries, including, without limitation, the ACSC Services, the
GBCC Services, the PCC Services and the Special Services.  These Services will
be performed by the President of HCC and such other employees of HCC, or any HCC
subsidiary, as may be necessary.  In providing such Services HCC or such
subsidiary shall provide whatever facilities, supplies and administrative office
functions, which may be required by GBCC, including, without limitation, office
space, equipment, supplies, transportation, telephone and utility services,
bookkeeping, accounting and  record keeping services, insurance, advertising,
data processing, handling of cash receipts and cash disbursements, check
writing, training and such other functions, facilities and services as GBCC
shall require.

   3.  TERM; TERMINATION.
       ----------------- 

       a.    Term. This Agreement shall commence on the effective date hereof 
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and shall continue in effect for the term of one year, unless sooner terminated
in accordance with the terms and provisions hereof. Unless one party delivers
written notice of termination to the other party that is received no later than
thirty (30) days prior to the expiration date of the initial or any renewal term
of this Agreement, this Agreement shall be automatically renewed upon the same
terms and conditions for an additional one year period, and the same notice and
renewal terms shall apply to each renewal period. The initial term and any
renewal thereof are hereinafter referred to as the "TERM".

       b.    Reciprocal Termination. Notwithstanding any other provision of this
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Agreement, each party shall have the right to terminate this Agreement if the
non-defaulting party gives written notice to the defaulting party of the
occurrence of any of the following events of default and the defaulting party
shall fail to cure such default within thirty (30) days of the effective date of
such written notice:

       (i)   a material breach of this Agreement which is not cured prior to the
             expiration of the thirty (30) day period of cure specified above;
             or

       (ii)  an admission in writing of its inability to pay its debts generally
             as they become due; or

       (iii) a bankruptcy, dissolution, appointment of a receiver, or the
             voluntary filing of any petition therefor or consent thereto, or
             any assignment for the benefit of creditors, under any applicable
             insolvency laws; or

       (iv)  any action to suspend normal business operations; or

       (v)   any materially adverse levy or judgment is filed, which is not
             satisfied or otherwise removed or set aside within ten (10) days of
             the filing thereof.

                                      -3-
<PAGE>
 
       c.  Damages.  If this Agreement shall be terminated as set forth in this
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Paragraph 3 and the aggrieved party (i) has a claim for damages pursuant to the
specific terms of this Agreement, or (ii) believes it otherwise has a claim for
damages, it may claim such damages suffered by reason of the other's non-
compliance, breach or default.

   4.  FEES.  As remuneration for the Services rendered by HCC to GBCC and the
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GBCC Subsidiaries, (i) GBCC shall pay to HCC during the Term a fee equal to
$47,500 per month for the GBCC Services on the 1st day of each month, (ii)
GBCC shall cause ACSC to pay to HCC during the Term a fee equal to $9,000 per
month for the ACSC Services on the 1st day of each month, (iii) GBCC shall
cause PCC or its subsidiaries to pay to HCC during the Term a monthly fee equal
to the actual cost to HCC of the PCC Services for such month (which fee shall be
(A) set forth in an invoice delivered by HCC to GBCC on or before the 10th day
of the month following the month in which the services were performed (which
invoice shall describe such services and show the calculation of such fee) and
(B) payable on the 15th day of such month) and (iv) in the event that HCC
performs Special Services for GBCC and/or the GBCC Subsidiaries, GBCC shall pay
or shall cause such GBCC Subsidiaries to pay to HCC during the Term a monthly
fee equal to the actual cost to HCC of the Special Services for such month
(which fee shall be (A) set forth in an invoice delivered by HCC to GBCC or the
GBCC Subsidiaries on or before the 10th day of the month following the month
in which the services were performed (which invoice shall describe such services
and show the calculation of such fee) and (B) payable on the 15th day of such
month).  HCC and GBCC shall undertake a semi-annual review of the Services
rendered hereunder and the fees for such services beginning on June 30, 1999 and
continuing on June 30th of each succeeding year during the Term hereafter.
Based on such review, HCC and GBCC shall make any necessary adjustments to the
scope of the Services and the fees for such Services.

   5.  NOTICES.  All notices, requests, consents and other communications
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required or permitted under this Agreement shall be in writing and shall be:
(i) personally delivered; (ii) transmitted by United States certified or
registered mail, postage prepaid, return receipt requested, or by commercial
courier or express service; or (iii) transmitted by telecopier, to the party to
whom such notice, request, consent or other communication is being given at the
address of such party set forth below, or at such other address as any party may
designate by written notice to the other parties:

       (a) If to HCC, to it at:

           Hollywood Casino Corporation
           Two Galleria Tower, Suite 2200
           13455 Noel Road, LB 48
           Dallas, Texas 75240
           Attention:  William D. Pratt, Esq.

       (b) If to GBCC, to it at:

           Greate Bay Casino Corporation
           Two Galleria Tower, Suite 2200
           13455 Noel Road, LB 48
           Dallas, Texas 75240
           Attention: John C. Hull

   All notices, requests, consents and other communications shall be effective
or deemed delivered upon (i) the date of receipt if delivered personally, (ii)
the earlier to occur of the actual receipt thereof by the addressee or three (3)
days after the date of deposit if transmitted by mail or commercial courier or
express service or (iii) the date of transmission with confirmed answerback if
transmitted by telecopier.

                                      -4-
<PAGE>
 
   6.  AGENCY RELATIONSHIP.  In taking any action pursuant to this Agreement,
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HCC (or any of its subsidiaries providing services hereunder) shall act only as
the appointed agent or representative of GBCC and nothing in this Agreement
shall be construed as creating a tenancy, partnership, joint venture or any
other relationship between the parties hereto, except that of principal and
agent.

   7.  SEVERABILITY.  If any provision of this Agreement or the application
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hereof to any person or circumstances shall to any extent be held void,
unenforceable or invalid, then the remainder of this Agreement or the
application of such provision to persons or circumstances other than those as to
which it is held void, unenforceable or invalid shall not be effective hereby,
and each provision of this Agreement shall be valid and enforced to the fullest
extent permitted by law.

   8.  COSTS OF LITIGATION.  In any action or proceeding brought by any party
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against any other party under this Agreement, the prevailing party shall be
entitled to recover from the other party attorneys' fees, investigation costs,
and other legal expenses and court costs incurred by such party in such action
or proceeding as the court may find to be reasonable.

   9.  COUNTERPARTS.  This Agreement may be executed in counterparts, each of
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which shall be deemed an original, but all of which together shall constitute
one and the same instrument.

   10. HEADINGS.  Headings of paragraphs in this Agreement are for convenience
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of reference only and shall not define or limit any of the terms or provisions
hereof.

   11. ENTIRE AGREEMENT; WAIVER.  This Agreement contains the entire agreement
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between the parties hereto with respect to the transactions contemplated herein,
supersedes all prior written agreements and negotiations and oral
understandings, if any, and may not be amended, supplemented or discharged,
except by an instrument in writing signed by each party hereto.  No failure by
any party to insist upon strict compliance with the terms and conditions hereof
shall be deemed to be a waiver thereof.

   12. SUCCESSORS AND ASSIGNS.  This Agreement shall be binding upon, and shall
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inure to the benefit of and be enforceable by, the parties hereto and their
respective successors and assigns.

   13. GOVERNING LAW.  This Agreement shall be construed and enforced in
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accordance with the laws of the State of Texas, provided, however, that this
Agreement shall be specifically subject to the provisions of the Gaming Laws (if
applicable) and the requirements of the Gaming Regulatory Authorities (if
applicable).

                                      -5-
<PAGE>
 
   IN WITNESS WHEREOF, the parties have caused this agreement to be executed and
delivered by their respective officers hereunto duly authorized as of the
effective date hereof.


                          HOLLYWOOD CASINO CORPORATION



                          By:  /s/ William D. Pratt
                               ---------------------------------------- 
                               Name:  William D. Pratt
                               Title: Executive Vice President, General Counsel
                                         and Secretary


 

                         GREATE BAY CASINO CORPORATION


                         By:   /s/ John C. Hull
                               ---------------------------------------- 
                               Name:  John C. Hull
                               Title: Chairman of the Board and Chief Executive
                                         Officer

                                      -6-