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                                                                   EXHIBIT 10.79

KIRKLAND INVESTMENT CORPORATION

                                                      July 1, 1997


Alliance Gaming Corporation
6601 South Bermuda Road
Las Vegas, Nevada  89119

             Re:  Amendment to Agreement dated as of July 1, 1997

Ladies and Gentlemen:

            Reference is made to the agreement dated as of July 1, 1997 (the
"Agreement") between Alliance Gaming Corporation (the "Company") and Kirkland
Investment Corporation or its designee ("Kirkland").

            We have reviewed the operation of the Agreement and wish to amend
the Agreement to provide that the Company will (i) pay directly, effective as of
the date hereof, the rent and utilities associated with the Kirkland New York
area office, as well as the salaries, bonuses and employee benefits of the
secretarial and analyst support staff in that office, and (ii) upon written
notice from Kirkland, pay directly those additional overhead expenses that
Kirkland identifies to the Company, beginning within 10 business days after the
date of such notice.

            Under this revised arrangement, all such costs and expenses as
designated pursuant to the preceding paragraph that are paid directly by the
Company shall be credited against, and shall reduce dollar for dollar, the
Company's obligation to make the $950,000 payment (as increased from time to
time under the Agreement), other than the cost of reasonable and customary
employee benefits for the Kirkland secretarial and analyst support staff, which
benefits costs shall not be so credited.

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

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            If the foregoing terms meet with your approval, please indicate your
acceptance by signing and returning the enclosed copy of this letter to
Kirkland, whereupon it will become a binding amendment to the Agreement between
Kirkland and the Company. All of the other provisions of the Agreement shall
remain in full force and effect.


                                        Very truly yours,

                                        Kirkland Investment Corporation


                                        By    /s/ JOEL KIRSCHBAUM
                                              ----------------------------------
                                              Title: PRESIDENT


ACCEPTED AND AGREED:                    Date:              7/31/97
                                              ----------------------------------

Alliance Gaming Corporation

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

Date:
     -----------------------------------

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                                   - 2 -

            If the foregoing terms meet with your approval, please indicate your
acceptance by signing and returning the enclosed copy of this letter to
Kirkland, whereupon it will become a binding amendment to the Agreement between
Kirkland and the Company. All of the other provisions of the Agreement shall
remain in full force and effect.


                                        Very truly yours,

                                        Kirkland Investment Corporation


                                        By    /s/ JOEL KIRSCHBAUM
                                              ----------------------------------
                                              Title: PRESIDENT


ACCEPTED AND AGREED:                    Date:              7/31/97
                                              ----------------------------------

Alliance Gaming Corporation

By /s/ DAVID JOHNSON
   -------------------------------------
   Title: Secretary, Senior Vice President
          and General Counsel

Date:             7-31-97
     -----------------------------------