<PAGE>   1

                                                                 EXHIBIT 4.2(b)


                       FIRST AMENDMENT TO CREDIT AGREEMENT


     FIRST AMENDMENT TO CREDIT AGREEMENT (this "Amendment"), dated as of January
30, 2001, among AMERISTAR CASINOS, INC., a Nevada corporation (the "Borrower"),
the various lenders party to the Credit Agreement referred to below (the
"Lenders"), WELLS FARGO BANK, N.A., as Co-Arranger and Syndication Agent, BEAR
STEARNS CORPORATE LENDING INC., as Documentation Agent, DEUTSCHE BANK SECURITIES
INC., as Lead Arranger and sole Book Manager and BANKERS TRUST COMPANY, as
Administrative Agent (all capitalized terms used herein and not otherwise
defined herein shall have the respective meaning provided such terms in the
Credit Agreement as defined below).


                              W I T N E S S E T H:
                              - - - - - - - - - -


     WHEREAS, the Borrower, the Lenders, the Lead Arranger, the Syndication
Agent, the Documentation Agent and the Administrative Agent are party to a
Credit Agreement, dated as of December 20, 2000 (the "Credit Agreement"); and

     WHEREAS, the Borrower and the undersigned Lenders wish to provide the
amendment provided for herein;

     NOW, THEREFORE, it is agreed:

     1. Section 4.02(A)(g) of the Credit Agreement is hereby amended by adding
the following proviso at the end thereof ", provided that the net proceeds of
the Permanent Senior Subordinated Notes exceeding $350,000,000 shall not be
required to be applied pursuant to this clause (g) to the extent that such net
proceeds not so applied pursuant to this proviso do not exceed $25,000,000".

     2. Section 4.02(A)(h) of the Credit Agreement is hereby amended by
deleting, in the first sentence thereof, "and" at the end of clause (i) thereof,
inserting a comma in lieu thereof and adding at the end of the first sentence
thereof the following: "and (iii) the net Asset Sale Proceeds received in
respect of the Disposition being applied to repay the Term Loans and the then
outstanding Revolving Loans shall not be required to be so applied until
February 1, 2001."

     3. Section 3.03(j) of the Credit Agreement is hereby amended by deleting
"on the date of the consummation of the Disposition" and inserting, in lieu
thereof, the following: "on the later of the date of the consummation of the
Disposition and February 1, 2001."

     4. The Borrower hereby represents and warrants that (i) no Default or Event
of Default exists as of the Amendment Effective Date (as defined below) after
giving effect to this Amendment and (ii) on the Amendment Effective Date, both
before and after giving effect to this Amendment, all representations and
warranties (other than those representations made as of



<PAGE>   2

a specified date) contained in the Credit Agreement and in the other Credit
Documents are true and correct in all material respects.

     5. This Amendment shall become effective on the date (the "Amendment
Effective Date") when the Required Lenders and the Borrower shall have signed a
counterpart hereof (whether the same or different counterparts) and shall have
delivered (including by way of facsimile transmission) the same to the
Administrative Agent at its Notice Office.

     6. This Amendment is limited as specified and shall not constitute a
modification, acceptance or waiver of any other provision of the Credit
Agreement or any other Credit Document.

     7. This Amendment may be executed in any number of counterparts and by the
different parties hereto on separate counterparts, each of which counterparts
when executed and delivered shall be an original, but all of which shall
together constitute one and the same instrument. A complete set of counterparts
shall be lodged with the Borrower and the Administrative Agent.

     8. THIS AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE PARTIES HEREUNDER
SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF
NEW YORK.

                                      * * *




<PAGE>   3


     IN WITNESS WHEREOF, the parties hereto have caused their duly authorized
officers to execute and deliver this Amendment as of the date first above
written.


                                AMERISTAR CASINOS, INC.


                                By:  /s/ Gordon R. Kanofsky
                                   ---------------------------------------------
                                     Name: Gordon R. Kanofsky
                                     Title: Senior Vice President of
                                            Legal Affairs


                                BANKERS TRUST COMPANY,
                                     Individually and as Administrative Agent


                                By:      /s/ Steven P. Lapham
                                   ---------------------------------------------
                                     Title: Director


                                WELLS FARGO BANK, N.A.
                                     Individually and as Co-Arranger and
                                     Syndication Agent



                                By:     /s/ Casey Potter
                                   ---------------------------------------------
                                     Title: Vice President


                                BEAR STEARNS CORPORATE LENDING INC.
                                     Individually and as Documentation Agent



                                By:    /s/ Victor F. Bulzuchelli
                                   ---------------------------------------------
                                     Title: Managing Director



<PAGE>   4




                                SIGNATURE PAGE TO FIRST AMENDMENT DATED AS OF
                                   JANUARY 30, 2001 , TO THE CREDIT AGREEMENT
                                   DATED AS OF DECEMBER 20, 2000, AMONG
                                   AMERISTAR CASINOS, INC., A NEVADA CORPORATION
                                   , THE VARIOUS LENDERS PARTY TO THE CREDIT
                                   AGREEMENT REFERRED TO BELOW, WELLS FARGO
                                   BANK, N.A., AS CO-ARRANGER AND SYNDICATION
                                   AGENT, BEAR STEARNS CORPORATE LENDING INC.,
                                   AS DOCUMENTATION AGENT, DEUTSCHE BANK
                                   SECURITIES INC., AS LEAD ARRANGER AND SOLE
                                   BOOK MANAGER AND BANKERS TRUST COMPANY, AS
                                   ADMINISTRATIVE AGENT


                                NATIONAL CITY BANK OF INDIANA


                                By:       /s/ Mark A. Minnick
                                    --------------------------------------------
                                     Title: Senior Vice President


                                THE CIT GROUP/EQUIPMENT FINANCING, INC.

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


                                HELLER FINANCIAL, INC.


                                By:       /s/ Robert M. Reeg
                                    --------------------------------------------
                                     Title: Assistant Vice President


                                THE SUMITOMO TRUST AND BANKING CO.,
                                   LTD., NEW YORK BRANCH

                                By:      /s/ Stephen A. Stratico
                                    --------------------------------------------
                                     Title: Vice President




<PAGE>   5


                               AMMC CDO II, LIMITED,
                                  By: American Money Management Corp.
                                      as Collateral Manager


                               By:       /s/ David P. Meyer
                                    --------------------------------------------
                                     Title: Vice President


                               MUIRFIELD TRADING LLC

                               By:        /s/ Ann E. Morris
                                    --------------------------------------------
                                     Title: Asst. Vice President


                               SRV-HIGHLAND, INC.

                               By:       /s/ Ann E. Morris
                                    --------------------------------------------
                                     Title: Asst. Vice President


                               SRF 200 LLC

                               By:        /s/ Ann E. Morris
                                    --------------------------------------------
                                     Title: Asst. Vice President


                               GLENEAGLES TRADING LLC

                               By:        /s/ Ann E. Morris
                                    --------------------------------------------
                                     Title: Asst. Vice President


                               OLYMPIC FUNDING TRUST, SERIES 1999-1

                               By:        /s/ Ann E. Morris
                                    --------------------------------------------
                                     Title:


                               SRF 2000 LLC

                               By:        /s/ Ann E. Morris
                                    --------------------------------------------
                                     Title: Asst. Vice President


                               BLACK DIAMOND CDO 2000-1 LTD.

                               By:        /s/ David Dyer
                                    --------------------------------------------
                                     Title: Director




<PAGE>   6

                               CARLYLE HIGH YIELD PARTNERS, LP

                               By:         /s/ Linda M. Pace
                                   ---------------------------------------------
                                     Title: Vice President


                               CARLYLE HIGH YIELD PARTNERS II, LP

                               By:         /s/ Linda M. Pace
                                   ---------------------------------------------
                                     Title: Vice President


                               CARLYLE HIGH YIELD PARTNERS III, LP

                               By:         /s/ Linda M. Pace
                                   ---------------------------------------------
                                     Title: Vice President


                               SIERRA CLO - I

                               By:         /s/ John Casparian
                                   ---------------------------------------------
                                     Title: Chief Operating Office


                               SEQUILS - CUMBERLAND I, LTD.,
                                    By: Deerfield Capital Management LLC,
                                        as its Collateral Manager

                               By:         /s/ Matt Stouffer
                                   ---------------------------------------------
                                     Title: Vice President


                               HIGHLAND LEGACY LIMITED,
                                    By: Highland Capital Management, L.P.,
                                        as Collateral Manager

                               By:         /s/ Todd Travers
                                   ---------------------------------------------
                                     Title: Senior Portfolio Manager


                               HIGHLAND OFFSHORE PARTNERS, L.P.,
                                    By: Highland Capital Management, L.P.,
                                        as Collateral Manager

                               By:         /s/ Todd Travers
                                   ---------------------------------------------
                                     Title: Senior Portfolio




<PAGE>   7

                               ELF FUNDING TRUST I,
                                    By: Highland Capital Management, L.P.,
                                        as Collateral Manager

                               By:         /s/ Todd Travers
                                   ---------------------------------------------
                                    Title: Senior Portfolio Manager


                               SL LOANS I LIMITED

                               By:         /s/ Todd Travers
                                   ---------------------------------------------
                                    Title: Senior Portfolio Manager


                               ARCHIMEMDES FUNDING III, LTD.,
                                   By: ING Capital Advisors LLC,
                                       as Collateral Manager

                               By:         /s/ Wade T. Winter, CFA
                                   ---------------------------------------------
                                    Title: Vice President


                               ARCHIMEMDES FUNDING IV (CAYMAN), LTD.,
                                   By: ING Capital Advisors LLC,
                                       as Collateral Manager

                               By:         /s/ Wade T. Winter, CFA
                                  ----------------------------------------------
                                    Title: Vice President


                               NEMEAN CLO, LTD.,
                                  By: ING Capital Advisors LLC,
                                      as Investment Manager

                               By:         /s/ Wade T. Winter, CFA
                                   ---------------------------------------------
                                    Title: Vice President


                               SEQUILS-ING I (HBDGM), LTD.,
                                   By: ING Capital Advisors LLC,
                                       as Collateral Manager

                               By:         /s/ Wade T. Winter, CFA
                                   ---------------------------------------------
                                    Title: Vice President




<PAGE>   8

                               DEBT STRATEGIES FUND, INC.

                               By:         /s/ John M. Johnson
                                   ---------------------------------------------
                                    Title: Authorized Signatory


                               SENIOR HIGH INCOME PORTFOLIO, INC.


                               By:         /s/ John M. Johnson
                                   ---------------------------------------------
                                    Title: Authorized Signatory


                               MASTER SENIOR FLOATING RATE TRUST


                               By:         /s/ John M Johnson
                                   ---------------------------------------------
                                    Title: Authorized Signatory


                               MERRILL LYNCH SENIOR FLOATING RATE FUND, INC.


                               By:         /s/ John M. Johnson
                                   ---------------------------------------------
                                    Title: Authorized Signatory


                               LONGHORN CDO (CAYMAN) LTD.
                                    By: Merrill Lynch Investment Managers, L.P.
                                        its Investment Advisor


                               By:         /s/ John M. Johnson
                                   ---------------------------------------------
                                    Title: Authorized Signatory


                               STANDFIELD CLO LTD.,
                                    By: Stanfield Capital Partners LLC
                                        as its Collateral Manager


                               By:         /s/ Gregory L. Smith
                                   ---------------------------------------------
                                    Title: Partner




<PAGE>   9

                               STANDFIELD/RMF TRANSATLANTIC CDO LTD.,
                                    By: Stanfield Capital Partners LLC
                                        as its Collateral Manager


                               By:         /s/ Gregory L. Smith
                                   ---------------------------------------------
                                    Title: Partner


                               WINDSOR LOAN FUNDING, LIMITED,
                                    By: Stanfield Capital Partners LLC as its
                                        Collateral Manager


                               By:         /s/ Gregory L. Smith
                                   ---------------------------------------------
                                    Title: Partner


                               STEIN ROE FLOATING RATE LIMITED
                                    LIABILITY COMPANY


                               By:         /s/ Brian W. Good
                                   ---------------------------------------------
                                    Title: Senior Vice President


                               LIBERTY - STEIN ROE ADVISOR FLOATING
                                    RATE ADVANTAGE FUND
                                    By: Stein Roe & Farnham Incorporated, as
                                         Advisor


                               By:         /s/ Brian W. Good
                                   ---------------------------------------------
                                    Title: Sr. Vice President & Portfolio
                                           Manager


                               TORONTO DOMINION (NEW YORK), INC.


                               By:         /s/ Gwen Zirkle
                                   ---------------------------------------------
                                    Title: Vice President


                               EMERALD ORCHARD LIMITED


                               By:         /s/ Gwen Zirkle
                                   ---------------------------------------------
                                    Title: Attorney In Fact




<PAGE>   10



                               STEIN ROE & FARNHAM CLO I LTD., by Stein Roe
                                   & Farnham Incorporated


                               By:         /s/ Brian W. Good
                                   ---------------------------------------------
                                    Title: Senior Vice President &
                                           Portfolio Manager