<PAGE>
                                                                 EXHIBIT 10.4(c)


                                  AMENDMENT TO
                             AMERISTAR CASINOS, INC.
                      1999 STOCK INCENTIVE PLAN, AS AMENDED

                       (EFFECTIVE AS OF JANUARY 24, 2003)

This Amendment to Ameristar Casinos, Inc. 1999 Stock Incentive Plan, as amended
(this "Amendment") is made and effective as of January 24, 2003.

      WHEREAS, Ameristar Casinos, Inc., a Nevada corporation (the "Company"),
maintains a 1999 Stock Incentive Plan, as amended (the "Plan"); and

      WHEREAS, the Board of Directors of the Company (the "Board") desires to
amend the Plan in certain respects as provided in this Amendment and as
permitted by Section 10 of the Plan; and

      WHEREAS, except as amended pursuant to this Amendment, the terms of the
Plan as currently in effect shall remain in full force and effect.

1. Amendment to Section 11. Section 11 of the Plan is hereby amended to read in
its entirety as follows:

      "Section 11. Acceleration of Vesting in Certain Circumstances.

      11.1  Notwithstanding any other provision of the Plan, unless otherwise
            determined by the Committee and expressly set forth in the agreement
            evidencing the Stock Option or Restricted Stock award, in the event
            of a Change in Control, (i) each Stock Option outstanding under the
            Plan which is not otherwise fully vested or exercisable with respect
            to all of the shares of Stock at that time subject to such Stock
            Option shall automatically accelerate so that each such Stock Option
            shall, immediately upon the effective time of the Change in Control,
            become exercisable for all the shares of Stock at the time subject
            to such Stock Option and may be exercised for any or all of those
            shares as fully vested shares of Stock, and (ii) all shares of
            Restricted Stock outstanding under the Plan which are not otherwise
            fully vested shall automatically accelerate so that all such shares
            of Restricted Stock shall, immediately upon the effective time of
            the Change in Control, become fully vested, free of all
            restrictions.

      11.2  Notwithstanding any other provision of the Plan, unless otherwise
            determined by the Committee and expressly set forth in the

<PAGE>

            agreement evidencing the Stock Option or Restricted Stock award, in
            the event of a Corporate Transaction, (i) each Stock Option
            outstanding under the Plan which is not otherwise fully vested or
            exercisable with respect to all of the shares of Stock at that time
            subject to such Stock Option shall automatically accelerate so that
            each such Stock Option shall, immediately prior to the effective
            time of the Corporate Transaction, become exercisable for all the
            shares of Stock at the time subject to such Stock Option and may be
            exercised for any or all of those shares as fully vested shares of
            Stock, and (ii) all shares of Restricted Stock outstanding under the
            Plan which are not otherwise fully vested shall automatically
            accelerate so that all such shares of Restricted Stock shall,
            immediately prior to the effective time of the Corporate
            Transaction, become fully vested, free of all restrictions.

      11.3  As used in the Plan, a "Change in Control" shall be deemed to have
            occurred if:

            (a)   Individuals who, as of January 24, 2003, constitute the entire
                  Board ("Incumbent Directors") cease for any reason to
                  constitute a majority of the Board; provided, however, that
                  any individual becoming a director subsequent to such date
                  whose election, or nomination for election by the Company's
                  stockholders, was approved by the vote of a majority of the
                  then Incumbent Directors (other than an election or nomination
                  of an individual whose assumption of office is the result of
                  an actual or threatened election contest relating to the
                  election of directors of the Company), also shall be an
                  Incumbent Director; or

            (b)   Any Person (as defined below) other than a Permitted Holder
                  (as defined below) shall become the beneficial owner (as
                  defined in Rules 13d-3 and 13d-5 under the Exchange Act),
                  directly or indirectly, of securities of the Company
                  representing in the aggregate fifty percent (50%) or more of
                  either (i) the then outstanding shares of Stock or (ii) the
                  Combined Voting Power (as defined below) of all then
                  outstanding Voting Securities (as defined below) of the
                  Company; provided, however, that notwithstanding the
                  foregoing, a Change in Control shall not be deemed to have
                  occurred for purposes of this clause (b) solely as the result
                  of:

                        (A)   An acquisition of securities by the Company which,
                              by reducing the number of shares of Stock or other
                              Voting Securities outstanding, increases (i) the
                              proportionate number of shares of Stock
                              beneficially owned by any Person to fifty percent
                              (50%) or more of the shares of


                                      -2-
<PAGE>

                              Stock then outstanding or (ii) the proportionate
                              voting power represented by the Voting Securities
                              beneficially owned by any Person to fifty percent
                              (50%) or more of the Combined Voting Power of all
                              then outstanding voting securities; or

                        (B)   An acquisition of securities directly from the
                              Company, except that this Paragraph (B) shall not
                              apply to:

                                    (1)   any conversion of a security that was
                                          not acquired directly from the
                                          Company; or

                                    (2)   any acquisition of securities if the
                                          Incumbent Directors at the time of the
                                          initial approval of such acquisition
                                          would not immediately after (or
                                          otherwise as a result of) such
                                          acquisition constitute a majority of
                                          the Board.

      11.4  As used in the Plan, "Corporate Transaction" means (a) any merger,
            consolidation or recapitalization of the Company (or, if the capital
            stock of the Company is affected, any subsidiary of the Company), or
            any sale, lease or other transfer (in one transaction or a series of
            transactions contemplated or arranged by any party as a single plan)
            of all or substantially all of the assets of the Company (each of
            the foregoing being an "Acquisition Transaction") where (i) the
            stockholders of the Company immediately prior to such Acquisition
            Transaction would not immediately after such Acquisition Transaction
            beneficially own, directly or indirectly, shares representing in the
            aggregate more than fifty percent (50%) of (A) the then outstanding
            common stock of the corporation surviving or resulting from such
            merger, consolidation or recapitalization or acquiring such assets
            of the Company, as the case may be (the "Surviving Corporation") (or
            of its ultimate parent corporation, if any) and (B) the Combined
            Voting Power of the then outstanding Voting Securities of the
            Surviving Corporation (or of its ultimate parent corporation, if
            any) or (ii) the Incumbent Directors at the time of the initial
            approval of such Acquisition Transaction would not immediately after
            such Acquisition Transaction constitute a majority of the board of
            directors of the Surviving Corporation (or of its ultimate parent
            corporation, if any) or (b) the liquidation or dissolution of the
            Company.

      11.5  For purposes of this Section 11:

                  (a)   "Combined Voting Power" shall mean the aggregate votes
                        entitled to be cast generally in the election of
                        directors of a


                                      -3-
<PAGE>

                        corporation by holders of the then outstanding Voting
                        Securities of such corporation;

                  (b)   "Permitted Holder" shall mean (i) the Company or any
                        trustee or other fiduciary holding securities under an
                        employee benefit plan of the Company, (ii) to the extent
                        they hold securities in any capacity whatsoever, Craig
                        H. Neilsen and Ray Neilsen and their respective estates,
                        spouses, heirs, ancestors, lineal descendants,
                        stepchildren, legatees and legal representatives, and
                        the trustees of any bona fide trusts of which one or
                        more of the foregoing are the sole beneficiaries or
                        grantors thereof and (iii) any Person controlled,
                        directly or indirectly, by one or more of the foregoing
                        Persons referred to in the immediately preceding clause
                        (ii), whether through the ownership of voting
                        securities, by contract, in a fiduciary capacity,
                        through possession of a majority of the voting rights
                        (as directors and/or members) of a not-for-profit
                        entity, or otherwise;

                  (c)   "Person" shall mean any individual, entity (including,
                        without limitation, any corporation (including, without
                        limitation, any charitable corporation or private
                        foundation), partnership, limited liability company,
                        trust (including, without limitation, any private,
                        charitable or split-interest trust), joint venture,
                        association or governmental body) or group (as defined
                        in Section 13(d)(3) or 14(d)(2) of the Exchange Act and
                        the rules and regulations thereunder); provided,
                        however, that "Person" shall not include the Company,
                        any of its subsidiaries, any employee benefit plan of
                        the Company or any of its majority-owned subsidiaries or
                        any entity organized, appointed or established by the
                        Company or such subsidiary for or pursuant to the terms
                        of any such plan; and

                  (d)   "Voting Securities" shall mean all securities of a
                        corporation having the right under ordinary
                        circumstances to vote in an election of the board of
                        directors of such corporation."

2. Confirmation. Except as amended pursuant to this Amendment, the terms of the
Plan as currently in effect shall remain in full force and effect.


                                      -4-