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Exhibit 31.1 CERTIFICATION PURSUANT TO RULES 13a-14 AND
15d-14 UNDER THE SECURITIES EXCHANGE ACT OF 1934,
AS ADOPTED PURSUANT TO SECTION 302
OF THE SARBANES-OXLEY ACT OF 2002 I, Craig H. Neilsen, certify that: 1. I have reviewed this Annual Report on Form 10-K of Ameristar Casinos, Inc.; 2. Based on my knowledge, this report does not contain any untrue statement of
a material fact or omit to state a material fact necessary to make the
statements made, in light of the circumstances under which such statements were
made, not misleading with respect to the period covered by this report; 3. Based on my knowledge, the financial statements, and other financial
information included in this report, fairly present in all material respects
the financial condition, results of operations and cash flows of the registrant
as of, and for, the periods presented in this report; 4. The registrants other certifying officer(s) and I are responsible for
establishing and maintaining disclosure controls and procedures (as defined in
Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant and have: (a) Designed such disclosure controls and procedures, or caused such
controls to be designed under our supervision, to ensure that material
information relating to the registrant, including its consolidated
subsidiaries, is made known to us by others within those entities, particularly
during the period in which this report is being prepared; and (b) Evaluated the effectiveness of the registrants disclosure controls
and procedures and presented in this report our conclusions about the
effectiveness of the disclosure controls and procedures as of the end of the
period covered by this report based on such evaluation; and (c) Disclosed in this report any change in the registrants internal
control over financial reporting that occurred during the registrants most
recent fiscal quarter (the registrants fourth quarter in the case of an annual
report) that has materially affected, or is reasonably likely to materially
affect, the registrants internal control over financial reporting; and 5. The registrants other certifying officer(s) and I have disclosed, based on
our most recent evaluation of internal control over financial reporting, to the
registrants auditors and the audit committee of registrants board of
directors (or persons performing the equivalent functions): (a) All significant deficiencies and material weaknesses in the design or
operation of internal control over financial reporting which are reasonably
likely to affect the registrants ability to record, process, summarize and
report financial information; and (b) Any fraud, whether or not material, that involves management or other
employees who have a significant role in the registrants internal control over
financial reporting. March 12, 2004 By:
    
    /s/ Craig H. NeilsenCraig H. NeilsenPresident and Chief Executive Officer




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On
this 12th day of March, 2004, Craig H. Neilsen directed Connie Wilson,
in his presence as well as our own, to sign the foregoing document as Craig H.
Neilsen. Upon viewing the signature as signed by Connie Wilson and in our
presence, Craig H. Neilsen declared to us that he adopted it as his own
signature. /s/ Janet
CatronWitness/s/
Lisa K. NowakWitness
 STATE OF NEVADA
    
    ))  ss.COUNTY OF CLARK
    
    )
 I,
Margene M. Otten, Notary Public in and for said county and state, do hereby
certify that Craig H. Neilsen personally appeared before me and is known or
identified to me to be the person whose name is subscribed to the within instrument. Craig H.
Neilsen, who being unable due to physical incapacity to sign his name or offer
his mark, did direct Connie Wilson in his presence, as well as my own, to sign
his name to the foregoing document as Craig H. Neilson. Craig H. Neilsen, after viewing his name as
signed by Connie Wilson, thereupon adopted the signature as his own by
acknowledging to me his intention to so adopt as if he had personally
executed the same. IN WITNESS WHEREOF, I have hereunto set my hand and official seal this
12th day of March, 2004. /s/
Margene M. OttenNotary Public
 Residing at:   Las Vegas, NVMy
Commission Expires:July
23, 2006