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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)) and internal control over financial reporting (as defined in Exchange Act Rules
13a-15(f) and 15d-15(f)) 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; (b) Designed such internal control over financial reporting, or caused such internal control
over financial reporting to be designed under our supervision, to provide reasonable assurance
regarding the reliability of financial reporting and the preparation of financial statements for
external purposes in accordance with generally accepted accounting principles; (c) 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 (d) 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 the 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 16, 2005 By:
    
    /s/ Craig H. Neilsen by C. WilsonCraig H. NeilsenPresident and Chief Executive Officer




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On this 16th day of March, 2005, 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/  Shirley LizotteWitness
 STATE OF NEVADA      )   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 President
and Chief Executive Officer of Ameristar Casinos, Inc., the corporation that executed the within
instrument or the person who executed the instrument on behalf of said corporation. 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. 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 it as if he had personally executed the
same both in his individual capacity and on behalf of said corporation, and further acknowledged to
me that such corporation executed the same. IN WITNESS WHEREOF, I have hereunto set my hand and official seal this 16th day of March,
2005. /s/ Margene M. OttenNotary Public
 My Commission Expires:July 23, 2006 Residing at:      Las Vegas, NV