<PAGE>

                                                            EXHIBIT 10.4(b)

                             AMERISTAR CASINOS, INC.
                      NON-QUALIFIED STOCK OPTION AGREEMENT
                (Non-Qualified Stock Option Agreement Form 99-4)

Name and Address of Optionee:          ________________________
                                       ________________________
                                       ________________________

Date of Grant:                         ________________________

No. of Shares:                         ________________________

Exercise Price:                        ________________________

Vesting Schedule:                      _____ shares on ________

                                       _____ shares on ________

                                       _____ shares on ________

                                       _____ shares on ________

                                       _____ shares on ________

Expiration Date:                       ________________________

                  [Remainder of page intentionally left blank.]

<PAGE>

         THIS AGREEMENT is made as of the date set forth above, between
AMERISTAR CASINOS, INC., a Nevada corporation (hereinafter called the
"Company"), and the optionee named above (hereinafter called the "Optionee").

                                     RECITAL

         The Committee (as defined below) responsible for administering the
Ameristar Casinos, Inc. 1999 Stock Incentive Plan, as amended (the "Plan"), has
determined that it is to the advantage and interest of the Company and its
stockholders to grant, pursuant to the Plan, the option provided for herein to
the Optionee as an inducement to remain in the service of the Company or Related
Company (as defined for purposes of the Plan) and as an incentive for increased
effort during such service.

         As used herein, the term "Committee" shall mean the Compensation
Committee or such other committee of directors appointed by the Board of
Directors of the Company to administer the Plan, or, if no committee has been
appointed for such purpose, reference to the "Committee" shall be deemed a
reference to the Board of Directors of the Company. If the Optionee is not a
person subject to Section 16 of the Securities Exchange Act of 1934, as amended,
the term "Committee" shall extend to and include any officer of the Company to
which the Committee has properly delegated any of its authorities to administer
the Plan.

         In consideration of the mutual covenants herein contained, the parties
agree as follows:

         1.       Grant of Option. The Company hereby grants to the Optionee the
right and option (the "Option") to purchase on the terms and conditions set
forth herein all or any part of an aggregate of the number shares (the "Shares")
of the Common Stock of the Company (whether authorized and unissued or treasury
shares) identified above next to the heading "No. of Shares" at the purchase
price per Share identified above next to the heading "Exercise Price" as the
Optionee may, from time to time, elect. The Option shall vest and become
exercisable on a cumulative basis in an amount equal to 20% per year for five
years beginning on the day before the anniversary of the Date of Grant, as
described in the vesting schedule set forth above under the heading "Vesting
Schedule". The Option shall expire on the date set forth above next to the
heading "Expiration Date" unless terminated sooner in accordance with the
provisions of Section 5 below.

         Nothing contained herein shall be construed to limit or restrict the
right of the Company or any of its subsidiaries to terminate the Optionee's
employment or other Relationship at any time, with or without cause, or to
increase or decrease the Optionee's compensation from the rate in existence at
the time the Option is granted. As used herein, the term "Relationship" shall
mean that the Optionee is or has agreed to become an officer, director,
employee, consultant, adviser or independent contractor of the Company or any
Related Company.

         2.       Term of Option. The right to exercise the Option granted
hereunder, to the extent unexercised, shall remain in effect until the seventh
anniversary of the grant of this Option, unless another date is specified in
Section 1 hereof or unless sooner terminated in accordance with Section 5
hereof.

         3.       Method of Exercise.

                  (a)      To the extent that the Option has become exercisable
hereunder, the Option may be exercised from time to time by written notice to
the Company stating the number of Shares with respect to which the Option is
being exercised, together with payment in full of the purchase price therefor.
Payment of the purchase price for such Shares shall be made (i) in cash, (ii) by
certified or cashier's check payable to the order of the Company, (iii) other
cash equivalents acceptable to the Committee in its sole discretion, (iv) in the
Committee's sole discretion, by delivery of shares of the Common Stock of the
Company already owned by the Optionee or subject to vested stock options under
the Plan, subject to such delivery being permissible under the General
Corporation Law of the State of Nevada, including without limitation Section
78.288 thereof, or (v) any combination of the foregoing. If requested by the
Committee, prior to the delivery of any Shares, the Optionee, or any other
person entitled to exercise the Option, shall supply the Committee with a
representation that the Shares are not being acquired with a

                                      -2-

<PAGE>

view to distribution and will be sold or otherwise disposed of only in
accordance with applicable federal and state statutes, rules and regulations. As
soon after the notice of exercise as the Company is reasonably able to comply,
the Company shall, without transfer or issue tax to the Optionee or other person
entitled to exercise the Option, deliver to the Optionee or such other person,
at the principal office of the Company or such other place as shall be mutually
acceptable, a certificate or certificates for the Shares being purchased.

                  (b)      If payment is made with shares of Common Stock of the
Company already owned by the Optionee, the Optionee, or other person entitled to
exercise the Option, shall deliver to the Company with the notice of exercise
certificates representing the number of shares of Common Stock in payment for
the Shares, duly endorsed for transfer to the Company. In addition, if requested
by the Committee, prior to the acceptance of such certificates in payment for
the Shares, the Optionee, or any other person entitled to exercise the Option,
shall supply the Committee with a written representation and warranty that he or
she has good and marketable title to the shares represented by the
certificate(s), free and clear of liens and encumbrances. The value of the
shares of Common Stock so tendered in payment for the Shares being purchased
shall be their Fair Market Value Per Share (as defined below) on the date of the
Optionee's notice of exercise.

                  (c)      If payment is to be made in shares of Common Stock
subject to vested stock options under the Plan, the per share value attributable
to the shares underlying the stock option(s) to be surrendered or canceled shall
be the Fair Market Value Per Share of such shares less the exercise price per
share of such option(s). The Company and the Optionee or other person entitled
to exercise the Option shall execute and deliver such instruments or
modifications of stock options as shall be necessary to give effect to such an
exercise of the Option.

                  (d)      If for any reason a purported exercise of the Option
providing for payment to be made in whole or in part through the delivery of
shares of Common Stock already owned or underlying vested stock options is
rejected by the Committee or is otherwise not permitted, such purported exercise
shall not be effective unless, following notice thereof from the Company, the
Optionee or other person entitled to exercise the Option promptly pays the
exercise price in an acceptable form.

                  (e)      If the Optionee or other person entitled to exercise
the Option desires to exercise the Option with funds borrowed from a
broker-dealer in a margin transaction under Regulation T of the Board of
Governors of the Federal Reserve System, and such method of exercise is
acceptable to the Committee in its sole discretion, the Optionee's notice of
exercise may be delivered to the Company by such broker-dealer and the Company
may deliver the certificate(s) for the Shares being purchased to such
broker-dealer on behalf of the Optionee or other person entitled to exercise the
Option.

                  (f)      For purposes hereof, the "Fair Market Value Per
Share" of the Company's Common Stock shall mean, if the Common Stock is publicly
traded, the mean between the highest and lowest quoted selling prices of the
Common Stock on such date or, if not available, the mean between the bona fide
bid and asked prices of the Common Stock on such date. In any situation not
covered above, the Fair Market Value Per Share shall be determined by the
Committee in accordance with one of the valuation methods described in Section
20.2031-2 of the Federal Estate Tax Regulations (or any successor provision
thereto), which determination shall be final, binding and conclusive, which
determination shall be final, binding and conclusive.

                  (g)      Notwithstanding the foregoing, the Company shall have
the right to postpone the time of exercise of the Option or the delivery of the
Shares for such period as may be required for the Company with reasonable
diligence (i) to comply with any applicable listing, registration or
qualification requirements of any national securities exchange or
over-the-counter market or under any federal or state law or (ii) to obtain the
consent or approval of any governmental regulatory body. In addition, in
connection with any exercise of the Option, the Committee may require the
Optionee or other person entitled to exercise the Option to agree not to dispose
of any of the Shares acquired upon exercise thereof except upon the satisfaction
of specified conditions which the Committee, in its sole discretion, then deems
necessary or desirable in connection with any then existing and effective
requirement or interpretation of any applicable federal or state securities law,
rule or regulation.

                                      -3-

<PAGE>

                  (h)      The Option may be exercised for less than the total
number of Shares for which the Option is then exercisable, provided that a
partial exercise may not be for less than 100 Shares, except in the final year
of the term of the Option, and shall not, in any event, include any fractional
Shares.

         4.       Tax Withholding. The Optionee shall, no later than the date as
of which any value attributed to the Option first becomes includible in the
Optionee's gross income for applicable tax purposes, pay to the Company, or make
arrangements satisfactory to the Committee (which in the sole discretion of the
Committee may include delivery of shares of Common Stock already owned by the
Optionee or subject to awards under the Plan subject to and in accordance with
the provisions of Section 3(b) or Section 3(c), as applicable) regarding payment
of, any federal, state, local or other taxes of any kind required by law to be
withheld with respect thereto, to enable the Company to claim a deduction in
connection with the exercise of the Option or otherwise to satisfy any legal
requirements. The obligations of the Company hereunder shall be conditional on
such payment or arrangements, and the Company (and, where applicable, any
Related Company), shall, to the extent permitted by law, have the right to
deduct any such taxes from any payment of any kind otherwise due to the
Optionee.

         5.       Termination of Option.

                  (a)      If the Optionee ceases to have a Relationship for any
reason other than the Optionee's death or Permanent Disability (as defined in
Section 5(d)), the Option shall terminate 90 days from the date on which such
Relationship terminates unless the Optionee has resumed or initiated a
Relationship and has a Relationship on such date. During such 90-day period, the
Optionee may exercise the Option but only to the extent the Option was
exercisable on the date of termination of the Optionee's Relationship and
provided that the Option has not expired in accordance with Section 2 or
otherwise terminated as provided herein. A leave of absence approved in writing
by the Committee shall not be deemed a termination of Relationship for purposes
of this Section 5, but the Option may not be exercised during any such leave of
absence, except during the first 90 days thereof. Notwithstanding the foregoing,
if the Relationship is terminated for cause (as defined in Section 5(d)), the
Option shall terminate upon the termination of the Relationship.

                  (b)      For purposes hereof, termination of Optionee's
Relationship for reasons other than death or Permanent Disability shall be
deemed to take place upon the earliest to occur of the following: (i) the date
of the Optionee's retirement from employment under the normal retirement
policies of the Company or any Related Company; (ii) the date of the Optionee's
retirement from employment with the approval of the Committee because of
disability other than Permanent Disability; (iii) the date the Optionee receives
notice or advice that the Optionee's employment or other Relationship is
terminated; (iv) the date the Optionee ceases to render the services for which
the Optionee was employed, engaged or retained by the Company or any Related
Company (absences for temporary illness, emergencies and vacations or leaves of
absence approved in writing by the Committee excepted); or (v) in the case of a
director of the Company, the date on which such person ceases to be a director
of the Company unless such person has an other Relationship at such time. The
fact that the Optionee may receive payment from the Company or any Related
Company after termination for vacation pay, for services rendered prior to
termination, for salary in lieu of notice or for other benefits shall not affect
the termination date.

                  (c)      If the Optionee shall die at a time when the Optionee
is in a Relationship or if the Optionee shall cease to have a Relationship by
reason of Permanent Disability, the Option shall terminate one year after the
date of the Optionee's death or termination of Relationship due to Permanent
Disability unless by its terms it shall expire before such date or otherwise
terminate as provided herein, and shall only be exercisable to the extent that
it would have been exercisable on the date of the Optionee's death or the
Optionee's termination of Relationship due to Permanent Disability. In the case
of death, the Option may be exercised by the person or persons to whom the
Optionee's rights under the Option shall pass by will or by the laws of descent
and distribution.

                  (d)      As used herein, the term "Permanent Disability" shall
mean termination of a Relationship with the Company or any Related Company with
the consent of the Company or such Related Company by reason of permanent and
total disability within the meaning of Section 22(e)(3) of the Internal Revenue
Code of 1986, as amended. As used herein, the term "for cause" shall mean that
the Relationship is terminated by the Company or a Related Company due to (i)
the commission by the Optionee of a substantial violation, through intentional
conduct

                                      -4-

<PAGE>

or through a pattern of behavior not corrected within a reasonable period of
time after written notice to the Optionee by the Company or such Related Company
of such behavior (in either case, whether by action or omission), of the
Optionee's duties on behalf of the Company or a Related Company or the workplace
policies or rules of the Company or a Related Company which conduct or behavior
actually results in substantial harm to the Company or a Related Company or
could reasonably be expected to put personnel of the Company or a Related
Company in serious jeopardy of imminent harm to their safety, health or
well-being or to cause substantial harm to the business of the Company or a
Related Company or (ii) the commission by the Optionee of any act(s) or
omission(s) constituting dishonesty, a felony or fraud or (iii) the failure of
the Optionee to satisfy any requirements under applicable gaming laws or
regulations for the continuance of the Optionee's Relationship with the Company
or such Related Company. Notwithstanding the foregoing sentence, in the event of
any conflict between the definition of "for cause" set forth above and the
definition of "for cause" or "cause" in any employment agreement Optionee may
have with the Company or a Related Company, the definition of "for cause" or
"cause" in such employment agreement shall control to the extent that it imposes
a broader definition of such term(s). For purposes of the Option, whether a
Relationship is or has been terminated "for cause" shall be finally determined
by the Committee.

         6.       Adjustments. In the event of any merger, reorganization,
consolidation, sale of substantially all assets, recapitalization, stock
dividend, stock split, spin-off, split-up, split-off, distribution of assets or
other change in corporate structure affecting the Company's Common Stock, a
substitution or adjustment, as may be determined to be appropriate by the
Committee in its sole discretion, shall be made in the number of shares subject
to the Option and the exercise price under the Option; provided, however, that
no such adjustment or substitution shall increase the aggregate value of the
Option and no such adjustment or substitution shall result in the Company being
required to sell or issue any fractional Shares.

         7.       Change in Control; Corporate Transaction. In the event of a
Change in Control (as that term is defined in the Plan), any portion of the
Option which is not otherwise fully vested and exercisable with respect to all
of the Shares at that time subject to the Option shall automatically accelerate
so that the Option shall, immediately upon the effective time of the Change in
Control, become exercisable for all the Shares at the time subject to the Option
and may be exercised for any or all of those Shares as fully vested shares of
Common Stock of the Company. In the event of a Corporate Transaction (as that
term is defined in the Plan), any portion of the Option which is not otherwise
fully vested and exercisable with respect to all of the Shares at that time
subject to the Option shall automatically accelerate so that the Option shall,
immediately prior to the effective time of the Corporate Transaction, become
exercisable for all the Shares at the time subject to the Option and may be
exercised for any or all of those Shares as fully vested shares of Common Stock
of the Company.

         8.       Provisions Regarding Transferability. The Optionee may
transfer the Option to the Optionee's children, grandchildren or spouse
("Immediate Family"), to one or more trusts for the benefit of the Optionee's
Immediate Family members, or to one or more partnerships or limited liability
companies in which such Immediate Family members are the only partners or
members only upon the express written consent of the Committee, and provided the
Optionee does not receive any consideration in any form whatsoever for such
transfer other than the receipt of an interest in the trust, partnership or
limited liability company to which the Option is transferred. Upon any such
transfer of the Option, the Option shall continue to be subject to the terms and
conditions as were applicable to the Option immediately prior to the transfer
thereof. Except as expressly provided in the first sentence of this Section 8,
the Option is not assignable or transferable by the Optionee, either voluntarily
or by operation of law, otherwise than by will or by the laws of descent and
distribution, and is exercisable, during the Optionee's lifetime, only by the
Optionee.

         9.       No Stockholder Rights. The Optionee or other person entitled
to exercise the Option shall have no rights or privileges as a stockholder with
respect to any Shares subject hereto until the Optionee or such person has
become the holder of record of such Shares, and no adjustment (except such
adjustments as may be effected pursuant to the provisions of Section 6 hereof)
shall be made for dividends or distributions of rights in respect of such Shares
if the record date is prior to the date on which the Optionee or such person
becomes the holder of record.

         10.      Investment Representation. The Optionee hereby represents that
the Option and any Shares purchased hereunder are being acquired for the
Optionee's own account and not with a view to or for sale in

                                      -5-

<PAGE>

connection with any distribution thereof except as may be permitted by the
Securities Act of 1933, as amended, and the rules and regulations promulgated
thereunder.

         11.      Conditions to Issuance of Shares. THE COMPANY'S OBLIGATION TO
ISSUE OR DELIVER SHARES OF ITS COMMON STOCK UPON EXERCISE OF THE OPTION IS
EXPRESSLY CONDITIONED UPON THE COMPLETION BY THE COMPANY OF ANY REGISTRATION OR
OTHER QUALIFICATION OF SUCH SHARES UNDER ANY STATE AND/OR FEDERAL LAW OR RULINGS
OR REGULATIONS OF ANY GOVERNMENT REGULATORY BODY OR THE MAKING OF SUCH
INVESTMENT REPRESENTATIONS OR OTHER REPRESENTATIONS AND AGREEMENTS BY THE
OPTIONEE (OR ANY PERSON ENTITLED TO EXERCISE THE OPTION) IN ORDER TO COMPLY WITH
THE REQUIREMENTS OF ANY EXEMPTION FROM ANY SUCH REGISTRATION OR OTHER
QUALIFICATION OF SUCH SHARES WHICH THE COMMITTEE SHALL, IN ITS SOLE DISCRETION,
DEEM NECESSARY OR ADVISABLE. SUCH REQUIRED REPRESENTATIONS AND AGREEMENTS MAY
INCLUDE REPRESENTATIONS AND AGREEMENTS THAT THE OPTIONEE, OR ANY OTHER PERSON
ENTITLED TO EXERCISE THE OPTION, (A) IS NOT PURCHASING SUCH SHARES FOR
DISTRIBUTION AND (B) AGREES TO HAVE PLACED UPON THE FACE AND/OR REVERSE OF ANY
CERTIFICATES FOR SUCH SHARES A LEGEND SETTING FORTH ANY REPRESENTATIONS AND
AGREEMENTS WHICH HAVE BEEN GIVEN TO THE COMMITTEE OR A REFERENCE THERETO AND
STATING THAT, PRIOR TO MAKING ANY SALE OR OTHER DISPOSITION OF ANY SUCH SHARES,
THE OPTIONEE, OR ANY OTHER PERSON ENTITLED TO EXERCISE THE OPTION, WILL GIVE THE
COMPANY NOTICE OF INTENTION TO SELL OR DISPOSE OF THE SHARES NOT LESS THAN FIVE
DAYS PRIOR TO SUCH SALE OR DISPOSITION.

         12.      Optionee Subject to Section 16. If the Optionee is a person
subject to Section 16 of the Securities Exchange Act of 1934, as amended, and if
for any reason the Option has not been approved in the manner provided for in
clause (d)(1) or (d)(2) of Rule 16b-3 of the Securities and Exchange Commission,
neither the Option (except upon its exercise) nor the Common Stock underlying
the Option may be disposed of by the Optionee until six months have elapsed
following the date of grant of the Option, unless the Committee otherwise
specifically permits such disposition.

         13.      Method of Acceptance. This Agreement is addressed to the
Optionee in duplicate and shall not be effective until the Optionee executes the
acceptance below and returns one copy to the Company, thereby acknowledging that
the Optionee has read and agreed to all the terms and conditions of this
Agreement and the Plan. The Optionee hereby acknowledges and agrees that the
acceptance of the Option constitutes satisfaction in full of any and all
pre-existing understandings or commitments between the Company and Optionee
relating to Optionee's right to acquire equity securities of the Company.

                                      -6-

<PAGE>

         14.      Plan Terms. The Option shall be subject to and governed by the
terms and provisions of the Plan, which by this reference are incorporated
herein. In the event of any conflict between the provisions of this Agreement
and the Plan, the Plan shall govern. All determinations and interpretations
thereof made by the Committee shall be conclusive and binding on all parties
hereto and upon their successors and assigns.

         EXECUTED as of the_______day of_______________________________

                                       AMERISTAR CASINOS, INC.

                                       By: _____________________________________

ACCEPTED:

_____________________________________________________          _________________
Signature of Optionee                                          Date

                                      -7-