<PAGE>

                                                                   Exhibit 10.13

                                 GREY WOLF, INC
               AMENDMENT TO NON-QUALIFIED STOCK OPTION AGREEMENTS
                                  [TPR - FORM]

                                November 13, 2001


         THIS AMENDMENT TO NON-QUALIFIED STOCK OPTION AGREEMENT (this
"Agreement") is by and between Grey Wolf, Inc. (the "Corporation"), a Texas
Corporation, and Thomas P. Richards (the "Optionee"), and is an amendment to all
of those certain Non-Qualified Stock Option Agreements entered into by and
between the Corporation and the Optionee as more particularly described on
Exhibit "A" hereto (the "Original Option Agreements") pursuant to the
Corporation's 1996 Employee Stock Option Plan dated effective July 29, 1996 (the
"Plan").

         WHEREAS, the Corporation granted certain options to Optionee under the
Plan as more particularly described on Exhibit "A" hereto; and

         WHEREAS, the Board of Directors of the Corporation has approved certain
changes to the Original Option Agreements in this Agreement pursuant to that
certain Consent of Directors dated November 13, 2001; and

         WHEREAS, the Corporation and the Optionee deem it desirable, for and in
the best interests of the parties to this Agreement, to modify the Original
Option Agreements as provided herein.

         NOW THEREFORE BE IT RESOLVED, that the Corporation and the Optionee do
hereby agree to amend the Original Option Agreements as follows:

         1. Corporate Proceedings of the Corporation. Section 9(b) and 9(c) of
the Original Option Agreements shall be deleted in their entirety and the
following new Sections 9(b) and 9(c) substituted therefor and new Section 9(f)
shall be added:

                  "9. Corporate Proceedings of the Corporation.

                           (b) If the Corporation merges into or with or
                  consolidates with (such events collectively referred herein as
                  a "Merger") any corporation or corporations and is not the
                  surviving corporation, then the Corporation shall cause the
                  surviving corporation to assume the Option or substitute a new
                  option of the surviving corporation for the Option (with an
                  Exercise Period at least equal to the period remaining until
                  the Expiration Date for the Option). In the event that the
                  Option is assumed or a new option of the surviving corporation
                  is substituted for the Option (i) if, on the effective date of
                  the Merger, the Option is "in the money" the excess of the
                  aggregate fair market value of the shares subject to the
                  Option immediately after such assumption, or the new option
                  immediately after such substitution, over the aggregate
                  Exercise Price of such shares must be, based upon a good faith
                  determination by the Board of Directors of the Corporation,
                  not less than the excess of the aggregate fair market value of
                  the Common Stock subject to the Option
<PAGE>
                  immediately before such substitution or assumption over the
                  aggregate Exercise Price of such Common Stock and (ii) if, on
                  the effective date of the Merger, the Option is "out of the
                  money" the excess of the aggregate Exercise Price of the
                  shares subject to the Option immediately after such
                  assumption, or the new option immediately after such
                  substitution over the fair market value of such shares must
                  be, based upon a good faith determination by the Board of
                  Directors of the Corporation, not more than the excess of the
                  aggregate Exercise Price of the Common Stock subject to the
                  Option immediately before such assumption or substitution over
                  the aggregate fair market value of such Common Stock.

                           (c) In the event of a dissolution or liquidation of
                  the Corporation, the Corporation shall cause written notice of
                  such dissolution or liquidation (and the material terms and
                  conditions thereof) to be delivered to the Optionee at least
                  ten (10) days prior to the proposed effective date (the
                  "Effective Date") of such event. The Optionee shall be
                  entitled to exercise the Option (as to all Option Shares,
                  whether or not the Option is then otherwise exercisable under
                  Section 2) until the Effective Date, or until the Expiration
                  Date if earlier. Any Option which has not been exercised on or
                  before the Effective Date shall terminate.

                           (f) In the event that neither the shares of stock of
                  the Corporation nor shares of stock of the surviving
                  corporation are listed on an established exchange as a result
                  of a "going private" transaction, the Fair Market Value of the
                  Option (as to all Option Shares, whether or not the Option is
                  then exercisable under Section 2) shall be determined as soon
                  as practicable after completion of the "going private"
                  transaction. Optionee shall be paid the Fair Market Value of
                  such Option by cashiers check or wire transfer of immediately
                  available funds within ten (10) days after the determination
                  of such Fair Market Value. The Option shall terminate upon
                  receipt of such payment by the Optionee. For purposes of this
                  Section 9(f), the "Fair Market Value" of the Option purchased
                  shall be determined as follows: (i) If the Optionee and the
                  Corporation can agree on the Fair Market Value of the Option
                  within fifteen (15) days following completion of the going
                  private transaction, the Fair Market Value will be the agreed
                  value of the Option; (ii) If the Optionee and Corporation
                  cannot agree on the Fair Market Value of the Option, the value
                  will be determined as follows: (1) Each party shall, within
                  thirty (30) days following completion of the going private
                  transaction, provide written notice of the appointment of an
                  appraiser to the other party. If the parties appoint the same
                  appraiser or if only one appraiser is timely appointed, then
                  the timely appointed appraiser shall be the only appraiser and
                  shall prepare and deliver the appraised value of the Option
                  taking into consideration the "Black-Scholes" method of
                  valuation of such Option within thirty (30) days following its
                  appointment; (2) If the parties each timely appoint different
                  appraisers, such appraisers shall agree upon a third appraiser
                  within fifteen (15) days following their appointment. If such
                  appraisers cannot agree upon a third appraiser within fifteen
                  (15) days following their appointment, either the Optionee or
                  the Corporation may petition any United States federal
                  district court in the Southern District of Texas to appoint
                  such appraiser; (3) Each appraiser shall complete his
                  appraisal of the Option taking into consideration the
                  "Black-Scholes" method of valuation of such Option and deliver
                  a copy of his written appraisal to the Optionee

                                       2
<PAGE>
                  and the Corporation within thirty (30) days of such
                  appraiser's appointment; (4) If there is more than one
                  appraiser, the Fair Market Value shall be the mathematical
                  average of the two closest appraisals; (5) Each appraiser
                  appointed hereunder shall have been actively involved in the
                  business of valuing and appraising companies in the oil and
                  gas service industry for the five year period immediately
                  preceding the date of appointment; and (6) The parties
                  understand and agree that the value of the Option is dependent
                  upon a valuation of the Corporation and that the appraisers
                  shall have access to the business records, assets and
                  properties of the Corporation as they may reasonably request
                  for the purpose of appraising the value of the Option."

         2. Termination. Section 11 of the Original Option Agreements shall be
deleted in their entirety and the following new Section 11 substituted therefor:

                           "11. Termination. Except as otherwise provided in
                  this Section 11, if the Optionee for any reason whatsoever
                  ceases to be employed by the Corporation, or a parent or
                  subsidiary corporation of the Corporation, and prior to such
                  cessation, the Optionee was employed at all times from the
                  date of the granting of the Option until the date of such
                  cessation, the Option shall be exercisable by the Optionee
                  (whether previously exercisable or not) at any time on or
                  before the Expiration Date. Notwithstanding the foregoing:

                           (a) If the Optionee is terminated for Cause (as
                  defined below), the Option will terminate as to all of the
                  unexercised Option Shares on the thirtieth day following such
                  termination, during which thirty (30) days the Optionee may
                  exercise the Option as to the Option Shares exercisable on or
                  prior to the date of such termination for Cause; provided,
                  however, no unvested Option shall vest during such thirty (30)
                  day period; and

                           (b) If the Optionee's employment is terminated as a
                  result of a voluntary resignation (which is neither a
                  termination without cause nor a constructive termination
                  without cause as described in the Optionee's employment
                  agreement with the Corporation) the Optionee may exercise the
                  Option as to all of the Option Shares as provided above in
                  this Section 11; provided that no unvested Option shall vest
                  as a result of such voluntary resignation or thereafter.

                           For purposes of this Agreement, the term "Cause"
                  shall mean and include (i) chronic alcoholism or controlled
                  substance abuse as determined by a doctor mutually acceptable
                  to the Corporation and the Optionee, (ii) an act of proven
                  fraud or dishonesty on the part of the Optionee with respect
                  to the Corporation or its subsidiaries; (iii) knowing and
                  material failure by the Optionee to comply with material
                  applicable laws and regulations relating to the business of
                  the Corporation or its subsidiaries; (iv) the Optionee's
                  material and continuing failure to perform (as opposed to
                  unsatisfactory performance) his duties to the Corporation
                  except, in each case, where such failure is caused by the
                  illness or other similar incapacity or disability of the
                  Optionee; or (v) conviction of a crime involving moral
                  turpitude or a felony. Prior to the effectiveness of
                  termination for Cause under subclause (i), (ii), (iii) or (iv)
                  above, the Optionee shall be given thirty (30) days prior
                  notice from the

                                       3
<PAGE>
                  Board specifically identifying the reasons which are alleged
                  to constitute Cause hereunder and an opportunity to be heard
                  by the Board in the event Optionee disputes such allegations.

                           Nothing in (a) or (b) shall extend the time for
                  exercising the Option granted pursuant to the Original Option
                  Agreements beyond the Expiration Date."

         3. In all other respect, the terms and provisions of the Original
Option Agreements are hereby reaffirmed by the Corporation and the Optionee.

         IN WITNESS WHEREOF, the parties have executed this Amendment to
Non-Qualified Stock Option Agreements as of the date first above written.

                                  GREY WOLF, INC.


                                  By:
                                     --------------------------------
                                  Name:   STEVEN A. WEBSTER
                                  Title:  CHAIRMAN, COMPENSATION COMMITTEE
                                          BOARD OF DIRECTORS


                                  THOMAS P. RICHARDS


                                  -----------------------------
                                  Title:  PRESIDENT AND CHIEF EXECUTIVE OFFICER


                                        4
<PAGE>
                                   EXHIBIT "A"
                                       TO
                                 GREY WOLF, INC.
               AMENDMENT TO NON-QUALIFIED STOCK OPTION AGREEMENTS

                                NOVEMBER 13, 2001


<TABLE>
<CAPTION>
                                                               NUMBER OF OPTIONS
     OPTIONEE           DATE OF ORIGINAL OPTION AGREEMENTS          GRANTED
     --------           ----------------------------------          -------
<S>                     <C>                                    <C>
Thomas P. Richards            March 5, 1998                         147,700
                              February 15, 1999                     500,000
                              February 24, 2000                     400,000
                              February 9, 2001                      400,000
                                                                    -------
               TOTAL OUTSTANDING                                  1,447,700
</TABLE>