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                                                                   EXHIBIT 10.29


                            HORSESHOE GAMING, L.L.C.

                              UNIT OPTION AGREEMENT

         THIS UNIT OPTION AGREEMENT (this "Agreement") is entered into as of
February 1, 1997 by and between Horseshoe Gaming, L.L.C. (the "Company") and
Clifford D. Kortman ("Optionee") pursuant to the Company's 1997 Unit Option Plan
(the "Plan"). All capitalized terms not otherwise defined herein shall have the
meaning set forth in the Plan.


                                    RECITALS

         A. The Company considers it desirable to give Optionee an incentive to
advance the Company's interest through the opportunity to acquire an equity
interest and thus participate in the Company's growth, development and financial
success.

         B. The Company has determined to grant Optionee the right to purchase
Units pursuant to the terms and conditions of this Agreement.


                                    AGREEMENT

         NOW, THEREFORE, in consideration of the covenants hereinafter set
forth, the parties agree as follows:

         1. Option; Number of Units. The Company hereby grants to Optionee the
right (the "Option") to purchase up to 126,245 Units (the "Units") at a price of
$3.47 per Unit (the "Purchase Price"). The Option and the right to purchase all
or any portion of the Units are subject to the terms and conditions stated in
this Agreement and in the Plan, including, without limitation, the provisions of
Sections 4, 10, 13 (b), and 14 of the Plan and Sections 3 and 4 hereof. Upon
exercise of the Option, Optionee shall become a member of the Company, with the
rights and benefits, and subject to the terms and conditions, set forth in the
Company's Limited Liability Company Agreement and the Company's Limited
Liability Company Agreement shall (if necessary) be amended to so provide. The
Optionee agrees to comply with, and be subject to, the provisions of the
Company's Limited Liability Company Agreement and to do all acts required
thereunder.

         2. Vesting. The Option shall vest in three (3) equal annual
installments of 33 1/3% of the Units covered by the Option on each of the first
through third anniversaries of the date of Optionee's employment with the
Company pursuant to the Employment Agreement between the Company and Optionee
dated December 1, 1995, as amended by that certain First Amendment to


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Employment Agreement dated July 1, 1996. Notwithstanding the foregoing, in the
event Jack B. Binion (including any entities through which Jack B. Binion holds
his ownership interest in the Company), family members of Jack B. Binion and/or
trusts established for the benefit of his heirs transfer controlling interest in
the Company to a third party in a transaction other than a public offering, the
Option shall immediately become fully vested.

         3. Term of Option. Except for the rights conferred upon the Company
pursuant to Section 7 below, the Option, and Optionee's right to exercise the
Option, shall terminate when the first of the following occurs:

                  (a) termination pursuant to Section 13 (b) or Section 14 of
                  the Plan;

                  (b) the expiration of ten (10) years from the date hereof; or

                  (c) ninety (90) days after the date of termination of
                  Optionee's (i) employment or (ii) consulting relationship, as
                  applicable, with the Company and all of the Subsidiaries and
                  Related Entities, unless such termination results from
                  Optionee's death or disability (within the meaning of Section
                  105 (d) (4) of the Internal Revenue Code of 1986, as amended)
                  or Optionee dies within ninety (90) days after the date of
                  termination of Optionee's employment or consulting
                  relationship with the Company and all of the Subsidiaries and
                  Related Entities, in which case this Agreement and the Option
                  shall terminate 180 days after the date of termination of
                  Optionee's employment or consulting relationship with the
                  Company and all of the Subsidiaries and Related Entities.

         4. Termination of Employment. The termination for any reason of
Optionee's employment or consulting relationship with the Company and all of the
Subsidiaries and Related Entities shall not accelerate the vesting of the Option
or affect the number of Units with respect to which the Option may be exercised;
provided, however, that the Option may only be exercised with respect to that
number of Units which could have been purchased under the Option had the Option
been exercised by Optionee on the date of such termination and shall in all
events be subject to Section 3 hereof.

         5. Death of Optionee; No Assignment. The rights of Optionee under this
Agreement may not be assigned or transferred except by will, by the laws of
descent or distribution or inter vivos to a trust for the benefit of Optionee or
Optionee and Optionee's spouse and may be exercised during the lifetime of
Optionee only by such Optionee; provided, however, that in the event of
disability (within the meaning of Section 105 (d) (4) of the Internal Revenue
Code of 1986, as amended) of Optionee, a designee of Optionee (or the Optionee's
legal representative if Optionee has not designated anyone) may exercise the
Option on behalf of Optionee (provided the Option would have been exercisable by
Optionee) until the right to exercise the Option expires pursuant to Section 3
hereof. Any attempt to sell, pledge, assign, hypothecate, transfer or otherwise
dispose of the Option in contravention of this Agreement or the Plan shall be
void and shall have no effect. If Optionee should die while Optionee is engaged
in an employment or consulting relationship with the Company and/or any
Subsidiary or Related Entity, and provided 


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Optionee's rights hereunder shall have vested, in whole or in part, pursuant to
Section 2 hereof, Optionee's, designee, legal representative, or legatee, the
successor trustee of Optionee's inter vivos trust or the person who acquired the
right to exercise the Option by reason of the death of Optionee (individually, a
"Successor") shall succeed to Optionee's rights under this Agreement. After the
death of Optionee, only a Successor may exercise the Option.

         6. Exercise of Option. On or after the vesting of all or any portion of
the Option in accordance with Section 2 hereof and until termination of the
Option in accordance with Section3 hereof, the Option may be exercised by
Optionee (or such other person specified in Section 5 hereof) to the extend
exercisable as determined under Section 2 hereof, upon delivery of the following
to the Company at its principal executive offices:

                  (a) a written notice of exercise which identifies this
                  Agreement and states the number of Units to be purchased;

                  (b) a check, cash or an combination thereof in the amount of
                  the aggregate Purchase Price (or payment of the aggregate
                  Purchase Price in such other form of lawful consideration as
                  the Committee may approve from time to time under the
                  provisions of Section 7 of the Plan); Unless Optionee has
                  simultaneously, with such exercise of the Option, also
                  exercised his "put" right set forth in Section 13 hereinbelow,
                  in which case no consideration need be paid by Optionee, but
                  the exercise price shall be deducted from the proceeds to be
                  received by the Optionee upon determination of Fair Market
                  Value through agreement or completion of the appraisal process
                  set forth herein;

                  (c) unless the "put" right has been exercised by Optionee, a
                  written representation and undertaking, if requested by the
                  Company pursuant to Section 8 (b) hereof, in such form and
                  substance as the Company may require, setting forth the
                  investment intent of Optionee, or a Successor, as the case may
                  be, and such other agreements, representations and
                  undertakings as described in the Plan; and

                  (d) unless the "put right has been exercised by Optionee, such
                  further acts as may be necessary to admit Optionee as a member
                  of the Company, including becoming a party to the Company's
                  Limited Liability Company Agreement, as then in effect. 

         7. Representations and Warranties of Optionee.

                  (a) Optionee represents and warrants that the Option is being
                  acquired by Optionee for Optionee's personal account, for
                  investment purposes only, and not with a view to the
                  distribution, resale or other disposition thereof.

                  (b) Optionee acknowledges that the Company may issue Units
                  upon the exercise of the Option without registering or
                  qualifying such securities under federal or state securities
                  laws on the basis of certain exemptions from such registration
                  or qualification requirements. Accordingly, Optionee agrees
                  that Optionee's exercise of the Option may be expressly
                  conditioned upon Optionee's delivery to the Company of such
                  representations and undertakings as the 


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                  Company may reasonably require in order to secure the
                  availability of such exemptions, including a representation
                  that Optionee is acquiring the Units for investment and not
                  with a present intention of selling or otherwise disposing of
                  such Units. Optionee acknowledges that, because Units received
                  upon exercise of an Option may be unregistered, Optionee may
                  be required to hold the Units indefinitely unless they are
                  subsequently registered for resale under the Act or an
                  exemption from such registration is available.

                  (c) Optionee acknowledges that the Company's obligation to
                  issue the Units upon exercise of the Option is expressly
                  conditioned upon the compliance by the Company with any
                  registration or other qualification obligations with respect
                  to such Units under any state and/or federal law or rulings
                  and regulations of any government regulatory body, including
                  without limitation, any and all applicable gaming regulatory
                  authorities of the states in which the Company's Subsidiaries
                  operate or intend to operate, and/or the filing by Optionee of
                  any background applications required by such gaming
                  authorities.

                  (d) Optionee acknowledges receipt of this Agreement granting
                  the Option, and the Plan, and understands that all rights and
                  liabilities connected with the Option are set forth herein and
                  in the Plan, including without limitation, the Company's right
                  to repurchase from Optionee all Units acquired upon exercise
                  of the Option as provided in Section 13 hereof and in Section
                  20 of the Plan.

                  (e) Optionee acknowledges receipt of a copy of the Company's
                  Limited Liability Company Agreement, as in effect on the dates
                  hereof and understands that any Unit acquired by exercise of
                  the Option will be subject to the provisions of the Company's
                  Limited Liability Company Agreement applicable to all of the
                  Company's members, as in effect from time to time.

         8. No Rights As a Member. Optionee shall have no rights as a member in
connection with the Units covered by the Option until the date (the "Exercise
Date") an entry evidencing such ownership is made in the appropriate records of
the Company. Except as may be provided under Section 10 of the Plan, the Company
will make no adjustment for dividends (ordinary or extraordinary, whether in
cash, securities, or other property) or distributions or other rights for which
the record date is prior to the Exercise Date.

         9. This Agreement Subject to Plan. This Agreement is made under the
provisions of the Plan and shall be interpreted in a manner consistent with it.
To the extent that any provision in this Agreement is inconsistent with the
Plan, the provisions of the Plan shall control. A copy of the Plan is available
to Optionee at the Company's principal executive offices upon request and
without charge. The good faith interpretation of the Committee of any provision
of the Plan, the Option or this Agreement, and any determination with respect
thereto or hereto by the Committee, shall be final, conclusive and binding on
all parties.


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         10. Restrictive Legends. Optionee hereby acknowledges that federal
securities laws and the securities laws of the state in which Optionee resides
may require the placement of certain restrictive legends upon the Units issued
upon exercise of the Option, and Optionee hereby consents to the placing of any
such legends upon certificates evidencing the Units as the Company, or its
counsel, may reasonably deem necessary; provided, however, that any such legend
or legends shall be removed when no longer applicable.

         11. Notices. All notices, requests and other communications hereunder
shall be in writing and, if given by telegram, telecopy or telex, shall be
deemed to have been validly served, given or delivered when sent, if given by
personal delivery, shall be deemed to have been validly served, given or
delivered upon actual delivery and, if mailed, shall be deemed to have been
validly served, given or delivered three business days after deposit in the
United States mails, as registered or certified mail, with proper postage
prepaid and addressed to the party or parties to be notified, at the following
addresses (or such other address(es) as a party may designate for itself by like
notice):

                  If to the Company:
                  Horseshoe Gaming, L.L.C.
                  330 South Fourth Street
                  Las Vegas, NV  39101

                  If to Optionee:
                  Clifford D. Kortman
                  1722 Chestnut Grove Lane
                  Kingwood, TX 77345

         12. Not an Employment Agreement. Nothing contained in this Agreement
shall confer, intend to confer or imply any rights to an employment relationship
or rights to a continued employment relationship with the Company and/or any
Subsidiary or Related Entity in favor of Optionee or limit the ability of the
Company and/or any Subsidiary or Related Entity to terminate, with or without
cause, in its sole and absolute discretion, its employment relationship with
Optionee, subject to the terms of any written employment agreement to which
Optionee is a party.

         13. Put/Call Option Upon Termination. In the event of the termination
of Optionee's employment with Company, for whatever reason, then the Company
shall have the right to purchase (the "Call right") the Units of Optionee,
acquired pursuant to the terms of this Agreement, at the Fair Market Value of
such Units as determined pursuant to the terms of this Agreement (the "Purchase
Price"). In a similar fashion, Optionee shall have a right to require the
Company to purchase back his Units in the Company (the Put right") at the
Purchase Price. The Company or the Optionee, as the case may be, may exercise
their respective rights provided for in this Section 13 by tendering written
notice to the other party of its exercise of such right within thirty (30) days
after the termination of Optionee's employment an/or consulting relationship
with the Company. In the event that either right described herein should be
exercised by the Optionee or the Company, then the Optionee and the Company
agree to 


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promptly convene and attempt in good faith to determine the Fair Market Value of
the Units to be purchased by the Company from Optionee. In the event that the
Company and the Optionee are unable to agree upon such Fair Market Value, then
the parties hereto agree to submit such matter to an independent appraisal to be
conducted in Las Vegas, Nevada in accordance with the terms set forth below.
Either party may initiate such appraisal process by delivery of written notice
to the other party to such effect, designating the name of a appraiser that is
to represent it in such appraisal process. Thereafter, within ten (10) days of
receipt of such notice the other party shall designate an appraiser to represent
it in such process. Within ten (10) days after designation of the second
appraiser, the two appraisers shall convene and agree upon a third appraiser. In
the event that said two appraisers are unable to agree upon a third appraiser,
then the third appraiser shall be selected by lottery, with each appraiser to
submit the name of another reputable appraiser, and with the appraiser whose
name is drawn in such lottery being designated for all purposes as the third
appraiser.

Within ten (10) days after selection of the third appraiser, the three
appraisers shall convene and attempt to agree on the Fair market Value of the
Units to be purchased by the Company. If unable to agree, then each appraiser
shall, within thirty (30) days thereafter, prepare his own independent appraisal
report and such report shall be submitted to the Company and the Optionee.
Provided that the Middle appraisal is within ten percent (10%) of either the
high or low appraisal, then the middle appraisal (the highest and lowest
appraisals being disregarded) shall be deemed to be the Fair Market Value and
thus the valuation to be used for purposes of the Company's acquisition of
Optionee's Units.

In the event that the middle appraisal is not within ten percent (10%) of either
the high or low appraisal, then the determination of the Fair Market Value of
Optionee's Units shall be submitted to binding arbitration, to be conducted in
Las Vegas, Nevada pursuant to the then prevailing rules and regulations of the
American Arbitration Association. In such arbitration, each of the appraisers
shall be entitled to submit their appraisal report and testify on behalf of the
Company or the Optionee. The arbitration panel, after hearing all evidence
desired to be submitted by the Company and the Optionee, shall determine said
Fair Market Value and such decision by said arbitration panel shall be binding
upon the Company and the Optionee. The cost of the arbitration shall be borne
equally by the Company and the Optionee.

The Purchase Price to be paid by the Company, as determined by agreement or
appraisal as described herein, shall be paid in three (3) equal annual principal
installments, with the first payment being due within ten (10) days after
determination of or agreement as to Fair market Value, the second payment shall
be due and payable one (1) year thereafter, and the third payment shall be due
and payable two (2) years thereafter; provided, however, that if the Purchase
Price is less than $750,000 then the entire Purchase Price shall be paid to
Optionee in one lump sum within ten (10) days after determination or agreement
as to Fair Market Value.

Notwithstanding the foregoing , in the event that any of the Company's loan
agreements prohibit payment of the Purchase Price to be made over the period set
forth above, then the Optionee agrees that the Purchase Price shall be paid in
equal principal installments over the time period permitted by such loan
agreements, but in no event in excess of five (5) years, with such 


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principal payments to be made on an annual basis. In addition, such obligation
shall bear interest at the prime rate of interest, as quoted from time by the
largest commercial bank, in terms of assets, in the State of Nevada, and accrued
but unpaid interest shall be due and payable together with each annual principal
installment.

The Company and the Optionee agree that all persons chosen to represent them as
appraisers shall be qualified and competent MAI appraisers or a Certified public
Accountant with one of the "Big Six" accounting firms experienced in valuing
similar types of partnerships or corporations.

The Company shall bear the cost of its appraiser, the Optionee shall bear the
cost of its appraiser, and the Company and the Optionee shall each bear on-half
(1/2) of the cost of the third appraiser.

         14. Governing Law. This Agreement shall be construed under and governed
by the laws of the State of Delaware without regard to the conflict of law
provisions thereof.

         15. Counterparts. This Agreement may be executed in counterparts, each
of which shall be deemed an original and both of which together shall be deemed
one Agreement.










         IN WITNESS WHEREOF, the Company and Optionee have executed this
Agreement as of the date first above written.

                                    HORSESHOE GAMING, L.L.C.

                                    By:


                                    --------------------------------------------

                                    OPTIONEE



                                    --------------------------------------------
                                    CLIFFORD D. KORTMAN


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