Exhibit 2.1(b)

AMENDMENT NO. 1 TO STOCK PURCHASE AGREEMENT

AMENDMENT NO. 1 TO STOCK PURCHASE AGREEMENT (this “Amendment”), dated as of June 25, 2004, by and among HARRAH’S OPERATING COMPANY, INC., a Delaware corporation (“HOC”), HORSESHOE GAMING HOLDING CORP., a Delaware corporation (the “Company”), and Jack B. Binion (the “Sellers’ Representative”).  Capitalized terms used herein and not otherwise defined shall have the respective meanings assigned to them in the Stock Purchase Agreement dated as of September 10, 2003, by and among Harrah’s Entertainment, Inc., a Delaware corporation (“Parent”), the Company and the parties listed on Exhibit A thereto, as subsequently assigned by Parent to HOC (the “Stock Purchase Agreement”).

RECITALS

WHEREAS, the Stock Purchase Agreement provides that immediately prior to Closing all Options and SARs shall be cancelled, that no Options or SARs shall remain outstanding following Closing and that all plans relating to Options and SARs shall be terminated; and

WHEREAS, the Stock Purchase Agreement provides that the holders of SARs (all Options terminate by their terms) are to be paid the portion of the consideration for the sale to which they are entitled at the Closing based upon estimates of the consideration for the sale less $50 million as an estimate of expenses incurred and to be incurred by the Company and the Sellers’ Representative in connection with the sale and other Liabilities of the Company and the Sellers’ Representative (the “$50 Million Deduction”); and

WHEREAS, the Company and the Sellers desire to eliminate the $50 Million Deduction from the calculation of the Equity Spreads and to pay the Equity Spreads based on the Estimated Transaction Consideration and subject to all the adjustments set forth in Section 2.1 of the Stock Purchase Agreement other than the $50 Million Deduction.

NOW, THEREFORE, in consideration of the foregoing and the respective representations, warranties, covenants and agreements set forth in this Amendment and intending to be legally bound hereby, the parties hereto agree as follows:

1.             Amendment.  The Stock Purchase Agreement shall be amended as follows:

(a)           Section 1.3(b) of the Stock Purchase Agreement shall be amended and restated in its entirety as follows:

“Allocation.  The Total Transaction Consideration, when and as received, less the Equity Spreads (but only if the Equity Spreads are being paid by the Sellers’ Representative out of the Closing Payment and not by the Company immediately prior to the Closing), the Sellers’ Tax Cost and the Severance Escrow, shall be allocated among the Sellers holding Shares of Class A Common Stock and/or Class B Common Stock on an equal per share basis, as evidenced by a certificate signed by the Sellers’ Representative in the form set forth as Schedule 1.3(b) hereto (the “Sellers’ Representative Certificate”), certifying as to the allocation of the Total Transaction

Consideration.  The Sellers’ Tax Cost that is attributable to a Seller shall be allocated to such Seller.”

(b)           Section 1.3(c) of the Stock Purchase Agreement shall be amended and restated in its entirety as follows:

“Equity Spreads.  The holders of Options and SARs shall collectively be entitled to the Equity Spreads and in the amount set forth on Schedule 2.1.  The Equity Spreads shall be allocated among the holders of Options and SARs based on the equity spread for each such Option or SAR, as evidenced by the Sellers’ Representative Certificate (subject to Section 2.1 hereof).  The amount of the Equity Spreads shall, pursuant to Section 2.1, either be paid by the Company immediately prior to the Closing or be included within the Total Transaction Consideration and paid by the Sellers’ Representative concurrently with the Closing and nothing in this Agreement shall be interpreted to require Parent to make an additional payment to the holders of SARs and/or Options.”

(c)           Section 2.1 of the Stock Purchase Agreement shall be amended and restated in its entirety as follows:

“The Company Equity Plans.  Prior to the Closing, the Board of Directors of the Company (the “Company Board”) (or, if appropriate, any committee thereof) shall adopt appropriate resolutions, amend such plans and take all other actions necessary and appropriate to provide that, immediately prior to the Closing, each unexpired and unexercised option or similar rights to purchase Company Common Stock (the “Options”) or “stock appreciation right” (the “SARs”), under any stock option plan or stock appreciation right plan of the Company, including without limitation the Company Equity Incentive Plan dated as of January 1, 1999, or any other plan, agreement or arrangement (the “Company Equity Plans”), whether or not then exercisable or vested, shall be cancelled and, in exchange therefor, each former holder of any such cancelled Option or SAR shall be entitled to receive from the Company in cancellation thereof a payment in cash (subject to applicable Income Tax withholding, and other Taxes required by applicable Law to be withheld) in an amount equal to (i) the excess of (A) an amount equal to (1) the sum of (x) $915,000,000, plus the estimate of the Capital Expenditure Amount pursuant to Section 1.3(d), plus an amount equal to the estimated cash and cash equivalents on hand of the Company at the Beginning of the Closing Gaming Day prior to the payment of the Equity Spreads, less the amount of the payments made to employees of the Acquired Companies pursuant to Section 6.16(c), plus (y) the sum of the aggregate per share strike price of each SAR (as defined or specified in the agreement evidencing such SAR), divided by (2) the sum of (x) the total number of shares of Class A Common Stock and Class B Common Stock outstanding on the Closing Date plus (y) the number of shares of Company Common Stock subject to SARs, over (B) the aggregate strike price of such SAR, multiplied by (ii) the number of shares of the Company Common Stock subject to such cancelled Option or cancelled SAR (such amount in the aggregate is referred to herein as the “Equity Spreads”); provided, however, that a holder of a SAR which has been issued in tandem with an Option shall receive the Equity Spread with respect to the SAR only and not the Option.  The amount of the Equity Spreads is set forth on Schedule 2.1.  The Equity Spreads shall be paid by the Company immediately prior to the Closing out of the Company’s cash (and such payment shall be taken into account in calculating the Cash Adjustment Amount) or, at the option of the Company, shall be paid by the Sellers’

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Representative on behalf of the Company in cash concurrently with the Closing, and shall be paid from the Closing Payment.  From and after the Closing, there shall be no outstanding and exercisable Options or SARs.  The Company Equity Plans and any and all other agreements, plans, programs or arrangements of the Company and its Subsidiaries that provide for the issuance or grant of Options or SARs or any other interest in respect of the capital stock of the Company or capital stock of or other ownership interest in any of its Subsidiaries shall terminate as of the Closing.  Immediately following the Closing, no holder of an Option or SAR or any participant in the Company Equity Plans or any other agreement, plan, program or arrangement of the Company shall have any right thereunder to acquire equity securities or other ownership interests of the Company or any Subsidiary thereof.”

(d)           Schedule 2.1 of the Stock Purchase Agreement shall be amended and restated in its entirety as set forth on Exhibit A attached hereto.

2.             Miscellaneous.

(a)           Reference to and Effect on the Stock Purchase Agreement.  This Amendment modifies the Stock Purchase Agreement to the extent set forth herein, is hereby incorporated by reference into the Stock Purchase Agreement and is made a part thereof.  Except as specifically amended by this Amendment, the Stock Purchase Agreement shall remain in full force and effect and is hereby ratified and confirmed.  The execution, delivery and performance of this Amendment shall not constitute a waiver of any provision of, or operate as a waiver of any right, power or remedy of the parties to the Stock Purchase Agreement.

(b)           Headings.  The headings contained in this Amendment are for reference purposes only and shall not affect in any way the meaning or interpretation of this Amendment.

(c)           Entire Agreement; No Third Party Beneficiaries.  This Amendment, the Stock Purchase Agreement and all documents and instruments referred to herein constitute the entire agreement and supersede all prior agreements and understandings, both written and oral, among the parties with respect to the subject matter hereof; provided that the Confidentiality Agreement shall remain in full force and effect until the Closing.

(d)           Severability.  If any term or other provision of this Amendment is invalid, illegal or incapable of being enforced by any rule of Law or public policy, all other conditions and provisions of this Amendment shall nevertheless remain in full force and effect so long as the economic or legal substance of the transactions contemplated hereby is not affected in any manner materially adverse to any party.  Upon such determination that any term or other provision is invalid, illegal or incapable of being enforced, the parties hereto shall negotiate in good faith to modify this Amendment so as to effect the original intent of the parties as closely as possible in an acceptable manner to the end that transactions contemplated hereby are fulfilled to the extent possible.

(e)           Governing Law; Consent to Jurisdiction; Waiver of Trial by Jury.

(i)            This Amendment and all disputes between the parties under or related to the Amendment or the facts and circumstances leading to its execution, whether in contract, tort or otherwise, shall be governed by and construed in accordance with the Laws of

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the State of New York, applicable to contracts executed in and to be performed entirely within the State of New York.

(ii)           Each of the parties hereto hereby irrevocably and unconditionally submits, for itself and its property, to the exclusive jurisdiction of any New York State court, or Federal court of the United States of America, sitting in New York, and any appellate court from any thereof, in any action or proceeding arising out of or relating to this Amendment or for recognition or enforcement of any judgment relating thereto, and each of the parties hereby irrevocably and unconditionally (A) agrees not to commence any such action or proceeding except in such courts, (B) agrees that any claim in respect of any such action or proceeding may be heard and determined in such New York State court or, to the extent permitted by law, in such Federal court, (C) waives, to the fullest extent it may legally and effectively do so, any objection which it may now or hereafter have to the laying of venue of any such action or proceeding in any such New York State or Federal court, (D) waives, to the fullest extent permitted by law, the defense of an inconvenient forum to the maintenance of such action or proceeding in any such New York State or Federal court, and (E) to the extent such party is not otherwise subject to service of process in the State of New York, appoints Corporation Service Company, 80 State Street, Albany, NY 12207, as such party’s agent in the State of New York for acceptance of legal process and agrees that service made on any such agent shall have the same legal force and effect as if served upon such party personally within such state.  Each of the parties hereto agrees that a final judgment in any such action or proceeding shall be conclusive and may be enforced in other jurisdictions by suit on the judgment or in any other manner provided by law.  Each party to this Amendment irrevocably consents to service of process in the manner provided for notices in Section 10.3 of the Stock Purchase Agreement.  Nothing in this Amendment will affect the right of any party to this Amendment to serve process in any other manner permitted by law.

(iii)          EACH PARTY ACKNOWLEDGES AND AGREES THAT ANY CONTROVERSY WHICH MAY ARISE UNDER THIS AMENDMENT IS LIKELY TO INVOLVE COMPLICATED AND DIFFICULT ISSUES, AND THEREFORE IT HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES ANY RIGHT IT MAY HAVE TO A TRIAL BY JURY IN RESPECT OF ANY LITIGATION DIRECTLY OR INDIRECTLY ARISING OUT OF OR RELATING TO THIS AMENDMENT.  EACH PARTY CERTIFIES AND ACKNOWLEDGES THAT (A) NO REPRESENTATIVE, AGENT OR ATTORNEY OF ANY OTHER PARTY HAS REPRESENTED, EXPRESSLY OR OTHERWISE, THAT SUCH OTHER PARTY WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE EITHER OF SUCH WAIVERS, (B) IT UNDERSTANDS AND HAS CONSIDERED THE IMPLICATIONS OF SUCH WAIVERS, (C) IT MAKES SUCH WAIVERS VOLUNTARILY, AND (D) IT HAS BEEN INDUCED TO ENTER INTO THIS AMENDMENT BY, AMONG OTHER THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS IN THIS SECTION 2(e).

(f)            Counterparts.  This Amendment may be executed in one or more counterparts, and by the different parties hereto in separate counterparts, each of which when executed shall be deemed to be an original but all of which taken together shall constitute one and the same agreement.

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IN WITNESS WHEREOF, the undersigned have caused this Amendment to be signed by their respective duly authorized officers as of the date first written above.