FIRST AMENDMENT TO MORGANS LAS VEGAS, LLC LIMITED LIABILITY COMPANY AGREEMENT

Exhibit 10.4

FIRST AMENDMENT TO MORGANS LAS VEGAS, LLC

LIMITED LIABILITY COMPANY AGREEMENT

THIS FIRST AMENDMENT (“Amendment”) made effective as of the 15th day of May, 2006 (“Effective Date”), by and between MORGANS LAS VEGAS LLC, a Delaware limited liability company (“Morgans”), and ECHELON RESORTS CORPORATION, a Nevada corporation (“Boyd”). Morgans and Boyd may hereinafter be referred to singularly as a “Party” or “Member” or collectively as the “Parties” and the “Members”.

W I T N E S S E T H:

WHEREAS, Morgans and Boyd entered into a certain Limited Liability Company Agreement, dated January 3, 2006, for the formation of the Company (the “Operating Agreement”).

WHEREAS, each of the Members desire to enter into this Amendment to amend the Operating Agreement upon the terms and conditions hereinafter set forth.

NOW, THEREFORE, for and in consideration of the mutual promises of the Members and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Members agree as follows:

A. Incorporation of Recitals/Definitions. The foregoing recitals are hereby incorporated herein and made a part hereof as if fully set forth herein. Unless specifically defined herein, all defined terms used in this Amendment shall have the same meanings as those set forth in the Operating Agreement.

B. Operative Amendments.

1. Definitions. The following definitions are hereby added to the Operating Agreement:

“Hard Rock Property” shall mean, collectively, (a) that certain hotel casino property currently known as the “Hard Rock Hotel and Casino” and located at 4455 Paradise Road, Las Vegas, Nevada 89109, comprised of, but not necessarily limited to, Clark County Assessor’s Parcel Numbers 162-22-202-001, 002, and 003, 162-22- 103-004, 162-21-504-005, 162-21-602-002, 003, (b) any expansions of such hotel casino property and improvements, and (c) other adjacent or otherwise related properties and assets to be acquired by Morgans or a Morgans Affiliate.

“Non-Recourse Financing” shall mean, in this instance, loan financing pursuant to which neither Morgans Parent nor any of its Affiliates, shall have any financial or credit obligations or any related liability to any lender or other third party, related to any capital contributions or payment or credit support arising from or related to such financing of the Hard Rock Property (other than carve-outs and exceptions that may be reasonably customary for non-recourse financings).

2. Collateral for Funding Obligations and Commitments. The following new Section 5.09 is hereby added to the Operating Agreement:

Section 5.09. Morgans Collateral and Failure to Proceed.

(a) Upon the closing of the acquisition by Morgans or a Morgans Affiliate of the Hard Rock Property, Morgans agrees to wire transfer to Boyd, into a segregated account designated by Boyd, a cash deposit in the amount of Thirty Million Dollars ($30,000,000) (the “Deposit”), and such Deposit shall be maintained in such account by Boyd and shall be retained or applied by Boyd, or refunded to Morgans, in accordance with this Section 5.09. As consideration for Boyd’s agreement with respect to the acquisition of the Hard Rock Property (as permitted by Section 8.05(b) of the Operating Agreement, as amended pursuant to this Amendment), Boyd shall have the right to retain and shall have no obligation to return or otherwise reimburse to Morgans the amount of the Deposit upon the occurrence of any of the following: (i) Morgans fails to satisfy any of its financial commitments contained in this Operating Agreement following written notice from Boyd and the expiration of any applicable cure period set forth in the Operating Agreement and the Hotel Management Agreement, including, without limitation, any obligation to fund a Capital Contribution or Cost Overruns, and/or (ii) the Contribution Date does not occur prior to the Outside Start Date (“Contribution Date Passage”) due to a breach by Morgans of its obligations under the Operating Agreement and/or the Hotel Management Agreement following written notice from Boyd and expiration of all applicable cure periods set forth in the Operating Agreement (the occurrence of either (i) or (ii) above shall hereinafter be referred to as a “Morgans Default”). In the event that the Contribution Date shall occur in accordance with this Operating Agreement, then the amount of the Deposit shall be applied by Boyd against the Morgans Capital Commitment required to be contributed by Morgans on such date. The parties agree that the Contribution Date Passage date shall be extended day for day as a result of any decision by Boyd, made prior to the Outside Start Date, to delay the commencement of construction and/or pre-construction activities of a material portion of Echelon Place (excluding the Hotels, to the extent caused by a breach of Morgans as set forth above) beyond June 30, 2008. Morgans and Boyd each agree to proceed at all times in good faith in connection with the pre-development of the Hotels pursuant to the Operating Agreement.

(b) Notwithstanding Section 4.03 or any other provision of the Operating Agreement to the contrary, in the event of a Morgans Default, Boyd shall have the exclusive right to use at Echelon Place (and Morgans shall not use within the greater Las Vegas metropolitan area, including, but not limited to, Clark County, Nevada), without payment of any fee or any other compensation to the Company or to Morgans or any of its Affiliates, (i) the plans, specifications, reports, test results or other work product prepared in connection with the Project for Boyd to use in its construction of the Hotels on the Land or anywhere else within Echelon Place, and (ii) for the period of time commencing on the date of the Contribution Date Passage or the dissolution of the Company as set forth above through December 31, 2055, the names “Delano Las Vegas” and “Mondrian Las Vegas”, and other marks and names that are derivative from such names, pursuant to the brand standards for the Delano and Mondrian brands in effect

-2-

from time to time and pursuant to other customary non-monetary terms and conditions for licensing arrangements of this type.

(c) Notwithstanding anything to the contrary contained in the Operating Agreement or the Hotel Management Agreement, the Members agree that in the event of a Morgans Default, Boyd may, in its sole discretion, terminate the Hotel Management Agreement, and neither the Company nor any Member or Affiliate of such Member, shall have any other rights or obligations thereunder.

(d) Morgans agrees that to the extent a dispute arises between the Members under the Operating Agreement or Hotel Management Agreement relating to or arising from the use of the Morgans brand names by Boyd, as set forth above in Section 5.09(b) above, Boyd shall continue to have the right to (i) use the Morgans Brand Names for the Hotels, during the pendency of such dispute in accordance with such Section 5.09(b), and (ii) use the plans and specifications and other materials referenced in Section 5.09(b)(i) above, regardless of the outcome of such dispute; provided, however, that to the extent that it is determined by a court of law, with proper jurisdiction over the dispute, that Boyd does not have a right to use the Brand Names, the use of such Brand Names shall be discontinued by Boyd in accordance with such ruling or finding, as of that date, in connection with Boyd’s development, construction, and/or operation of the Hotels.

(e) Boyd agrees that its rights under Section 5.09(a) and (b) shall be deemed terminated and void upon the occurrence of any of the following on or prior to the date of the Contribution Date Passage: (w) any sale or other disposition or conveyance by Boyd or a Boyd Affiliate of (i) the Land or a material portion thereof, or its direct or indirect interests therein or (ii) its ownership interest in substantially all of the land on which Echelon Place is to be built, if such sale or other disposition, as contemplated under sections (i) and (ii) above, is made to a third party, but which shall not include an entity that is a Boyd Affiliate or a Boyd Controlled Affiliate, provided that nothing in this clause (w) is intended to, or shall have the effect of, granting to Boyd any rights with respect to the direct or indirect transfer of the Land or Boyd’s interests therein beyond Boyd’s rights as currently set forth in the Operating Agreement (without giving effect to this Amendment), (x) the occurrence of the Contribution Date Passage for any reason other than a Morgans Default, (y) a merger, sale, consolidation or other transaction (or series of transactions) shall occur resulting in the change of the direct or indirect ownership of 50% or more of the outstanding common stock of Boyd Parent, other than (i) through the trading of publicly held securities in the ordinary course or (ii) as a result of transfers between and among family members of William S. Boyd, including estate planning related transfers, or (z) the acquisition by Boyd of the Morgans Interest pursuant to Section 12.05 of the Operating Agreement. Upon the occurrence of any such event described in this Section 5.09(e), Boyd shall not have the right to retain, and shall promptly return or otherwise reimburse to Morgans, the amount of the Deposit and Boyd shall have no rights under Section 5.09(b) above.

(f) The obligations of Boyd under this Section 5.09 shall be guaranteed by the Boyd Parent.

-3-

(g) The obligations of Morgans under this Section 5.09 shall be guaranteed by the Morgans Parent.

3. Duties and Conflicts. The following sentence shall be added at the end of Section 8.05(b) of the Operating Agreement:

“Notwithstanding anything in this Section 8.05(b), the provisions of this subsection shall not apply to any acquisition, investment, management, development or other activity described in the preceding sentence by Morgans or any Morgans Affiliate in, at (or of) the Hard Rock Property. In addition, the provisions of Section 3.5 of the Hotel Management Agreement shall not be applicable to the Hard Rock Property, and the Hotel Management Agreement shall be deemed to be amended by this sentence in accordance with Section 22.13 of the Hotel Management Agreement.”

4. Additional Representation and Covenant. As a material inducement to Boyd to enter into this Amendment, Morgans represents, warrants and covenants with Boyd that any financing obtained in connection with the acquisition of the Hard Rock Property shall be Non-Recourse Financing with respect to Morgans Parent and any of its Affiliates.

C. Effective Upon Hard Rock Closing. Notwithstanding anything in this Amendment to the contrary, this Amendment shall only be effective upon, and shall have no force or effect prior to, the closing by a Morgans Affiliate of the acquisition of the Hard Rock Property. If, prior to the date of the Contribution Date Passage, the agreement of a Morgans Affiliate to acquire the Hard Rock Property shall terminate and if Morgans shall notify Boyd in writing of such termination, then this Amendment shall thereafter be null, void and of no force or effect.

D. Counterparts. This Amendment may be executed in one or more counterparts, each of which shall be deemed to be the same document. The provisions of this Amendment shall survive any termination or dissolution of the Company.

E. No Other Amendments. Except as specifically amended hereby, all of the other terms and conditions of the Operating Agreement remain in full force and effect in accordance with its terms.

F. Governing Law. All questions concerning the construction, validity, and interpretation of this Amendment will be governed by and construed in accordance with the internal law (and not the law of conflicts) of Delaware.

[SIGNATURE PAGE FOLLOWS]

-4-

IN WITNESS WHEREOF, the Parties have executed this Amendment as of the day and year first above set forth.

[Signatures Continue on Next Page]

-5-

[Signatures Continued]

[Signatures Continue on Next Page]

-6-

[Signatures Continued]

-7-