Exhibit (a)(1)(D)

Offer to Purchase for Cash

All Outstanding Shares of Common Stock

of

Entertainment Gaming Asia Inc.

at

$2.35 Net Per Share

by

EGT Nevada Holding Inc.

a wholly owned indirect subsidiary of

Melco International Development Limited

THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT 5:00 P.M., NEW YORK CITY

TIME, ON JUNE 6, 2017, UNLESS THE OFFER IS EXTENDED.

May 5, 2017

To Brokers, Dealers, Commercial Banks, Trust Companies and Other Nominees:

EGT Nevada Holding Inc. (“Purchaser”), a Nevada corporation and a wholly owned indirect subsidiary of Melco International Development Limited (“Melco”), a Hong Kong-listed company, is offering to purchase all outstanding shares of common stock, par value $0.001 per share (individually, a “Share” and collectively, the “Shares”), of Entertainment Gaming Asia Inc. (“Entertainment Gaming”), a Nevada corporation, that are not already owned by Purchaser or its affiliates for $2.35 per Share, net to the seller in cash, without interest and less any applicable withholding taxes, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated May 5, 2017 (together with any amendments or supplements thereto, the “Offer to Purchase”), and the related letter of transmittal (together with any amendments or supplements thereto, the “Letter of Transmittal” and, together with the Offer to Purchase, the “Offer”) enclosed herewith.

Please furnish copies of the enclosed materials to those of your clients for whose accounts you hold Shares registered in your name or in the name of your nominee.

Enclosed herewith for your information and forwarding to your clients are copies of the following documents:

1. The Offer to Purchase dated May 5, 2017.

2. The Letter of Transmittal for your use in accepting the Offer and tendering Shares and for the information of your clients. Facsimile copies of the Letter of Transmittal may be used to tender Shares.

3. The Notice of Guaranteed Delivery to be used to accept the Offer if certificates representing Shares and all other required documents cannot be delivered to Continental Stock Transfer & Trust Company (the “Depositary”), or if the procedures for book-entry transfer cannot be completed, prior to the expiration of the Offer.

4. A letter that may be sent to your clients for whose accounts you hold Shares registered in your name or in the name of your nominee, with space provided for obtaining such clients’ instructions with regard to the Offer.

5. Internal Revenue Service Form W-9.

6. A return envelope addressed to the Depositary.

YOUR PROMPT ACTION IS REQUESTED. WE URGE YOU TO CONTACT YOUR CLIENTS AS PROMPTLY AS POSSIBLE. PLEASE NOTE THAT THE OFFER AND WITHDRAWAL RIGHTS EXPIRE AT 5:00 P.M., NEW YORK CITY TIME, ON JUNE 6, 2017, UNLESS THE OFFER IS EXTENDED.

As of the date of the Offer to Purchase, the board of directors of Entertainment Gaming has not made a recommendation regarding the Offer. Entertainment Gaming is required to make a recommendation or state that it is neutral or is unable to take a position with respect to the Offer, and to publish such recommendation or send it to Entertainment Gaming stockholders within 10 business days from the date of the Offer to Purchase.

There is no financing condition to the Offer. The Offer is conditioned upon, among other things, there being validly tendered and not properly withdrawn prior to the expiration of the Offer such number of Shares that (x) would represent at least a majority of the issued and outstanding Shares, excluding Shares owned by Purchaser or its affiliates and (y) when combined with the Shares currently owned by Purchaser and its affiliates, will constitute at least 90% of the outstanding Shares as of the date the Shares are accepted for payment pursuant to the Offer. The Offer is also subject to certain other conditions described in “The Offer—Section 11. Conditions of the Offer.”

In all cases (including during any Subsequent Offering Period, as defined in “The Offer—Section 1. Terms of the Offer”), Purchaser will pay for Shares accepted for payment pursuant to the Offer only after timely receipt by the Depositary of (i) certificates representing such Shares (except in the case of Shares held in a book-entry/direct registration account maintained by Entertainment Gaming’s transfer agent) or confirmation of book-entry transfer of such Shares into the Depositary’s account at the Book-Entry Transfer Facility (as defined in “The Offer—Section 3. Procedure for Tendering Shares”) (a “Book-Entry Confirmation”), (ii) a properly completed and duly executed Letter of Transmittal (or a manually signed facsimile thereof) with all required signature guarantees or, in the case of a book-entry transfer, an Agent’s Message (as defined in “The Offer—Section 3. Procedure for Tendering Shares”) in lieu of the Letter of Transmittal and (iii) any other documents required by the Letter of Transmittal. Accordingly, tendering stockholders may be paid at different times depending upon when certificates for Shares or Book-Entry Confirmations with respect to Shares are actually received by the Depositary. Under no circumstances will interest be paid on the consideration paid for Shares accepted for purchase in the Offer, regardless of any extension of the Offer or any delay in making payment for such Shares.

The Offer is not being made to (nor will tenders be accepted from or on behalf of) holders of Shares in any jurisdiction in which the making of the Offer or the acceptance thereof would not be in compliance with the securities, blue sky or other laws of such jurisdiction or any administrative or judicial action pursuant thereto. Purchaser may, in its discretion, take such action as it deems necessary to make the Offer to holders of Shares in such jurisdiction. In any jurisdiction where the securities, blue sky or other laws require the Offer to be made by a licensed broker or dealer, the Offer will be deemed to be made on behalf of Purchaser or by one or more registered brokers or dealers licensed under the laws of such jurisdiction.

Neither Melco nor Purchaser will pay any fees or commissions to any broker or dealer or any other person (other than Innisfree M&A Incorporated (the “Information Agent”) and the Depositary as described in the Offer to Purchase) for soliciting tenders of Shares pursuant to the Offer. Purchaser will, however, upon request, reimburse brokers, dealers, commercial banks, trust companies and other nominees for reasonable and necessary costs and expenses incurred by them in forwarding the enclosed materials to their customers.

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Any stock transfer taxes applicable to the sale of Shares to Purchaser pursuant to the Offer will be paid by Purchaser, except as otherwise set forth in Instruction 6 of the Letter of Transmittal.

If a stockholder wishes to tender Shares in the Offer, but: (a) the certificates representing such Shares are not immediately available or cannot be delivered to the Depositary prior to the expiration of the Offer; (b) such stockholder cannot comply with the procedures for book-entry transfer prior to the expiration of the Offer; or (c) such stockholder cannot deliver all required documents to the Depositary prior to the expiration of the Offer, such stockholder may tender Shares by complying with the guaranteed delivery procedures set forth in “The Offer—Section 3. Procedure for Tendering Shares.”

Any inquiries you may have with respect to the Offer should be addressed to, and additional copies of the enclosed materials may be obtained from, the Information Agent at its address and telephone numbers set forth on the back cover of the Offer to Purchase.

Very truly yours,

Melco International Development Limited

NOTHING CONTAINED HEREIN OR IN THE ENCLOSED DOCUMENTS SHALL RENDER YOU THE AGENT OF MELCO, PURCHASER, ENTERTAINMENT GAMING, THE INFORMATION AGENT OR THE DEPOSITARY, OR ANY AFFILIATE OF ANY OF THEM OR AUTHORIZE YOU OR ANY OTHER PERSON TO USE ANY DOCUMENT OR MAKE ANY STATEMENT ON BEHALF OF ANY OF THEM IN CONNECTION WITH THE OFFER OTHER THAN THE DOCUMENTS ENCLOSED HEREWITH AND THE STATEMENTS CONTAINED THEREIN.

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