575 Madison Avenue New York, NY 10022-2585 212.940.8800 tel 212.940.8776 fax www.kattenlaw.com

Exhibit 5.1

[DRAFT FORM OF LEGAL OPINION]

[            ], 2013

Math-Based Asset Services LLC

as Sponsor to Winklevoss Bitcoin Trust

30 West 24th Street, 4th Floor

New York, NY 10010

Winklevoss Bitcoin Trust (Registration No. 333-189752)

Ladies and Gentlemen:

We have acted as counsel for Math-Based Asset Services LLC, a Delaware limited liability company (the “Sponsor”), the sponsor of Winklevoss Bitcoin Trust, a grantor trust formed under the laws of the State of New York (the “Trust”), in connection with the Trust’s filing on July 1, 2013 with the Securities and Exchange Commission (the “Commission”) of its Registration Statement on Form S-1 (as amended, the “Registration Statement”), including the prospectus included in Part I of the Registration Statement (the “Prospectus”), under the Securities Act of 1933 (the “1933 Act”) (No. 333-189752) and the Trust’s filing with the Commission of its Amendment No. 1 to the Registration Statement on October 8, 2013, and its Amendment No. 2 to the Registration Statement on [            ], 2013, relating to the issuance and sale by the Trust of [    ],000,000 Winklevoss Bitcoin Shares (the “Shares”).

In connection with this opinion, we have examined originals or copies, certified or otherwise identified to our satisfaction, of such instruments, documents and records as we have deemed relevant and necessary to examine for the purpose of this opinion, including (a) the Registration Statement, (b) the Trust’s Trust Agreement, (c) the pertinent provisions of the constitution and laws of the State of New York; and (d) such other instruments, documents, statements and records of the Trust and others and other such statutes as we have deemed relevant and necessary to examine and rely upon for the purpose of this opinion.

AUSTIN        CENTURY CITY        CHARLOTTE        CHICAGO        HOUSTON        IRVING         LOS ANGELES

NEW YORK        ORANGE COUNTY        SAN FRANCISCO BAY AREA        SHANGHAI        WASHINGTON, DC

LONDON: KATTEN MUCHIN ROSENMAN UK LLP

A limited liability partnership including professional corporations

[            ], 2013

Page 2

In connection with this opinion, we have assumed the legal capacity of all natural persons, the accuracy and completeness of all documents and records that we have reviewed, the genuineness of all signatures, the authenticity of the documents submitted to us as originals and the conformity to authentic original documents of all documents submitted to us as certified, conformed or reproduced copies.

Based upon the foregoing, we are of the opinion that the Shares proposed to be offered and sold pursuant to the Registration Statement, when it is made effective by the Commission or otherwise pursuant to the rules and regulations of the Commission, will have been validly authorized and, when sold in accordance with the terms of the Registration Statement and the requirements of applicable federal and state law and delivered by the Trust against receipt of the net asset value of the Shares, as described in the Registration Statement, will have been legally and validly issued and will be fully paid and non-assessable by the Trust.

This opinion is given as of the date hereof and we assume no obligation to advise you of changes that may hereafter be brought to our attention. This opinion is limited to the laws of the State of New York governing grantor trusts and matters such as the authorization and issuance of the Shares, the applicable provisions of the New York constitution and the reported judicial decisions interpreting such laws, and we do not express any opinion concerning any other laws.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement, to be filed with the Commission, and to the use of our name in the Prospectus under the caption “Legal Matters” and in any revised or amended versions thereof. In giving such consent, however, we do not admit that we are within the category of persons whose consent is required by Section 7 of the 1933 Act, as amended, and the rules and regulations thereunder.

Respectfully submitted,