Exhibit 99(d)(4)

DEED OF IRREVOCABLE UNDERTAKING

(Non-Director Shareholders)

To: Amaya Gaming Group Inc. (“Offeror”)

7600 Trans-Canada Hwy

Pointe-Claire

Canada QC H9R 1C8

From: Birkenshaw & Company Ltd.

102A – 1075 Bay Street

Suite 336

Toronto, Ontario

M5S 2B2

Dear Sirs,

Acquisition of CryptoLogic Limited (“Target”)

I understand that Offeror may offer to acquire the ordinary shares of no par value of the Target (the “Ordinary Shares”) by way of a takeover offer within the meaning of Part XVIII of the Companies (Guernsey) Law, 2008 (as amended) (the “Companies Law”). This undertaking sets out the terms and conditions on which I will accept the Offer (as defined in paragraph 13 of this undertaking).

Shareholdings

1. I irrevocably and unconditionally undertake, represent and warrant to the Offeror that:

(a) I am the registered holder of the number of Ordinary Shares in the capital of the Target shown in Part A of Schedule 1 (“Target Shares”) and I hold these free of any lien, charge, option, equity or encumbrance or other third party right of any kind;

(b) I am the beneficial owner of the number of Ordinary Shares in the capital of the Target shown in Part B of Schedule 1 (the “Beneficial Shares”) and I own these free of any lien, charge, option, equity or encumbrance or other third party right of any kind;

(c) other than as set out in this paragraph 1, I do not have any interest (as defined in the Code) in any securities of the Target or any rights to subscribe for, purchase or otherwise acquire any securities of the Target; and

(d) I have full power and authority to enter into this undertaking, to perform the obligations under it, to accept the Offer in respect of the Target Shares and to procure that the registered holder of the Beneficial Shares accepts the Offer in respect of the Beneficial Shares;

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Dealings and undertakings

2. I undertake to the Offeror, that before this undertaking lapses in accordance with paragraph 6 below, I shall not:

(a) sell, transfer, charge, encumber, grant any option over or otherwise dispose of any interest in any Target Shares or any other securities in the Target issued or unconditionally allotted to, or otherwise acquired by me before then (“Further Target Shares”);

(b) in respect of the Target Shares or Further Target Shares, accept any offer made to acquire shares in the Target or vote for any scheme of arrangement or support any Acquisition Proposal in competition or otherwise in conflict with the Acquisition;

(c) in respect of the Beneficial Shares, cause or permit the registered holder to sell, transfer, charge, encumber, grant any option over or otherwise dispose of any interest in any Beneficial Shares or any other securities in the Target of which I become the beneficial owner before such time (the “Further Beneficial Shares”);

(d) in respect of the Beneficial Shares and any Further Beneficial Shares, cause or permit the registered holder to accept any offer made to acquire shares in the Target or vote for any scheme of arrangement or support any Acquisition Proposal in competition or otherwise in conflict with the Acquisition;

(e) in respect of the Target Shares and any Further Target Shares vote in favour of any resolution, or in respect of the Beneficial Shares and any Further Beneficial Shares, cause or permit the registered holder thereof to vote in favour of, any resolution that would result in any condition of the Acquisition not being fulfilled or that otherwise might reasonably be expected to impede or frustrate the Acquisition in any way;

(f) (other than pursuant to the Acquisition) enter into any agreement or arrangement, incur any obligation or give any indication of intent:

(i) to do any of the acts referred to in paragraphs 2(a) to 2(e); or

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(ii) which, in relation to, or operating by reference to, the Target Shares, the Beneficial Shares or any Further Target Shares or Further Beneficial Shares, would or might restrict or impede me or, in the case of the Beneficial Shares, the registered holder thereof, from accepting the Offer,

and for the avoidance of doubt, references in this paragraph 2(e) to any agreement, arrangement, obligation or indication of intent includes any agreement, arrangement, obligation or indication of intent, whether or not it is legally binding or subject to any condition, or which is to take effect if the Offer lapses or is withdrawn or if this undertaking ceases to be binding or following any other event; or

(g) other than as set out in this paragraph 2, acquire any interest (as defined in the Code) or otherwise undertake any dealing (as defined in the Code) in any shares or other securities of the Target or in any other securities, options or derivatives referenced to the share capital of the Target and/or the share price of the Target’s shares.

Undertaking to accept the Offer

3. I irrevocably and unconditionally undertake:

(a) to accept the Offer in respect of the Target Shares in accordance with the procedure for acceptance set out in the formal document containing such Offer (“Offer Document”) not later than seven days after the Offeror posts the Offer Document to the Target shareholders and to accept the Offer in respect of any Further Target Shares in accordance with the same procedure not later than three days after I become the registered holder of the Further Target Shares;

(b) to procure that the registered holder of the Beneficial Shares accepts the Offer in respect of the Beneficial Shares in accordance with the procedure for acceptance set out in the Offer Document not later than seven days after the Offeror posts the Offer Document to the Target shareholders and to procure that the registered holder of any Further Beneficial Shares accepts the offer in respect of the Further Beneficial Shares in accordance with the same procedure not later than three days after they become the registered holder of the Further Beneficial Shares;

(c) not to withdraw any acceptances of the Offer in respect of the Target Shares or any Further Target Shares; and

(d) not to cause or permit the registered holder of the Beneficial Shares and any Further Beneficial Shares to withdraw any acceptances of the Offer in respect of the Beneficial Shares.

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Subparagraphs (c) and (d) above shall apply notwithstanding that the terms of the Offer Document and/or applicable law or regulation will confer rights of withdrawal on accepting shareholders.

Documentation

4. I consent to:

(a) this undertaking being disclosed to any relevant legal authority, where required;

(b) the issue of a press announcement in relation to the Offer substantially in the form of the draft in Appendix I attached hereto, subject to any amendments that may be agreed between the Offeror and the Target or as may be required to comply with the requirements of any relevant authority (“Press Announcement”) incorporating references (if any) to me substantially in the form and context in which they appear in the attached draft;

(c) the inclusion of references to me, and particulars of this undertaking and my legal and beneficial holdings of relevant securities of the Target being included in the Press Announcement and any Offer Document, and any other announcement made, or document issued, by or on behalf of the Offeror or the Target in connection with the Acquisition; and

(d) this undertaking being available for inspection in accordance with Rule 26 of the Code or the Listing Rules of the Financial Services Authority.

5. I undertake to:

(a) promptly give the Offeror and the Target all information relating to my shareholding in the Target and any assistance in relation to such shareholding as you may reasonably require for the preparation of the Press Announcement (if required) or Offer Document and any other announcement to be made, or document to be issued, by or on behalf of the Offeror or the Target in connection with the Acquisition in order to comply with any relevant regulatory requirement or authority, including requirements of the Code the Financial Services Authority, the London Stock Exchange and all applicable Canadian Securities Laws; and

(b) immediately notify you in writing of any change in the accuracy or import of any information previously given to you in relation to my shareholding in the Target.

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Termination

6. This undertaking shall lapse and be of no further effect if either (i) the Press announcement is not made by 6 February 2012 or (ii) the Offeror announces, with the consent of any relevant authority (if required) and before the Offer Document is posted, that it does not intend to proceed with the Acquisition and no new, revised or replacement Offer is announced in accordance with the Code at the same time or within 28 days thereafter.

7. If this undertaking lapses, I shall have no claim against the Offeror.

8. This undertaking shall not oblige the Offeror to announce or proceed with the Acquisition.

Higher Competing Offer

9. The undertakings set out in paragraph 3 shall be suspended if:

(a) at least two days prior to the first closing of the Offer, any person other than the Offeror or any person acting in concert with the Offeror announces a firm intention to make an offer howsoever structured (in accordance with Rule 2.7 of the Code) to acquire the entire issued and to be issued share capital of the Target (other than that already owned by such person) provided that the cash consideration per share of such offer represents an improvement of at least 10 per cent over the cash consideration per share under the Offer as at the date on which such firm intention to make an offer is announced (a “Higher Competing Offer”); and

(b) the Higher Competing Offer has been unanimously recommended by the directors of the Target.

All other provisions of this undertaking, including those set forth in paragraph 2, will remain in full force and effect.

10. If at or before 11:59 p.m. on the fifth business day after a Higher Competing Offer is announced, the Offeror or any person acting in concert with the Offeror announces a revision of the Offer so that the cash consideration per share is at least equal to the cash consideration per share under the Higher Competing Offer (the “Revised Offer”), the suspension referred to in paragraph 9 shall come to an end and the undertakings set out in paragraph 3 shall resume with full force and effect from the date of the Revised Offer with all relevant time periods applying to any revised Offer Document. If the Offeror does not announce a revision of the Offer in accordance with this paragraph 10, this undertaking shall lapse and be of no further effect.

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Secrecy

11. Except as required by applicable law, the Code, any court of competent jurisdiction or any stock exchange in accordance with whose regulations the Target is required to comply, I shall keep secret the possibility, terms and conditions of the Offer and the existence and terms of this undertaking until the Press Announcement is released, provided that I may disclose the same to the Target and its advisers in which case I will procure that they observe secrecy in the same terms. The obligations in this paragraph shall survive termination of this undertaking.

12. I understand that the information you have given to me in relation to the Offer must be kept confidential until Press Announcement is released or the information has otherwise become generally available. Before this time I will not behave in relation to any qualifying investments or relevant products (as defined in the Financial Services and Markets Act 2000 (“FSMA”) and the Code of Market Conduct made pursuant to the FSMA) in a manner which would amount to market abuse for the purposes of section 118 of FSMA or section 41A to 41G of the Protection of Investors (Bailiwick of Guernsey) Law, 1987, on the information.

Interpretation

13. In this undertaking:

(a) Acquisition means the proposed acquisition by, or on behalf of, the Offeror of the Ordinary Shares of the Target, whether pursuant to the Offer or otherwise;

(b) Acquisition Proposal means any action to solicit, assist, initiate, knowingly encourage or otherwise facilitate (including by way of furnishing information, permitting any visit to any facilities, property or properties of the Target or any of its subsidiaries, or entering into any form of written or oral agreement, arrangement or understanding) any inquiries, proposals or offers regarding (i) any merger, take-over bid, issuer bid, amalgamation, plan of arrangement, share exchange, business combination, consolidation, recapitalization, tender offer, reorganization, liquidation, dissolution or winding-up, (ii) any sale or acquisition of all, substantially all or a material amount of any assets of the Target or any of its subsidiaries; (iii) any sale, lease, pledge, exchange, mortgage, transfer, purchase or issuance of equity or convertible securities in respect of the Target or any of its subsidiaries; (iv) any similar business combination involving the Target or any of its subsidiaries other than with the Offeror or any other subsidiary of the Offeror; (v) any transaction the consummation of which would reasonably be expected to impede, interfere with, prevent or materially delay the Offer or other transactions contemplated hereby; (vi) any transaction or series of transactions in any manner similar to those

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stated in (i) to (v) involving the Target or any of its subsidiaries; or (vii) any proposal or offer to, or public announcement of an intention to do, any of the foregoing from any person other than the Offeror or any other subsidiary of the Offeror;

(c) Canadian Securities Laws means all applicable securities laws in the provinces in which Target is a reporting issuer and the respective rules, regulations, instruments, blanket orders and blanket rulings under such laws together with applicable published policies, policy statements and notices;

(d) Code means the City Code on Takeovers and Mergers; and

(e) Offer means any offer (including any new, increased, revised or renewed offer) to be made by or on behalf of the Offeror to acquire the Ordinary Shares of the Target.

(f) The term “acceptance” when referring to the Offer and similar expressions refer to the acceptance of the Offer in accordance with all of the procedures to be set forth in the Offer Document and include any requirements to approve, consent, accept, tender, provide information or to do such other things required of holders of Ordinary Shares in the Offer Document for the Offer to be implemented.

Time of the Essence

14. Any time, date or period mentioned in this undertaking may he extended by mutual agreement but as regards any time, date or period originally fixed or as extended, time shall be of the essence.

Specific Performance

15. I acknowledge that, if I fail to comply with the undertakings in paragraph 3 or breach any of my other obligations under this undertaking, damages would not be an adequate remedy and accordingly the Offeror shall be entitled to the remedies of specific performance, injunction or other equitable relief.

Power of Attorney

16. In order to secure the performance of my obligations under this undertaking, including but not limited to my obligations under paragraphs 3 and 20, I irrevocably and unconditionally appoint, until the Offer or Scheme (as defined below) becomes effective or shall lapse or be withdrawn, any director from time to time of the Offeror to be my attorney in my name and on my behalf to execute a form or forms of election, forms of proxy and/or such other documents and to do such other acts and things as may be necessary for the acceptance of the Offer or Scheme (as the case may be) and performance of my obligations under this undertaking. This power of attorney shall only be exercised if I fail to act in accordance with the terms of this undertaking.

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Independent Advice

17. I confirm that I have been given adequate opportunity to consider whether or not I should give this undertaking and that I have had an opportunity to receive independent about its nature and contents.

Governing Law

18. This undertaking shall be governed by and construed in accordance with English law and I submit to the exclusive jurisdiction of the English courts for all purposes in connection with this undertaking.

Application of the Code

19. I acknowledge that, for the purposes of this undertaking, I will treat express references to the Code in this undertaking as binding, notwithstanding that the Code may not apply to the Offeror, the Target or the Acquisition.

Scheme

20. I irrevocably and unconditionally undertake that if the Acquisition is switched to be implemented by way of a scheme of arrangement under Part VIII of the Companies Law (the “Scheme”) I will enter into an irrevocable undertaking in analogous terms to those contained within this letter in respect of the Scheme.

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SCHEDULE 1

EXISTING SHARES

PART A - Registered Holdings of Target Shares

Registered Holder	Ordinary Shares of no par value
David Birkenshaw	775 937

PART B - Beneficial Holdings of Target Shares

Registered Owner Ordinary Shares of no par value

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APPENDIX I

Press Announcement

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SIGNED and DELIVERED as a DEED by •

Yours faithfully,

Signature
Name	David Birkenshaw

in the presence of:

Signature of witness

Name	Neil Johnson
Address	161 Bay Street
	Suite 3100
	Toronto, ON
	M5J 2S1

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