<PAGE>   1
                                                                EXHIBIT 10(59)

                      SENIOR EXECUTIVE RETENTION AGREEMENT


     THIS SENIOR EXECUTIVE RETENTION AGREEMENT (this "Agreement") is made on
the 23rd day of January, 1998, by and between STRATOSPHERE GAMING CORP., a
Nevada corporation (the "Corporation") and STRATOSPHERE CORPORATION, a Delaware
corporation ("Stratosphere" and collectively with Corporation the "Debtors")
and ANDREW S. BLUMEN (the "Executive") with respect to the following facts and
circumstances:

                             PRELIMINARY STATEMENTS

     A. On January 27, 1997, the Debtors filed their Voluntary Petitions for
bankruptcy protection under Title 11, Chapter 11 of the United States
Bankruptcy Code (the "Bankruptcy Code") in the District of Nevada (the
"Bankruptcy Court") and have, since that date, been operating as
debtors-in-possession under the Bankruptcy Code.

     B. The Executive is currently employed by the Corporation as the Executive
Vice President and General Counsel and serves on the Board of Directors of the
Corporation (the "Board").

     C. The Debtors have determined that the Executive is a key Executive of
the Corporation and it is the desire of the Debtors to assure themselves of the
availability of the services of the Executive and to provide assurances to the
Executive in the event of (1) the entry of a final and non-appealable order
confirming a plan of reorganization for the Debtors ("Confirmation Event"); or
(2) the liquidation or consummation and closing of the sale of substantially
all of the assets of the Hotel ("Sales Event"); or (3) Executive's involuntary
termination without cause of Executive's employment (hereinafter defined as
"Involuntary Termination Event" and collectively with Confirmation Event and
Sales Event, an "Event").

     D. Until the occurrence of an Event, the Debtors believe it imperative
that they be able to rely upon the Executive to continue in his position and,
if required, to assess any proposal or transaction which would cause an Event
and advise Debtors as to whether such proposal or transaction would be in the
best interest of the Debtors.

                                   AGREEMENT

     NOW, THEREFORE, to assure the Debtors that they will have the continued
dedication of the Executive and the availability of his advice and counsel
notwithstanding the possibility, threat or occurrence of an Event and to induce
the Executive to remain in the employ of the Debtors, and for other good and
valuable consideration, the receipt, adequacy and sufficiency of which are
hereby acknowledged, the Debtors and the Executive agree as follows:



                                       1

<PAGE>   2


     1. Retention Compensation. In addition to the base salary of the
Executive, the Executive shall be entitled to additional compensation
("Retention Compensation") equal to one hundred percent (100%) ("100% Payment")
of the Executive's annual base salary as of May 1, 1997 upon the occurrence of
the earlier of (A) an Involuntary Termination Event or (B) the occurrence of a
Sales Event or a Confirmation Event.  Upon the Bankruptcy Court entering a
final and non-appealable order approving this Agreement, the Corporation will
place into escrow the 100% Payment.  It is understood and agreed that solely
for income tax purposes, Retention Compensation will not be deemed to be income
of the Executive until received by the Executive.  Retention Compensation
accrued but unpaid will not be paid to the Executive if the Executive
voluntarily terminates his or her employment prior to the Executive being
entitled to receive the 100% Payment from escrow.

     2. Termination "for cause."   For the purposes of this Agreement,
termination "for cause" shall mean:  (a) the commission of fraud, embezzlement
or theft against the Debtors or against any employee, customer or business
associated; and (b) a conviction of or guilty plea to a felony.

     3. Litigation Costs.  If litigation shall be brought to enforce or
interpret any provision contained herein or to recover from the Executive any
moneys paid pursuant to this Agreement, the Executive shall be entitled to
recover reasonable attorneys' fees and costs incurred if the Executive is the
prevailing party.

     4. Payment Obligations.  All amounts payable by the Corporation hereunder
shall be paid without notice or demand.  The obtaining by Executive of any
other employment shall in no event affect any reduction of the Corporation's
obligations to make the payments and arrangements required to be made under
this Agreement.

     5. Health Benefits.  Executive shall continue to receive healthcare
benefits (including dental and vision) for the Executive and his or her family
in accordance with the Corporation's pre-January 27, 1997 policies and
practices.  In the event of a termination of Executive's employment with the
Debtors without cause, such existing healthcare benefits will be extended for
the Executive until the earlier of (1) the end of the nine month period
following such termination and (2) the qualification and eligibility of the
Executive for healthcare plan benefits under another group health plan.

     6. Continuing Obligations.  The Executive shall retain in confidence any
confidential information known to him concerning the Debtors and their
respective businesses so long as such information is not publicly disclosed.

     7. Bankruptcy Court Approval.  This Agreement is subject to the approval
of the Bankruptcy Court.

     8. Successors.  This Agreement shall be binding upon and inure to the
benefit of the Executive and his estate and the Debtors and any successor of
the Debtors, but 




                                       2


<PAGE>   3

neither this Agreement nor any rights arising hereunder may be
assigned or pledged by the Executive.

     9. Severability.  Any provision in this Agreement which is prohibited or
unenforceable in any jurisdiction shall, as to such jurisdiction, be
ineffective only to the extent of such prohibition or unenforceability without
invalidating or affecting the remaining provisions hereof, and any such
prohibition or unenforceability in any jurisdiction shall not invalidate or
render unenforceable such provision in any other jurisdiction.

     10. Prior Agreements.  This Agreement supersedes any prior severance
agreement between the Executive and the Debtors, which shall be of no further
force and effect whatsoever.

     11. Choice of Law.  This Agreement has been entered into in the State of
Nevada and will be governed by those laws of the State of Nevada without regard
to conflict of laws principles.  Any disputes which arise under this Agreement,
even after the termination of this Agreement, that cannot be resolved through
good faith discussions, will be heard only in the State or Federal courts
located in Clark County, Nevada and both parties hereby consent to such
jurisdiction.

     12. Captions.  The article and section captions contained in this
Agreement are inserted for convenience only and shall not affect in any way,
the meaning or interpretation of this Agreement.

     IN WITNESS WHEREOF, the parties have executed this Agreement as of the day
first above written.

DEBTORS:


Stratosphere Corporation,         Stratosphere Gaming Corp.,
a Delaware corporation            a Nevada corporation

By: /s/ Thomas A. Lettero         By: /s/ Thomas A. Lettero
    ----------------------------      ----------------------------
Its: Chief Financial Officer      Its: Chief Financial Officer
    ----------------------------      ----------------------------


EXECUTIVE:

/s/ Andrew S. Blumen
-------------------------------
ANDREW S. BLUMEN

                                       3