LIMITED POWER OF ATTORNEY

    The undersigned hereby constitutes and appoints Derek Harmer, Andrea McCarty
and Mathew Ellis, as long as they are providing services to Accel Entertainment,
Inc. or its related entities (the "Company"), or either of them, the
undersigned's true and lawful attorney-in-fact to:

    (1) execute for and on behalf of the undersigned, in the undersigned's
        capacity as an officer and/or director of the Company, Forms 3, 4 and 5
        in accordance with Section 16(a) of the Securities Exchange Act of 1934,
        as amended (the "Exchange Act"), and the rules and regulations
        thereunder;

    (2) do and perform any and all acts for and on behalf of the undersigned
        that may be necessary or desirable to complete and execute any such
        Forms 3, 4 and 5 and timely file such forms with the Securities and
        Exchange Commission and any stock exchange or similar authority, if
        required; and

    (3) take any other action of any type whatsoever in connection with the
        foregoing that, in the opinion of such attorney-in-fact, may be of
        benefit to, in the best interest of, or legally required by, the
        undersigned, it being understood that the documents executed by such
        attorney-in-fact on behalf of the undersigned pursuant to this Power of
        Attorney shall be in such form and shall contain such terms and
        conditions as such attorney-in-fact may approve in such attorney-in-
        fact's discretion.

    The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform each and every act and thing whatsoever requisite,
necessary or proper to be done in the exercise of any of the rights and powers
herein granted, as fully to all intents and purposes as the undersigned might or
could do if personally present, with full power of substitution and revocation,
hereby ratifying and confirming all that each such attorney-in-fact, or each
such attorney-in-fact's substitute or substitutes, shall lawfully do or cause to
be done by virtue of this power of attorney and the rights and powers herein
granted.  The undersigned acknowledges that each of the foregoing attorneys-in-
fact, in serving in such capacity at the request of the undersigned, is not
assuming, nor is the Company assuming, any of the undersigned's responsibilities
to comply with Section 16 of the Exchange Act.

    The undersigned agrees that each such attorney-in-fact may rely entirely on
information furnished orally or in writing by the undersigned to each such
attorney-in-fact.  The undersigned also agrees to indemnify and hold harmless
the Company and each such attorney-in-fact against any losses, claims, damages
or liabilities (or actions in these respects) that arise out of or are based on
any untrue statement or omission of necessary facts in the information provided
by the undersigned to such attorney-in-fact for purposes of executing,
acknowledging, delivering and filing Forms 3, 4 or 5 (including amendments
thereto) and agrees to reimburse the Company and each such attorney-in-fact for
any legal or other expenses reasonably incurred in connection with investigating
or defending against any such loss, claim, damage, liability or action.

    This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4 and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

    IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 14th day of November, 2019.

                                        /s/ David W. Ruttenberg
                                        -----------------------------------
                                        Name:  David W. Ruttenberg