Significance of location in a sentence or absence of comma for purpose of determining noun modified by preposition

In consideration of the following sentence, I have a question about which word is modified by the final preposition, "without charge."

The sentence:

A “thing of value" means any form of credit or promise involving extension of a service, entertainment or a privilege of playing at a game or scheme without charge.

The placement of "without charge" at the end of the sentence with the participle "involving" and so many prepositions seems confusing. Is there a grammatical rule based upon the absence of comma after "scheme" or the location of "without charge" at the end of the sentence which determines whether "without charge" relates to "form," "credit or promise," "extension," "service, entertainment or privilege,""playing," or "game or scheme"?