Can any one tell me how gerund is used absolutely in the following sentence? Playing cards being aversion, we didn't play bridge.

In order to begin, I must conclude that you have omitted the necessary article an. You're sentence ought to read:
Playing cards being an aversion, we didn't play bridge.

Longmans Dictionary of Contemporary English Online is the best source for confirming word usage as they use clear models with definitions. Longmans shows that there are two usages of aversion. One usage model for aversion is aversion to something or someone. Their example is:

Despite his aversion to publicity, Arnold was persuaded to talk to the press.

The second model is have an aversion to something. Here aversion is followed by the complement to, but must be preceded by the article an. Your sentence falls under the second usage model for aversion, therefore must be preceded by the article an.

Now to the case of the word playing. A gerund is a manifestation of a verb. It is a verb in the present participle form. Present participle verbs end in -ing and follow or precede the conjugated forms of the verb to be.

Present participles forms are used for four syntactical functions: (1) as tense forming verbs and (2) at the head of participle clauses; (3) as adjectives; (4) and as nouns called gerunds.Examine each so you can identify what comprises a gerund.

(1) The present participle verb is formed with to be + [verb] + -ing (to be + -ing).

(2) A present participle clause (also called an adverbial clause) is formed with an -ing verb followed by a noun or noun phrase (popcorn (N), the theater (NP)): -ing + N/NP. Exs: Passing popcorn being awkward, I spilled it. Passing the shop, I saw I was lost.

(3) A present participle functions as an adjective when it forms part of a noun phrase: a flying bird: article + present participle adjective + noun.

(4) A present participle functioning as a noun gerund is formed in relation to the sentence Verb.

A gerund may precede the Verb when it fills the slot of a Subject or it may follow the Verb when it fills the slot of the Object. Examples: A gerund as Subject is Singing is good for you. A gerund as an Object is I enjoy singing.

A gerund is formed by the verb and the present participle, either as Verb + present participle gerund (V + -ing) or as present participle gerund + Verb (-ing + V).