To answer this question, I may have to get involved in the debate that how does prayers are answered.

Still, out of seventeen years+ of experience with cartomancy, I have a simple and perhaps a more scientific explanations that in turn some skeptics classified as "pseudo science".

My explanation involves the study a part of psychic energy and rather controversial theory of its mysterious form in the human brain called the Odyle. I shall some to that. Let us start with a cursory study of the human brain.

The human brain is divided in to two parts. The left brain controls the right side of the body and got more to do with involuntary actions like heart beat, digestion, breathing etc. The right brain controls left side of the body and it deals with intuitions, intelligence, grasping power.

To control things energy is needed, this energy is derived basically from food. How ever, human body or humans are capable of doing more that just biological and physiological actions and this is achieved through psychic energy.

The form of psychic energy that deals with intuition, premonitions and the aura of a person or rather the power of mind is called Odyle. It is very similar to electrical energy. The impulses in our brain, sounds far from reality? I guess not because,

What is "real"? How do you define "real"?
If real is what you can feel, smell, taste and see, then 'real' is simply electrical signals interpreted by your brain.
- Morpheus, The Matrix

Now when the cards are shuffled, it causes friction which in turn generate static electricity in the cards. The magnitude of this static electricity is far lower than the charge of the Odyle in the human brain.
Law energy transfer cannot be overruled. Hence, the charge of our mind is transferred to the cards and while shuffling these cards some how arrange themselves in a manner to get the desired result or provide an answer to our query.

That does not mean that if we are shuffling the (playing) cards for a game or for fun it will necessarily predict anything. That is the reason, a diviner or the enquirer has to concentrate on the question while shuffling the cards.

That is why there is nothing specified in any book in the whole world that is related to cartomancy, about how many times the deck is to be shuffled, at least I have not come across any such.

Most cartomancers would ask the enquirer to as many times as the enquirer feels to do so. However, we do find references to cutting the cards and the number of times a deck is to be cut, which mostly a maximum of three times. This is to enhance the energy transfer that the experts have discovered either by choice or through trail and error method and this works!

The predetermined number of cards are then laid out in a specific arrangement, that we call spreads and the meaning of the cards are interpreted. This process is known as TAROT reading.