This is not magic it is down to a mathematical sequence.
The chosen card is placed at the bottom of the pile that is then positioned on top of the other 2 piles, making it always the 3rd card in the deck of cards, This means there will always be 6 cards below it and 2 cards are above it.
All the numbers on the cards are no less than 3 letters long for example ace is 3 letters long, nine is 4 letter long and eight is 5 letters long, this means that the chosen card will always end up second bottom of the pile when counting (see figure 1) no matter how many letters the numbers have.
The crucial part is the use of the word 'of' are then transferred to the bottom of the pile (see figure 2) meaning that the chosen will always be in the middle of the pack in position 5 of 9 cards- 4 cards will be above it and 4 cards will be below it.
As long as the next step (the name of the suits) is greater than 5, of which they all are, then the chosen card will always remain in 5 position.
The word 'magic' contains 5 letters. This means that when you spell out the word 'magic', the c in magic is the 5th letter your chosen card will always be revealed as it is in the 5th place in the deck.