Is this a mathematically sound shuffle? It removes a random element from a sorted deck and then adds the element to a new deck. Python code below:

import random

def shuffle():

    random.seed()   
    sorted_deck = range(52)  # [0..51]
    shuffled_deck = []
    slots_avail = 52
    while slots_avail:

        idx = random.randint(0, slots_avail - 1)
        shuffled_deck.append(sorted_deck[idx])
        del sorted_deck[idx]
        slots_avail -= 1

    return shuffled_deck