why does this simple shuffle algorithm produce biased results? what is a simple reason?

Question

it seems that this simple shuffle algorithm will produce biased results:

# suppose $arr is filled with 1 to 52

for ($i < 0; $i < 52; $i++) { 
  $j = r         


        

Answer 1

The best explanation I've seen for this effect was from Jeff Atwood on his CodingHorror blog (The Danger of Naïveté).

Using this code to simulate a 3-card random shuffle...

for (int i = 0; i < cards.Length; i++)
{
    int n = rand.Next(cards.Length);
    Swap(ref cards[i], ref cards[n]);
}

...you get this distribution.

The shuffle code (above) results in 3^3 (27) possible deck combinations. But the mathematics tell us that there are really only 3! or 6 possible combinations of a 3 card deck. So some of the combinations are over-represented.

You would need to use a Fisher-Yates shuffle to properly (randomly) shuffle a deck of cards.