into exactly equal piles. These assumptions make it easier to understand the mapping, but are obviously not realistic. The below image maps the same shuffle but with more realistic assumptions. Here, instead of riffling exactly one card at a time from each pile, one card falls 80% of the time, two cards 17% of the time and three cards 3% of the time. These percentages were taken from The Theory of Gambling and Statistical Logic by Richard Epstein. Of course, they can be adjusted to any percentages and there have been other estimates of dealer riffle precision. In addition, grabs were made with randomly plus or minus six cards instead of perfectly. We can see that the paths from one stack to the other are no longer fanned out perfectly, the colors in the final stack are not as clean and some cards are way out of place. However, in general cards we still see large numbers of cards ending up in fairly predictable final locations.

Notes: It is important to identify dealer habits in this respect. Also, an advantage of using software is you can hit Reshuffle several times and the map is instantly recreated with different riffling and grab imperfections.

Now let us isolate an interesting subset of the cards. In the below image, we are only interested in the 78 cards that end up at the top of the final stack of cards. We see that they come from two areas of the original cards, the bottom 39 cards and 39 cards starting half way up the stack.

 © 2009 Norman Wattenberger