For those of you curious about the randomness of hands from the Dealing
Machine vs. hand shuffling it is very interesting.
Computer-Dealt Hands—Truly Random or Impishly Fixed?
by Dave Willmott
Computer-generated hands have a bad reputation in some circles-undeservedly
so. “These computer hands!” is a common cry, but how different are “computer
hands” from people-dealt hands?
Let’s tackle the second question first. It is a simple matter for a computer to deal
a set of 52 cards. To explain how this process works, using an oversimplified
analogy, consider how a postman places letters in a set of sorting office boxes.
Each piece of mail has an address, and the postman places each piece in the
correct box. Similarly, each card of the deck is randomly assigned a value which
determines which “box” (hand) it will be dealt to.
There is a catch, however, and it has to do with the word “randomly.” It is
important that the computer performs this task in a random fashion. Otherwise,
there is a risk that the same set of hands will be generated more than once.
Many computers use their internal clocks as a “random” starting value to assign
each of the cards an “address.” In practice, however, this method isn’t
sufficiently random enough. The software that is used is a random number
generator and uses a linear congruential algorithm that will repeat after 2 to the
47th power (140,737,488,355,328) deals have been generated.
Returning to the question of whether computer-dealt hands are different from
people-dealt ones, remember the great emphasis placed on creating a random
deal. To create a random deal manually, players must give the deck a thorough
shuffle at least seven times to guarantee that the cards are mixed. It is common,
however, to see players shuffle the deck only two or three times before dealing.
This is not a random deal.
It has been suggested by various mathematical authorities that this inadequate
shuffling may lead to “flatter” distributions. In other words, suits may break evenly
more often than expected. Players who are accustomed to their trump suits
dividing evenly all the time because of inadequate mixing seem genuinely
offended when they encounter a 4–1 trump split in a computer-dealt game, even
though that division will occur 28% of the time.
One riffle shuffle reorders the cards significantly. But the reordering is not
random, by any means. The top card is still near the top. The bottom card is still
near the bottom. Most pairs of cards are either still adjacent to each other, or not
very far apart. And so, several shuffles are necessary. How many shuffles?
Mathematics shows that at least seven shuffles are needed to randomize the
cards. More shuffles than that do not affect the randomness. Bridge players
often complain about the poor hands that result from computer dealt cards. This
would seem to indicate that these people are used to inadequate shuffling.
