## Class 34: Shuffling

Today we will talk about shuffling and try to settle the PEAR lab bet between Linda
and Laurie. On Friday, a blackjack expert is coming to class to teach us all how
to play.

### Discussion

As you read in the 1990 *New York Times* article, 7 shuffles is purported to completely
mix up a deck of cards, so that every ordering is equally likely. But in fact, 7
shuffles is not quite enough, as the game of Yin and Yang shows.

Yin are the rounded suits: hearts and clubs, and yang are the pointy suits: diamonds
and spades.

Everyone take a deck of cards. Shuffle it 7 times, then cut it, and then start removing
and revealing each card from the top of the deck, making a new pile of them face-up
(so if this were all you did, you'd just have the deck unchanged after going through it once, except that the deck would be lying face-up on the table).

Start the pile for each suit when you discover its ace, and add cards of the same
suit to each of these 4 piles, according to the rule that you must add the cards
of each suit in order.

Thus a single pass through the deck is not going to accomplish much in the way of
completing the 4 piles, so having made this pass, turn the remaining deck back over,
and make another pass.

Continue this until you complete either the two yin piles (hearts & clubs), or the
two yang piles (diamonds & spades). If the yang piles get completed first, we call
the game a win;
it's a loss if the ying piles get completed first.

If the deck has been thoroughly shuffled (by having put the cards through a clothes
dryer, say), then the yins and yangs will be equally likely to be first to get completed.
Thus our expected proportion of wins will be 1/2.

We would like you to help us settle our bet. Linda carried out a session on the REG
at the PEAR lab last Thursday. Recall that one trial on the REG consists of 200
"coin flips" in which the total number of "heads" is reported. So the outcome of
one trial is a single number around 100. Linda completed 1000 trials with the intention
"low", 1000 trials with the intention "high" and 1000 "baseline" trials with no particular
intention. (In fact each series of 1000 trials was done in 10 units of 100 trials each.) Without knowing the resullts, please come up with specific criteria for
the results to be "statistically significant". After discussing each group's criteria,
we will have the class vote on a single criteria, to settle the bet. We will go
with the majority decision; in the case of a tie we will toss a coin.

### Journals

Please hand in the final portion of your journals on Friday. Remember to also give us a brief progress report on your project.