Craps is a game of chance.
A player tosses a pair of dice and the outcome determines whether he wins
or loses. The operative word here is "chance". The outcome is
sensitive to the slightest variation in how the dice are thrown so there
is no formula for computing the outcome before a toss. Imagine trying
to toss two dice in exactly the same way. If there is any difference in
speed, direction, or orientation, the dice will strike the table with
different speeds, angles, and (or) orientations. Even if a player is really
good on the first bounce, ANY variation is amplified going to the second
and subsequent bounces. Inevitably, there is soon no resemblance between
trajectories of the dice.
Amazingly, amongst this chaos there is order. Here the operative word
is "order". Even though the trajectories are chaotic (unpredictable),
over many tosses each side of a die comes up on average 1/6 of the time.
As the number of tosses becomes arbitrarily large, the ratio of the number
of times a certain side occurs to the number of tosses becomes arbitrarily
close to 1/6. This is order from the chaos! In this case the probability
of a certain side occuring is defined to be 1/6.
Probability theory is used to study these long run averages. Over a long
series of tosses the long run averages CAN be predicted. Now, a casino
always maintains the long run edge. However, since an individual player
plays just so many times he has a chance to win. The following pages use
probability theory to establish ranges for a player's winnings and losings.
Experiments and simulations are included to support the theory. After
reading the following pages a player will be able to say with 95% confidence
the interval over which his winnings (or losings) fall. Three popular
craps wagers are studied: 1. Betting the Field. 2. Place Bets. 3. The
Pass Line.
