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CHAPTER 1 The Random Process and Gambling Theory

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ewill start with the simple coin-toss case.When you toss a coinin

the air thereis no way to tell for certain whetheritwill land heads

or tails.Yet over many tosses the outcome can be reasonably pre-

dicted.

This, then,is where we begin our discussion.

Certainaxioms will be developed as we discuss the random process.

The first of theseis thatthe outcome of an individual event in a ran-

dom process cannot be predicted. However, we can reduce the possible

outcomes to a probability statement.

Pierre Simon Laplace (1749–1827) defined the probability of an event

as the ratio of the number of waysinwhich the event can happen to the

total possible number of events.Therefore, when a coinis tossed, the prob-

ability ofgettingtailsis 1 (the number of tails on a coin) divided by 2 (the

number of possible events), for a probability of. 5 .In our coin-toss example,

we do not know whether the result will be heads or tails, but we do know

that the probability thatitwill be headsis.5 and the probabilityitwill be

tailsis. 5 .So,a probability statement is a number between 0 (there is no

chance of the event in question occurring) and 1 (the occurrence of the

event is certain).

Often you will have to convert from a probability statement to odds and

vice versa.The two areinterchangeable, as the oddsimply a probability,

and a probability likewiseimplies the odds.These conversions aregiven

now.The formula to convert to a probability statement, when you know

thegiven oddsis:

Probability=odds for/(odds for+odds against) (1.01)

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