Mathematical Modeling in Finance with Stochastic Processes

3.1. A COIN TOSSING EXPERIMENT 93

Tossn 71 72 73 74 75 76 77 78 79 80

H or T

Yn= +1,− 1

Tn=

∑n

i=1Yi

Tossn 81 82 83 84 85 86 87 88 89 90

H or T

Yn= +1,− 1

Tn=

∑n

i=1Yi

Tossn 91 92 93 94 95 96 97 98 99 100

H or T

Yn= +1,− 1

Tn=

∑n

i=1Yi

Some Outcomes

In an in-class experiment with 17 “gamblers”, the class members obtained
the following results:

1. 8 gamblers reached a net loss of−10 before reaching a net gain of +10,
   that is, acheived “victory”.


2. 7 gamblers reached a net gain of +10 before reaching a net loss of−10,
   that is, were “ruined”.


3. 2 gamblers still had not reached a net loss of +10 or−10 yet.

This closely matches the predicted outcomes of 1/2 the gamblers being ru-
ined, and 1/2 of the gamblers being victorious.

The durations of the games were 88, 78 , 133 , 70 , 26 , 76 , 92 , 146 , 153 , 24 , 177 , 67 , 24 , 34 , 42 ,90.
The mean duration is 82.5 which is a little short of the predicted expected
duration of 100.

Sources

This section is adapted from ideas in William Feller’s classic text,An Intro-
duction to Probability Theory and Its Applications, Volume I, Third Edition.