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Mathematical methods
HMMs
Mathematical Induction
Pigeonhole principle
Random Walk
Gambler's Ruin
An Analysis of the Problem
A Greedy Gambler
A Greedy Gambler Simulation
An One-server Queueing System
An Analysis of the Problem
Performance of the Queueing system
Infinite Waiting Space Queue
Solving Linear Systems
A Greedy Gambler
We observe that if one is greedy and expecting a large fortune of
N
then
lim
N
®¥
q
i
=
ì
í
î
1 -
X
i
where
X
= (
1 -
p
¾¾
p
) for
i
= 0, 1, ...,
N
if
p
¹
0.5
0 for
i
= 0, 1, ...,
N
if
p
= 0.5.
Department of Mathematics, HKU,
2010
