<s>
Originally	O
introduced	O
by	O
Richard	O
E	O
.	O
Bellman	O
in	O
,	O
stochastic	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
is	O
a	O
technique	O
for	O
modelling	O
and	O
solving	O
problems	O
of	O
decision	O
making	O
under	O
uncertainty	O
.	O
</s>
<s>
Closely	O
related	O
to	O
stochastic	B-Algorithm
programming	I-Algorithm
and	O
dynamic	B-Algorithm
programming	I-Algorithm
,	O
stochastic	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
represents	O
the	O
problem	O
under	O
scrutiny	O
in	O
the	O
form	O
of	O
a	O
Bellman	O
equation	O
.	O
</s>
<s>
Stochastic	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
can	O
be	O
employed	O
to	O
model	O
this	O
problem	O
and	O
determine	O
a	O
betting	O
strategy	O
that	O
,	O
for	O
instance	O
,	O
maximizes	O
the	O
gambler	O
's	O
probability	O
of	O
attaining	O
a	O
wealth	O
of	O
at	O
least	O
$6	O
by	O
the	O
end	O
of	O
the	O
betting	O
horizon	O
.	O
</s>
<s>
Stochastic	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
deals	O
with	O
problems	O
in	O
which	O
the	O
current	O
period	O
reward	O
and/or	O
the	O
next	O
period	O
state	O
are	O
random	O
,	O
i.e.	O
</s>
<s>
Markov	O
decision	O
processes	O
represent	O
a	O
special	O
class	O
of	O
stochastic	O
dynamic	O
programs	O
in	O
which	O
the	O
underlying	O
stochastic	O
process	O
is	O
a	O
stationary	B-Algorithm
process	I-Algorithm
that	O
features	O
the	O
Markov	O
property	O
.	O
</s>
<s>
However	O
,	O
like	O
deterministic	O
dynamic	B-Algorithm
programming	I-Algorithm
also	O
its	O
stochastic	O
variant	O
suffers	O
from	O
the	O
curse	B-Algorithm
of	I-Algorithm
dimensionality	I-Algorithm
.	O
</s>
<s>
Python	B-Language
implementation	O
.	O
</s>
<s>
The	O
one	O
that	O
follows	O
is	O
a	O
complete	O
Python	B-Language
implementation	O
of	O
this	O
example	O
.	O
</s>
<s>
An	O
introduction	O
to	O
approximate	O
dynamic	B-Algorithm
programming	I-Algorithm
is	O
provided	O
by	O
.	O
</s>
