<s>
In	O
decision	O
theory	O
,	O
the	O
odds	B-Algorithm
algorithm	I-Algorithm
(	O
or	O
Bruss	B-Algorithm
algorithm	I-Algorithm
)	O
is	O
a	O
mathematical	O
method	O
for	O
computing	O
optimal	O
strategies	O
for	O
a	O
class	O
of	O
problems	O
that	O
belong	O
to	O
the	O
domain	O
of	O
optimal	O
stopping	O
problems	O
.	O
</s>
<s>
The	O
odds	B-Algorithm
algorithm	I-Algorithm
applies	O
to	O
a	O
class	O
of	O
problems	O
called	O
last-success	O
problems	O
.	O
</s>
<s>
Note	O
that	O
represents	O
the	O
odds	O
of	O
the	O
kth	O
event	O
turning	O
out	O
to	O
be	O
interesting	O
,	O
explaining	O
the	O
name	O
of	O
the	O
odds	B-Algorithm
algorithm	I-Algorithm
.	O
</s>
<s>
The	O
importance	O
of	O
the	O
odds	O
strategy	O
,	O
and	O
hence	O
of	O
the	O
odds	B-Algorithm
algorithm	I-Algorithm
,	O
lies	O
in	O
the	O
following	O
odds	O
theorem	O
.	O
</s>
<s>
The	O
odds	B-Algorithm
algorithm	I-Algorithm
computes	O
the	O
optimal	O
strategy	O
and	O
the	O
optimal	O
win	O
probability	O
at	O
the	O
same	O
time	O
.	O
</s>
<s>
exist	O
for	O
all	O
sequences	O
,	O
so	O
that	O
the	O
odds	B-Algorithm
algorithm	I-Algorithm
is	O
,	O
at	O
the	O
same	O
time	O
,	O
optimal	O
as	O
an	O
algorithm	O
.	O
</s>
