<s>
The	O
expectiminimax	B-Algorithm
algorithm	O
is	O
a	O
variation	O
of	O
the	O
minimax	B-Algorithm
algorithm	I-Algorithm
,	O
for	O
use	O
in	O
artificial	B-Application
intelligence	I-Application
systems	O
that	O
play	O
two-player	O
zero-sum	O
games	O
,	O
such	O
as	O
backgammon	B-Application
,	O
in	O
which	O
the	O
outcome	O
depends	O
on	O
a	O
combination	O
of	O
the	O
player	O
's	O
skill	O
and	O
chance	O
elements	O
such	O
as	O
dice	O
rolls	O
.	O
</s>
<s>
In	O
addition	O
to	O
"	O
min	O
"	O
and	O
"	O
max	O
"	O
nodes	O
of	O
the	O
traditional	O
minimax	B-Algorithm
tree	O
,	O
this	O
variant	O
has	O
"	O
chance	O
"	O
(	O
"	O
move	O
by	O
nature	O
"	O
)	O
nodes	O
,	O
which	O
take	O
the	O
expected	O
value	O
of	O
a	O
random	O
event	O
occurring	O
.	O
</s>
<s>
In	O
game	O
theory	O
terms	O
,	O
an	O
expectiminimax	B-Algorithm
tree	I-Algorithm
is	O
the	O
game	O
tree	O
of	O
an	O
extensive-form	O
game	O
of	O
perfect	O
,	O
but	O
incomplete	O
information	O
.	O
</s>
<s>
In	O
the	O
traditional	O
minimax	B-Algorithm
method	O
,	O
the	O
levels	O
of	O
the	O
tree	O
alternate	O
from	O
max	O
to	O
min	O
until	O
the	O
depth	O
limit	O
of	O
the	O
tree	O
has	O
been	O
reached	O
.	O
</s>
<s>
In	O
an	O
expectiminimax	B-Algorithm
tree	I-Algorithm
,	O
the	O
"	O
chance	O
"	O
nodes	O
are	O
interleaved	O
with	O
the	O
max	O
and	O
min	O
nodes	O
.	O
</s>
<s>
Each	O
"	O
turn	O
"	O
of	O
the	O
game	O
is	O
evaluated	O
as	O
a	O
"	O
max	O
"	O
node	O
(	O
representing	O
the	O
AI	B-Application
player	O
's	O
turn	O
)	O
,	O
a	O
"	O
min	O
"	O
node	O
(	O
representing	O
a	O
potentially-optimal	O
opponent	O
's	O
turn	O
)	O
,	O
or	O
a	O
"	O
chance	O
"	O
node	O
(	O
representing	O
a	O
random	O
effect	O
or	O
player	O
)	O
.	O
</s>
<s>
For	O
example	O
,	O
consider	O
a	O
game	O
in	O
which	O
each	O
round	O
consists	O
of	O
a	O
single	O
die	O
throw	O
,	O
and	O
then	O
decisions	O
made	O
by	O
first	O
the	O
AI	B-Application
player	O
,	O
and	O
then	O
another	O
intelligent	O
opponent	O
.	O
</s>
<s>
The	O
expectiminimax	B-Algorithm
algorithm	O
is	O
a	O
variant	O
of	O
the	O
minimax	B-Algorithm
algorithm	I-Algorithm
and	O
was	O
firstly	O
proposed	O
by	O
Donald	O
Michie	O
in	O
1966	O
.	O
</s>
<s>
Its	O
pseudocode	B-Language
is	O
given	O
below	O
.	O
</s>
