<s>
Principal	B-General_Concept
variation	I-General_Concept
search	I-General_Concept
(	O
sometimes	O
equated	O
with	O
the	O
practically	O
identical	O
NegaScout	B-General_Concept
)	O
is	O
a	O
negamax	B-Algorithm
algorithm	O
that	O
can	O
be	O
faster	O
than	O
alpha-beta	B-Algorithm
pruning	I-Algorithm
.	O
</s>
<s>
Like	O
alpha-beta	B-Algorithm
pruning	I-Algorithm
,	O
NegaScout	B-General_Concept
is	O
a	O
directional	O
search	O
algorithm	O
for	O
computing	O
the	O
minimax	B-Algorithm
value	O
of	O
a	O
node	O
in	O
a	O
tree	B-Application
.	O
</s>
<s>
It	O
dominates	O
alpha-beta	B-Algorithm
pruning	I-Algorithm
in	O
the	O
sense	O
that	O
it	O
will	O
never	O
examine	O
a	O
node	O
that	O
can	O
be	O
pruned	O
by	O
alpha-beta	O
;	O
however	O
,	O
it	O
relies	O
on	O
accurate	O
node	O
ordering	O
to	O
capitalize	O
on	O
this	O
advantage	O
.	O
</s>
<s>
NegaScout	B-General_Concept
works	O
best	O
when	O
there	O
is	O
a	O
good	O
move	O
ordering	O
.	O
</s>
<s>
In	O
other	O
words	O
,	O
it	O
supposes	O
the	O
first	O
node	O
is	O
in	O
the	O
principal	B-General_Concept
variation	I-General_Concept
.	O
</s>
<s>
If	O
the	O
proof	O
fails	O
,	O
then	O
the	O
first	O
node	O
was	O
not	O
in	O
the	O
principal	B-General_Concept
variation	I-General_Concept
,	O
and	O
the	O
search	O
continues	O
as	O
normal	O
alpha-beta	O
.	O
</s>
<s>
Hence	O
,	O
NegaScout	B-General_Concept
works	O
best	O
when	O
the	O
move	O
ordering	O
is	O
good	O
.	O
</s>
<s>
With	O
a	O
random	O
move	O
ordering	O
,	O
NegaScout	B-General_Concept
will	O
take	O
more	O
time	O
than	O
regular	O
alpha-beta	O
;	O
although	O
it	O
will	O
not	O
explore	O
any	O
nodes	O
alpha-beta	O
did	O
not	O
,	O
it	O
will	O
have	O
to	O
re-search	O
many	O
nodes	O
.	O
</s>
<s>
Alexander	O
Reinefeld	O
invented	O
NegaScout	B-General_Concept
several	O
decades	O
after	O
the	O
invention	O
of	O
alpha-beta	B-Algorithm
pruning	I-Algorithm
.	O
</s>
<s>
He	O
gives	O
a	O
proof	O
of	O
correctness	O
of	O
NegaScout	B-General_Concept
in	O
his	O
book	O
.	O
</s>
<s>
Another	O
search	O
algorithm	O
called	O
SSS*	B-Algorithm
can	O
theoretically	O
result	O
in	O
fewer	O
nodes	O
searched	O
.	O
</s>
<s>
However	O
,	O
its	O
original	O
formulation	O
has	O
practical	O
issues	O
(	O
in	O
particular	O
,	O
it	O
relies	O
heavily	O
on	O
an	O
OPEN	O
list	O
for	O
storage	O
)	O
and	O
nowadays	O
most	O
chess	O
engines	O
still	O
use	O
a	O
form	O
of	O
NegaScout	B-General_Concept
in	O
their	O
search	O
.	O
</s>
<s>
Most	O
chess	O
engines	O
use	O
a	O
transposition	O
table	O
in	O
which	O
the	O
relevant	O
part	O
of	O
the	O
search	O
tree	B-Application
is	O
stored	O
.	O
</s>
<s>
This	O
part	O
of	O
the	O
tree	B-Application
has	O
the	O
same	O
size	O
as	O
SSS*'s	O
OPEN	O
list	O
would	O
have	O
.	O
</s>
<s>
A	O
reformulation	O
called	O
MT-SSS*	O
allowed	O
it	O
to	O
be	O
implemented	O
as	O
a	O
series	O
of	O
null	O
window	O
calls	O
to	O
Alpha-Beta	O
(	O
or	O
NegaScout	B-General_Concept
)	O
that	O
use	O
a	O
transposition	O
table	O
,	O
and	O
direct	O
comparisons	O
using	O
game	O
playing	O
programs	O
could	O
be	O
made	O
.	O
</s>
<s>
It	O
did	O
not	O
outperform	O
NegaScout	B-General_Concept
in	O
practice	O
.	O
</s>
<s>
Yet	O
another	O
search	O
algorithm	O
,	O
which	O
does	O
tend	O
to	O
do	O
better	O
than	O
NegaScout	B-General_Concept
in	O
practice	O
,	O
is	O
the	O
best-first	O
algorithm	O
called	O
MTD(f )	O
,	O
although	O
neither	O
algorithm	O
dominates	O
the	O
other	O
.	O
</s>
<s>
There	O
are	O
trees	O
in	O
which	O
NegaScout	B-General_Concept
searches	O
fewer	O
nodes	O
than	O
SSS*	B-Algorithm
or	O
MTD(f )	O
and	O
vice	O
versa	O
.	O
</s>
<s>
NegaScout	B-General_Concept
takes	O
after	O
SCOUT	O
,	O
invented	O
by	O
Judea	O
Pearl	O
in	O
1980	O
,	O
which	O
was	O
the	O
first	O
algorithm	O
to	O
outperform	O
alpha-beta	O
and	O
to	O
be	O
proven	O
asymptotically	O
optimal	O
.	O
</s>
<s>
Null	O
windows	O
,	O
with	O
β	O
=	O
α+1	O
in	O
a	O
negamax	B-Algorithm
setting	O
,	O
were	O
invented	O
independently	O
by	O
J.P.	O
Fishburn	O
and	O
used	O
in	O
an	O
algorithm	O
similar	O
to	O
SCOUT	O
in	O
an	O
appendix	O
to	O
his	O
Ph.D.	O
thesis	O
,	O
in	O
a	O
parallel	O
alpha-beta	O
algorithm	O
,	O
and	O
on	O
the	O
last	O
subtree	B-Application
of	O
a	O
search	O
tree	B-Application
root	B-Application
node	I-Application
.	O
</s>
<s>
The	O
exact	O
score	O
is	O
only	O
needed	O
in	O
principal	B-General_Concept
variation	I-General_Concept
(	O
a	O
sequence	O
of	O
moves	O
acceptable	O
for	O
both	O
players	O
)	O
which	O
is	O
expected	O
to	O
propagate	O
down	O
to	O
the	O
root	O
.	O
</s>
