<s>
Maven	B-General_Concept
is	O
an	O
artificial	B-Application
intelligence	I-Application
Scrabble	B-Application
player	O
,	O
created	O
by	O
Brian	O
Sheppard	O
.	O
</s>
<s>
It	O
has	O
been	O
used	O
in	O
official	O
licensed	O
Hasbro	O
Scrabble	B-Application
games	O
.	O
</s>
<s>
Maven	B-General_Concept
's	O
gameplay	O
is	O
sub-divided	O
into	O
three	O
phases	O
:	O
The	O
"	O
mid-game	O
"	O
phase	O
,	O
the	O
"	O
pre-endgame	O
"	O
phase	O
,	O
and	O
the	O
"	O
endgame	O
"	O
phase	O
.	O
</s>
<s>
(	O
While	O
a	O
Monte	O
Carlo	O
search	O
,	O
Maven	B-General_Concept
does	O
not	O
use	O
Monte	B-Application
Carlo	I-Application
tree	I-Application
search	I-Application
because	O
it	O
evaluates	O
game	O
trees	O
only	O
2-ply	O
deep	O
,	O
rather	O
than	O
playing	O
out	O
to	O
the	O
end	O
of	O
the	O
game	O
,	O
and	O
does	O
not	O
reallocate	O
rollouts	O
to	O
more	O
promising	O
branches	O
for	O
deeper	O
exploration	O
;	O
in	O
reinforcement	O
learning	O
terminology	O
,	O
the	O
Maven	B-General_Concept
search	O
strategy	O
might	O
be	O
considered	O
"	O
truncated	O
Monte	O
Carlo	O
simulation	O
"	O
.	O
</s>
<s>
The	O
shallow	O
search	O
is	O
because	O
the	O
Maven	B-General_Concept
author	O
argues	O
that	O
,	O
due	O
to	O
the	O
fast	O
turnover	O
of	O
letters	O
in	O
one	O
's	O
bag	O
,	O
it	O
is	O
typically	O
not	O
useful	O
to	O
look	O
more	O
than	O
2-ply	O
deep	O
,	O
because	O
if	O
one	O
instead	O
looked	O
deeper	O
,	O
e.g.	O
</s>
<s>
As	O
the	O
board	O
value	O
can	O
be	O
evaluated	O
with	O
very	O
high	O
accuracy	O
in	O
Scrabble	B-Application
,	O
unlike	O
games	O
such	O
as	O
Go	O
,	O
deeper	O
simulations	O
are	O
unlikely	O
to	O
change	O
the	O
initial	O
evaluation	O
.	O
)	O
</s>
<s>
Maven	B-General_Concept
uses	O
the	O
B-star	B-Protocol
search	I-Protocol
algorithm	I-Protocol
to	O
analyze	O
the	O
game	O
tree	O
during	O
the	O
endgame	O
phase	O
.	O
</s>
<s>
Maven	B-General_Concept
has	O
used	O
several	O
algorithms	O
for	O
move	O
generation	O
,	O
but	O
the	O
one	O
that	O
has	O
stuck	O
is	O
the	O
DAWG	B-General_Concept
algorithm	O
.	O
</s>
<s>
The	O
GADDAG	B-Data_Structure
algorithm	O
is	O
faster	O
,	O
but	O
a	O
DAWG	B-General_Concept
for	O
North	O
American	O
English	O
is	O
only	O
0.5	O
MB	O
,	O
compared	O
to	O
about	O
2.5	O
MB	O
for	O
a	O
GADDAG	B-Data_Structure
.	O
</s>
<s>
The	O
GADDAG	B-Data_Structure
is	O
perhaps	O
twice	O
as	O
fast	O
,	O
but	O
both	O
algorithms	O
are	O
fast	O
enough	O
.	O
)	O
</s>
<s>
The	O
first	O
(	O
1986	O
)	O
version	O
of	O
Maven	B-General_Concept
used	O
a	O
set	O
of	O
about	O
100	O
patterns	O
to	O
value	O
racks	O
.	O
</s>
<s>
Soon	O
after	O
the	O
first	O
version	O
,	O
Maven	B-General_Concept
acquired	O
rack	O
evaluation	O
terms	O
for	O
vowel/consonant	O
balance	O
and	O
Q/U	O
distribution	O
.	O
</s>
<s>
Shortly	O
thereafter	O
,	O
Maven	B-General_Concept
acquired	O
a	O
tile	O
duplication	O
evaluator	O
.	O
</s>
<s>
For	O
example	O
,	O
A	B-Application
is	I-Application
generally	O
better	O
than	O
I	O
as	O
a	O
tile	O
,	O
but	O
if	O
there	O
are	O
7	O
A	O
's	O
and	O
only	O
2	O
I	O
's	O
left	O
in	O
the	O
bag	O
,	O
then	O
maybe	O
we	O
should	O
prefer	O
to	O
keep	O
the	O
I	O
.	O
</s>
<s>
This	O
rack	O
evaluation	O
design	O
was	O
original	O
to	O
Maven	B-General_Concept
.	O
</s>
<s>
Maven	B-General_Concept
's	O
pattern	O
set	O
gradually	O
expanded	O
from	O
the	O
base	O
set	O
of	O
100	O
to	O
well	O
over	O
400	O
.	O
</s>
<s>
Maven	B-General_Concept
has	O
since	O
switched	O
to	O
a	O
completely	O
different	O
architecture	O
,	O
proposed	O
by	O
John	O
O'Laughlin	O
and	O
implemented	O
in	O
Quackle	O
.	O
</s>
<s>
The	O
downside	O
of	O
using	O
an	O
exhaustive	O
approach	O
is	O
that	O
Maven	B-General_Concept
lost	O
the	O
ability	O
to	O
vary	O
evaluations	O
as	O
a	O
function	O
of	O
the	O
tiles	O
that	O
remained	O
in	O
the	O
bag	O
.	O
</s>
<s>
Maven	B-General_Concept
's	O
version	O
of	O
exhaustive	O
rack	O
evaluation	O
has	O
added	O
that	O
ability	O
.	O
</s>
<s>
In	O
Maven	B-General_Concept
,	O
each	O
rack	O
has	O
its	O
own	O
liner	O
evaluator	O
,	O
where	O
the	O
value	O
of	O
that	O
rack	O
varies	O
as	O
a	O
function	O
of	O
the	O
chance	O
of	O
drawing	O
a	O
duplicate	O
,	O
the	O
chance	O
of	O
drawing	O
a	O
vowel	O
,	O
and	O
the	O
chance	O
of	O
drawing	O
Q	O
and	O
U	O
.	O
</s>
<s>
The	O
great	O
human	O
champion	O
Ron	O
Tiekert	O
had	O
studied	O
Scrabble	B-Application
by	O
playing	O
out	O
individual	O
positions	O
dozens	O
of	O
times	O
,	O
and	O
tabulating	O
results	O
.	O
</s>
<s>
He	O
suggested	O
that	O
with	O
Maven	B-General_Concept
's	O
speed	O
,	O
it	O
should	O
be	O
possible	O
to	O
automate	O
that	O
process	O
in	O
overnight	O
runs	O
.	O
</s>
<s>
By	O
the	O
mid-1990s	O
,	O
computers	O
had	O
become	O
fast	O
enough	O
that	O
Maven	B-General_Concept
used	O
simulation	O
to	O
choose	O
moves	O
in	O
competitive	O
games	O
under	O
tournament	O
time	O
controls	O
.	O
</s>
<s>
Analysis	O
of	O
games	O
played	O
by	O
Maven	B-General_Concept
's	O
simulation	O
engine	O
suggest	O
that	O
Maven	B-General_Concept
has	O
surpassed	O
the	O
skill	O
level	O
of	O
human	O
champions	O
.	O
</s>
<s>
Strong	O
play	O
in	O
Scrabble	B-Application
endgames	O
is	O
much	O
harder	O
than	O
it	O
looks	O
.	O
</s>
<s>
In	O
theory	O
,	O
endgames	O
are	O
a	O
game	O
of	O
perfect	O
information	O
,	O
so	O
the	O
Alpha-beta	B-Algorithm
pruning	I-Algorithm
algorithm	O
should	O
work	O
.	O
</s>
<s>
But	O
in	O
practice	O
Alpha	O
Beta	O
works	O
badly	O
on	O
Scrabble	B-Application
.	O
</s>
<s>
The	O
problem	O
with	O
Alpha	O
Beta	O
is	O
that	O
some	O
Scrabble	B-Application
endgames	O
require	O
14	O
moves	O
to	O
play	O
out	O
,	O
and	O
it	O
is	O
not	O
possible	O
to	O
search	O
that	O
deeply	O
.	O
</s>
<s>
Maven	B-General_Concept
uses	O
a	O
different	O
approach	O
.	O
</s>
<s>
The	O
B*	B-Protocol
search	I-Protocol
algorithm	I-Protocol
is	O
a	O
selective-depth	O
,	O
progressive-widening	O
algorithm	O
that	O
guarantees	O
to	O
find	O
optimal	O
solutions	O
to	O
two-player	O
games	O
when	O
one	O
can	O
compute	O
upper	O
and	O
lower	O
bounds	O
on	O
the	O
values	O
of	O
each	O
position	O
.	O
</s>
<s>
Since	O
B*	B-Protocol
is	O
reasonably	O
robust	O
in	O
the	O
presence	O
of	O
a	O
small	O
percentage	O
of	O
error	O
in	O
the	O
bounds	O
,	O
Maven	B-General_Concept
can	O
solve	O
endgames	O
that	O
other	O
approaches	O
cannot	O
.	O
</s>
<s>
A	O
further	O
refinement	O
makes	O
Maven	B-General_Concept
's	O
endgame	O
solutions	O
asymptotically	O
optimal	O
even	O
in	O
the	O
presence	O
of	O
errors	O
.	O
</s>
<s>
When	O
the	O
B*	B-Protocol
search	I-Protocol
terminates	O
with	O
a	O
proof	O
that	O
one	O
move	O
is	O
best	O
,	O
and	O
there	O
is	O
still	O
time	O
remaining	O
,	O
then	O
Maven	B-General_Concept
widens	O
its	O
estimates	O
by	O
1	O
point	O
and	O
searches	O
again	O
.	O
</s>
<s>
Maven	B-General_Concept
can	O
play	O
out	O
such	O
states	O
exhaustively	O
in	O
almost	O
all	O
cases	O
.	O
</s>
<s>
That	O
is	O
,	O
for	O
all	O
legal	O
moves	O
Maven	B-General_Concept
can	O
play	O
out	O
the	O
resulting	O
endgames	O
(	O
up	O
to	O
8	O
for	O
each	O
legal	O
move	O
)	O
,	O
and	O
calculate	O
which	O
side	O
will	O
win	O
the	O
game	O
in	O
each	O
case	O
.	O
</s>
<s>
That	O
is	O
,	O
Maven	B-General_Concept
expands	O
its	O
analysis	O
first	O
where	O
the	O
decision	O
is	O
close	O
and	O
relevant	O
.	O
</s>
<s>
In	O
a	O
PEG-2	O
it	O
is	O
normally	O
not	O
possible	O
to	O
exhaustively	O
examine	O
all	O
move	O
sequences	O
,	O
so	O
Maven	B-General_Concept
goes	O
as	O
far	O
as	O
it	O
can	O
in	O
the	O
time	O
available	O
.	O
</s>
<s>
Another	O
limitation	O
is	O
that	O
Maven	B-General_Concept
is	O
not	O
addressing	O
the	O
"	O
hidden	O
information	O
"	O
aspect	O
of	O
such	O
situations	O
.	O
</s>
<s>
Maven	B-General_Concept
is	O
choosing	O
pure	O
strategies	O
at	O
each	O
node	O
.	O
</s>
