What you are suggesting is quite similar to what human players do.
The problem is that Don is trying to bias for speed with a hash-table
like evaluation to quickly identify the board. I think that if there
were
a fast dependable algorithm for the identification of "irrelevant"
stones
prior to computing that hash, then we would not need to use Tromp-
Taylor rules. But there is not, so we do.
Cheers,
David
On 15, Oct 2006, at 4:40 AM, Jacques Basaldúa wrote:
Don Dailey wrote:
>Another question is how many illegal board configurations are
there ...
>by assigning each point on the board a random state of
(white,black,empty)
That does not represent real game positions. All positions have about
7x7x2/3 = 33 stones. (A normal distribution assuming the state is
uniform)
On 7x7, real positions have 1, 2, 3 .. stones. Obviously, the
probability
of a position being illegal depends on (increases with) the number
of stones.
>My intuition is that I probably can't get the serious memory
reduction
>I need to make it practical on my current computer.
Just an idea. I don't know if it will produce enough benefits to
compensate
the increase of complication, but here it is: Another way of
reducing the
number of positions is automatically finding "don't care" board
cells. Eg.
If you have a position with best move = a and value = v and the same
position with an irrelevant dead stone, with the same best move and
value v' which is v considering the ruleset. E.g. under Japanese
ruleset
v' = v + 1 in case of an opponent's dead stone v' = v - 1 in case
of an
own unnecessary stone filling territory. Once detected, both positions
are merged with the board cell marked as "don't care". Of course,
you need different classes of "don't care" such as:
"don't care in dame" (does not produce score variation)
"own or void" (cannot be an opponent's stone), "opponent or void",
etc.
These ideas are not new, but as far as I know that patterns have been
set up manually. What I suggest is doing this automatically from
comparing different board positions. Finding similar positions is not
impossible if they are identified by best move and some metric (or
a pseudometric where equivalence classes are relevant) is defined in
board space. Each time a new position is found, a quick search may
determine if it belongs to an existing class and can be merged with it
or it defines a new class and must be stored as it is. I believe, the
number of different positions belonging to a class (= same problem
with irrelevant differences) compensates the extra complications, but,
until someone tries, who knows ;-)
Jacques.
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