14. Monte Carlo Go

In Monte Carlo Go the engine plays random games to the end, generating moves from a pattern database within the context of the algorithm UCT (upper confidence bounds applied to trees). This algorithm allowed the program MoGo (http://www.lri.fr/~gelly/MoGo.htm, to become the first computer program to defeat a professional while taking a 9 stone handicap (http://senseis.xmp.net/?MoGo).

GNU Go 3.8 can play 9x9 Go with the option ‘--monte-carlo’ using the UCT algorithm. For command line options, see See section Invoking GNU Go: Command line options.

During reading, the engine makes incremental updates of local 3x3 neighborhood, suicide status, self-atari status, and number of stones captured, for each move.

GNU Go’s simulations (Monte Carlo games) are pattern generated. The random playout move generation is distributed strictly proportional to move values computed by table lookup from a local context consisting of 3x3 neighborhood, opponent suicide status, own and opponent self-atari status, number of stones captured by own and opponent move, and closeness to the previous move. Let’s call this local context simply "a pattern" and the table "pattern values" or simply "patterns".

There are three built-in databases that you can select using the option ‘--mc-patterns <name>’, where ‘<name>’ is one of

mc_montegnu_classic
mc_mogo_classic
mc_uniform

The first of these is an approximation of the previous random move generation algorithm. The mogo_classic pattern values is an approximation of the simulation policy used by early versions of MoGo, as published in the report odification of UCT with Patterns in Monte-Carlo Go RR-6062, by Sylvain Gelly, Yizao Wang, Rémi Munos, and Olivier Teytaud. The uniform pattern values is the so called "light" playout which chooses uniformly between all legal moves except single point proper eyes.

If you’re not satisfied with these you can also tune your own pattern values with a pattern database file and load it at runtime with ‘--mc-load-patterns <name>’ adding your own pattern database.

Let’s start with the uniform pattern values. Those are defined by the file ‘patterns/mc_uniform.db’, which looks like this:

oOo
O*O
oO?

:0

oOo
O*O
---

:0

|Oo
|*O
+--

:0

Patterns are always exactly 3x3 in size with the move at the center point. The symbols are the usual for GNU Go pattern databases:

* move
O own stone (i.e. the same color as the color to move)
o own stone or empty
X opponent stone
x opponent stone or empty
? own stone, opponent stone, or empty
| vertical edge
- horizontal edge
+ corner

There’s also a new symbol:

% own stone, opponent stone, empty, or edge

After the pattern comes a line starting with a colon. In all these patterns it says that the pattern has a move value of 0, i.e. must not be played. Unmatched patterns have a default value of 1. When all move values are zero for both players, the playout will stop. Including the three patterns above is important because otherwise the playouts would be likely to go on indefinitely, or as it actually happens be terminated at a hard-coded limit of 600 moves. Also place these patterns at the top of the database because when multiple patterns match, the first one is used, regardless of the values.

When using only these patterns you will probably notice that it plays rather heavy, trying hard to be solidly connected. This is because uniform playouts are badly biased with a high probability of non-solid connections being cut apart. To counter this you could try a pattern like

?X?
O*O
x.?

:20,near

to increase the probability that the one-point jump is reinforced when threatened. Here we added the property "near", which means that the pattern only applies if the previous move was played "near" this move. Primarily "near" means within the surrounding 3x3 neighborhood but it also includes certain cases of liberties of low-liberty strings adjacent to the previous move, e.g. the move to extend out of an atari created by the previous move. You have to read the source to find out the exact rules for nearness.

We could also be even more specific and say

?X?
O*O
x.?

:20,near,osafe,xsafe

to exclude the cases where this move is a self atari (osafe) or would be a self-atari for the opponent (xsafe).

It may also be interesting to see the effect of capturing stones. A catch-all pattern for captures would be

?X%
?*%
%%%

:10,ocap1,osafe
:20,ocap2
:30,ocap3

where we have used multiple colon lines to specify different move values depending on the number of captured stones; value 10 for a single captured stone, value 20 for two captured stones, and value 30 for three or more captured stones. Here we also excluded self-atari moves in the case of 1 captured stone in order to avoid getting stuck in triple-ko in the playouts (there’s no superko detection in the playouts).

The full set of pattern properties is as follows:

near: The move is "near" the previous move.
far: The move is not "near" the previous move.
osafe: The move is not a self-atari.
ounsafe: The move is a self-atari.
xsafe: The move would not be a self-atari for the opponent.
xunsafe: The move would be a self-atari for the opponent.
xsuicide: The move would be suicide for the opponent
xnosuicide: The move would not be suicide for the opponent.
ocap0: The move captures zero stones.
ocap1: The move captures one stone.
ocap2: The move captures two stones.
ocap3: The move captures three or more stones.
ocap1+: The move captures one or more stones.
ocap1-: The move captures at most one stone.
ocap2+: The move captures two or more stones.
ocap2-: The move captures at most two stones.
xcap0: An opponent move would capture zero stones.
xcap1: An opponent move would capture one stone.
xcap2: An opponent move would capture two stones.
xcap3: An opponent move would capture three or more stones.
xcap1+: An opponent move would capture one or more stones.
xcap1-: An opponent move would capture at most one stone.
xcap2+: An opponent move would capture two or more stones.
xcap2-: An opponent move would capture at most two stones.

These can be combined arbitrarily but all must be satisfied for the pattern to take effect. If contradictory properties are combined, the pattern will never match.

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14.1 Final Remarks

Move values are unsigned 32-bit integers. To avoid overflow in computations it is highly recommended to keep the values below 10000000 or so.
There is no speed penalty for having lots of patterns in the database. The average time per move is approximately constant (slightly dependent on how often stones are captured or become low on liberties) and the time per game mostly depends on the average game length.
For more complex pattern databases, see ‘patterns/mc_montegnu_classic.db’ and ‘patterns/mc_mogo_classic.db’.