A Complex Systems Introduction to GoHistory Rules Emergence Computers Future Background image by Wikpedia user Donar Resikoffer Wei Chi, Go, Baduk... • Oldest board game in the world

Background image by Juha Nieminen

A Complex Systems Introduction to Go

Eric JankowskiCSAAW

10-22-2007

History Rules Emergence Computers FutureBackground image by Wikpedia user Donar Resikoffer

Wei Chi, Go, Baduk...

• Oldest board game in the world (maybe)

• Developed by Chinese monks

• Spread to Japan by monks

• Popularized in Japan

• Spread back to China and Korea

History


Recent History

• Go spreads West ~ last 200 years

• First Western pro (1978) - Manfred Wimmer

• First American pro (1981) - Michael Redmond

• First computer go tournament - 1984

• Hikaru No Go bringing new young players

History


Go is simple

No Suicide

No Infinite loops

Whoever has more, wins

Rules


Definitions

• Group: 1 or more touching stones of the same color

• Touching: When two stones share an edge

• Liberty: An empty node adjacent to a group

Rules


How’s it played?

• Players alternate turns

• You can play a stone or pass

• Restrictions on stone placement:

• After removing enemy stones, can’t have any groups with zero liberties

• Can’t repeat the same board position twice

• Score = Prisoners + Territory (Japanese)

• Score = Stones + Territory (Chinese)

Rules


Wait... that’s it?

• Yes.

• Add stones to the board

• Try and make territory

• Can’t kill yourself or repeat a position

• And this is the greatest game in the history of the world.

Emergence


You have got to be kidding

• No. Seriously.

• It’s totally sweet.

• From those simple rules emerges incredible complexity

Emergence


Eyes and Life

• Invincible groups: Two eyes guarantees life!

• Seki: Life for groups without two eyes?!

Emergence


Ko Fights

• Arise from the “no repeats” rule

• Can make non-local positions matter

• Are pretty common

Emergence


Ladders

Emergence


Strategy

• “Good shape” and “bad shape”

• Balance between:

• Greed and safety

• Attack and defense

• Correctness and complexity

Emergence


Go is complex

• From 3 simple rules, way more possible games than particles in the universe

• Lots of different patterns emerge:

• live/dead groups

• ways of capturing stones

• ko’s create nonlocal interactions

Emergence


in siligo

• 1997 - Kasparov loses to Deeper Blue. People freak out as they slowly realize this means they will be inevitably enslaved by superintelligent robot overlords.

• Skeptics of robot uprising point to Go: “Computers will never beat people at Go, stop investing in EMP devices and get back to work.”

Computers


Challenges of Go AI

• Huge branching factor

• Game has about 200 moves- so you average about 200 move choices per turn

• Difficult move evaluation

• Very abstract for non-endgame positions

• Non-trivial for endgame positions

Computers


Current methods

• alpha-beta algorithm

• Upper confidence bounds applied to trees (UCT)

• Null-move pruning

• Expert information for common positions

Computers


alpha-beta

• Reduces branching factor out to some depth

• alpha = best result after opponent moves

• beta = worst case scenario for opponent

• Assume opponent makes best response

• Toss out any moves < alpha

• Toss out any moves > beta

• Efficiency depends on order of search

Computers


UCT

• UCT math is kinda complicated

• Builds lookahead tree with biased Monte Carlo sampling

• Ensures only “interesting” moves looked at

• Each state is a multi-armed bandit, each move is an arm to the bandit

• Does better than alpha-beta, requires lots of memory

Computers


UCT

• Given state s, depth d, and some position evaluation function...

• Initialize: Randomly generate some moves, evaluate them, d--;

• Values of arms = X(j)’s

• Loop: play move that maximizes X(ave) + sqrt( (2log n)/T(j,n) )

Computers


Null-move pruning

• What’s the worst possible situation if I pass?

• If I’m ok after a shallow search, sweet!

• Means that this is a really good move

• Null move pruning + alpha-beta reduces branching by ~ square root

Computers


MoGo

• Current world champion program

• UCT + expert knowledge to build lookahead trees

• Monte Carlo move evaluation

• Currently about 4k (30k-1k, 1d-9d)

Computers


Computer go to come...

• Improve and combine currently used methods

• UCT to build search trees

• Null-move pruning

• Newer and more specialized hardware

• “re-use” information from tree branches, transposing them to other locations

• F.S. Hsu thinks 100 trillion searches per second will be able to beat pros

Future


Robot overlords?

• Perhaps some serial brute-forcing can get eventually get close to human strength

• No immediate danger of robots enslaving us

• Human brains do a really good job (pattern recognition) with really hard stuff (go)

• Play go: it makes robots cry (if they had feelings)

Future


Advertisements

• www.umich.edu/~goclub

• www.usgo.org

• AADL; 2:00pm-3:00pm on Sunday!

• Michigan League: Dec 1: Tournament!


Some references

• http://www.lri.fr/~gelly/MoGo.htm - MOGO

• http://videolectures.net/otee06_gelly_umc/ - some nice talks on UCT and MOGO

• http://www.spectrum.ieee.org/print/5552 - article by Hsu on computer go

Documents

A Complex Systems Introduction to GoHistory Rules Emergence Computers Future Background image by Wikpedia user Donar Resikoffer Wei Chi, Go, Baduk... • Oldest board game in the world