Transcript INTELLIGENT SYSTEM FOR PLAYING TAROK

INTELLIGENT SYSTEM
FOR PLAYING TAROK
Mitja Luštrek & Matjaž Gams
Jožef Stefan Institute
Ljubljana, Slovenia
PERFECT AND IMPERFECT INFORMATION GAMES

Perfect information
(players have full knowledge of the state of the game)





Chess, backgammon
Checkers, Othello
Connect-four
...
Imperfect information
(players have only partial knowledge of the state of the game)

Bridge
 Poker
 Tarok
 ...
THE GAME – TAROK





Very popular in Central Europe
Many variants (tarock, taroky, königsrufen...)
Three players: two against one
54 cards: suits and trumps – taroks
The objective is winning tricks
THE PROGRAM – SILICON TAROKIST

Tarok-playing programs exist, but little is known of how they work.

Tarok.net (www.tarok.net)
 Tarock World (www.gatecentral.com/triangle)
 ...

We developed Silicon
Tarokist.

Freely available
(tarok.bocosoft.com)
 Plays reasonably well
as judged by human
players.
GAME TREE SEARCH

Alpha-beta algorithm is used to search a single game tree.
Nodes – game states
 Edges – moves

SAMPLING

Monte Carlo sampling is used to generate samples of other players’
hands.
ALPHA-BETA ENHANCEMENTS

Transposition table

Fuzzy transposition table
 Similar to partition search (bridge program GIB, M. L. Ginsberg, 1996)



Move ordering
Adjusting the width of search window
Pruning the game tree
TRANSPOSITION TABLE



Usually: transposition table
stores single game states and
their values.
Partition search: for each
encountered game state, a set
of states with equal value is
calculated and stored together
with the value.
Silicon Tarokist: the set of
equivalent game states is
determined heuristically.
OTHER ALPHA-BETA ENHANCEMENTS

Move ordering

Moves that cause cut-offs should be tried first.
 History heuristic: moves that have caused cut-offs in previously
searched game states are given priority.

Adjusting the width of search window

Narrower search window causes more cut-offs, thus speeding up the
search.
 Minimal window search: non-first children of a node are searched with
minimal window, since we are trying to show they are inferior to the first
one.

Pruning the game tree

Some moves can be discarded because they are either clearly bad or
redundant – the same effect can be achieved by another move.
MONTE CARLO SAMPLING ENHANCEMENT



Monte Carlo sampling has demonstrable deficiencies.
Nevertheless, it works.
Deficiency we observed:

An assumption about the state of the game is made.
 Sequence of bad, but inevitable move – good move is evaluated equally
as good move – bad, but inevitable move.
 Sometimes bad, but inevitable move is made first.
 Then it turns out it is not inevitable.

Solution:

In addition to full search, search to the depth of one trick is performed.
 This emphasizes immediate profit.
 A combination of both searches is used for the final decision.
RESULTS



Game tree search algorithm in Silicon Tarokist searches 184-times
less nodes than alpha-beta using uses 86-times less time.
The program does not play flawlessly, but it is a challenging
opponent.
For truly high-level play, game tree search that we use in
inadequate.

It is too shallow for long-term strategies to be developed.
 It will either have to be improved significantly
 or another – probably knowledge-based – way to develop long-term
strategies will have to be devised.