1. INTELLIGENT SYSTEM FOR PLAYING TAROK
Mitja Luštrek & Matjaž Gams
Jožef Stefan Institute
Ljubljana, Slovenia

2. 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

3. 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

4. THE PROGRAM – SILICON TAROKIST
Tarok-playing programs exist, but little is known of how they work.
Tarok.net (
Tarock World (
...
We developed Silicon Tarokist.
Freely available (tarok.bocosoft.com)
Plays reasonably well as judged by human players.

5. GAME TREE SEARCH
Alpha-beta algorithm is used to search a single game tree.
Nodes – game states
Edges – moves

6. SAMPLING
Monte Carlo sampling is used to generate samples of other players’ hands.

7. 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

8. 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.

9. 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.

10. 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.

11. 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.