Loading in 5 sec....

New Approximate Strategies for Playing Sum Games Based on Subgame TypesPowerPoint Presentation

New Approximate Strategies for Playing Sum Games Based on Subgame Types

- 277 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about '' - Gabriel

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

### New Approximate Strategies for Playing SumGames Based on Subgame Types

Outline

Authored by:

Manal M. Zaky

Cherif R. S. Andraos

Salma A. Ghoneim

Presented by:

Manal M. Zaky

Outline

- Sum Games
- Combinatorial Game Theory
- Previous Strategies
- New Strategies
- Experimental Results
- Conclusions and Future Work

ICCSE’06, Cairo, Egypt

Sum Games

- Let G1 ,...,Gn represent n games
- Playing in the sum game
G = G1 +...+Gn

consists of picking a component game Gi and making a move in it

ICCSE’06, Cairo, Egypt

+

+

Sum Games (cont.)- Example I: NIM
- Several heaps of coins
- In his turn, a player selects a heap, and removes any positive number of coins from it, maybe all

- Goal
- Take the last coins

- Example with 3 piles: (3,4,5)

ICCSE’06, Cairo, Egypt

Sum Games (cont.)

- Many games tend to decompose into a number of independent regions or subgames.
- Examples:
- Domineering
- GO
- Amazons

ICCSE’06, Cairo, Egypt

Sum Games (cont.)

- Example II: Domineering
- Start with the board empty
- In his turn a player places a domino on the board:
- Blue places them vertically
- Red places them horizontally

- Goal
- Place the last domino

- Example game

=

ICCSE’06, Cairo, Egypt

Sum Games (cont.)

- Example III: Go
- The standard Go board is 19X19; games are also played on 13X13 and 9X9.
- The Go board begins empty. One player uses the black stones and the other uses the white stones.
- Black always goes first. Players take turns placing one stone on the board.
- Once a stone is placed on the board, it is never moved unless it is captured
- Game ends when both players agree that there are no more moves to be played.

- Goal
- surround more territory than the opponent

ICCSE’06, Cairo, Egypt

Sum Games (cont.)

- Example III: Go (cont.)
- Towards endgame, board becomes partitioned into a number of independent subgames

ICCSE’06, Cairo, Egypt

Sum Games (cont.)

- Full game: high branching factor, long game
- Local game: low branching factor, short game

Challenge: how to combine local analyses

To achieve near optimal results

ICCSE’06, Cairo, Egypt

Sum Games (cont.)

- Tool for Local Game Search:
- minimax search
- Unable to consider successive moves by same player
- Cannot be used to find best global sequence

- Combinatorial game theory(CGT)
is used to perform the search due to its ability to represent a game as a sum of independent subgames

- minimax search

ICCSE’06, Cairo, Egypt

Sum Games

- CGT
- Deals with partitioned game
- Local analysis
- Search time exponential insize ofsubproblems

Minimax

- Considers the sum game as one unit
- Full board evaluation
- Search time exponential in size of thefull problem

ICCSE’06, Cairo, Egypt

Outline

- Sum Games
- Combinatorial Game Theory
- Previous Strategies
- New Strategies
- Experimental Results
- Conclusions and Future Work

ICCSE’06, Cairo, Egypt

Combinatorial Game Theory

- Developed by Conway, Berlekamp and Richard K. Guy in the 1960s
- A combinatorial game is any two player perfect information game satisfying the following conditions:
- Alternating moves
- Player who cannot move loses
- no draws
- No random element

ICCSE’06, Cairo, Egypt

Combinatorial Game Theory (cont.)

- Combinatorial game theory (cgt) provides abstract definition of combinatorial games
- A game position is defined by sets of follow-up positions for both players (Left, Right)
G={GL|GR}={L1,L2,L3|R1,R2}

ICCSE’06, Cairo, Egypt

Combinatorial Game Theory (cont.)

- Examples:
- The simplest game is the ‘zero game’ in which no player has a move:
0 = { | } with GL, GR empty

- The game 1 = {0 | } = { { | } | } represents one free move for Left
- Similarly, The game -1 = { | 0 } = { | { | } } represents one free move for Right
- G = { {14 | 10} | {7|3} }

- The simplest game is the ‘zero game’ in which no player has a move:

ICCSE’06, Cairo, Egypt

Combinatorial Game Theory (cont.)

- Hot Game
- A game in which each player is eager to play
- A hot game is not a number
- Example of a hot game:

ICCSE’06, Cairo, Egypt

Combinatorial Game Theory (cont.)

- Properties of Hot Games:
- Temperature:
- Measures urgency of move

- Type:
- Sente
- A sente move by a player implies a severe threat follow-up forcing the opponent to answer locally. This leaves the original player free to play where he chooses, thereby controlling the flow of the game.

- Double Sente
- is a move which is sente for either player

- Gote
- a move which loses the initiative, since it need not be answered by the opponent, thus giving him Sente

- Sente

- Temperature:

ICCSE’06, Cairo, Egypt

Combinatorial Game Theory (cont.)

- Properties of hot games (cont.)
- Thermograph

ICCSE’06, Cairo, Egypt

Combinatorial Game Theory (cont.)

- Thermographs of simple hot games of the form G={{A|B}{C|D}}

temperature

ICCSE’06, Cairo, Egypt

Combinatorial Game Theory (cont.)

- Approximate Strategies to Play Sum Games based on CGT
- Compute simple properties of each subgame
- Thermograph
- Temperature
- Type

- Make global decision based on one or more of these properties

- Compute simple properties of each subgame

ICCSE’06, Cairo, Egypt

Outline

- Sum Games
- Combinatorial Game Theory
- Previous Approximate Strategies
- New Strategies
- Experimental Results
- Conclusions and Future Work

ICCSE’06, Cairo, Egypt

Previous Approximate Strategies for Playing Sum Games

- ThermoStrat
- Graphical determination of the best subgame based on the compound thermograph of the sum

- MaxMove
- Compute the width of the thermograph at t=0 for each subgame
- Play in subgame with maximum value

- HotStrat:
- Compute temperature of each subgame
- Play in hottest subgame

- MaxThreat
- Choose the best subgame by comparing them two by two using minimax

ICCSE’06, Cairo, Egypt

Previous Approximate Strategies for Playing Sum Games

- Performance of Approximate Strategies Compared to Optimal
- Thermostrat is always good. For subgames with different types gives same result as optimal in 90% of the cases and slightly less in others.
- The performance of each of Hotstrat and Maxmove is highly dependent on the types of subgames participating in the sum.
- MaxMove strategy gives the same result as ThermoStrat for the pattern with only reverse sente games. Performs badly for the rest.
- HotStrat shows very low performance in dealing with patterns that contain reverse sente subgames alone or when combined with only sente games but very good otherwise.

ICCSE’06, Cairo, Egypt

Previous Approximate Strategies for Playing Sum Games - Performance

- Maxthreat’s performance depends on the order in which
subgames are considered when the sum contains one or more sente gamesas shown

ICCSE’06, Cairo, Egypt

Outline

- Sum Games
- Combinatorial Game Theory
- Previous Approximate Strategies
- New Strategies
- Experimental Results
- Conclusions and Future Work

ICCSE’06, Cairo, Egypt

Outline

- Sum Games
- Combinatorial Game Theory
- Previous Approximate Strategies
- New Strategies
- Experimental Results
- Conclusions and Future Work

ICCSE’06, Cairo, Egypt

- Sum Games
- Combinatorial Game Theory
- Previous Approximate Strategies
- New Strategies
- Experimental Results
- Conclusions and Future Work

ICCSE’06, Cairo, Egypt

Conclusions

ICCSE’06, Cairo, Egypt

Future Work

ICCSE’06, Cairo, Egypt

Thank You

ICCSE’06, Cairo, Egypt

Download Presentation

Connecting to Server..