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1 UM Stratego Collin Schepers Daan Veltman Enno Ruijters Leon Gerritsen Niek den Teuling Yannick Thimister

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2 Introduction (Yannick) Starting positions (Daan) Evaluation Function (Leon) Monte Carlo (Collin) Genetic Algorithm (Enno) Opponent modelling and strategy (Niek) Results (Yannick) Conclusion (Yannick)

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3 Starting Positions Distance to Freedom Being bombed in Partial obstruction Adjacency Flag defence Startup Pieces

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4 Starting Positions Distance to Freedom

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5 Starting Positions Flag defence

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6 Starting Positions Startup Pieces

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7 Starting Positions Flag:10 for DTF < when bombed in Spy: 1 for pieces > captain, adjacent with higher DTF 2 when bombed in 1 when DTF > 5 1 when DTF > 1, adjacent piece -1 or -2 = piece, adjacent piece higher DTF Scout: 2 for >2 in flag defence 2 when bombed in 1 when DTF > 5 1 when DTF > 1, adjacent piece -1 or -2 = piece, adjacent piece higher DTF 1 for > 5 in DTF < 2 Miner: 1 for >1 in flag defence 2 when bombed in 1 when DTF > 5 1 when DTF > 1, adjacent piece -1 or -2 = piece, adjacent piece higher DTF 1 when on front row 1 for each > 1 in DTF < 2 Sergeant: 1 for >1 in flag defence 1 when DTF > 1, adjacent piece -1 or -2 = piece, adjacent piece higher DTF 2 for > 3 in DTF < 2 Lieutenant: 1 for >1 in flag defence 1 when DTF > 1, adjacent piece -1 or -2 = piece, adjacent piece higher DTF 2 for > 3 in DTF < 2 Captain: 2 when bombed in 1 when DTF > 5 1 when DTF > 1, adjacent piece -1 or -2 = piece, adjacent piece higher DTF 2 for > 3 in DTF < 2 1 when spy adjacent 1 for each > 2 in DTF < 2 Major: 2 when bombed in 1 when DTF > when on flag side 1 when DTF > 1, adjacent piece -1 or -2 = piece, adjacent piece higher DTF 2 for > 2 in DTF < 2 Colonel: 2 when bombed in 1 when DTF > when on flag side 1 when DTF > 1, adjacent piece -1 or -2 = piece, adjacent piece higher DTF 1 for > 1 in DTF < 2 General: 2 when bombed in 1 when DTF > when on flag side and Marshal not on flag side 1 when DTF > 1, adjacent piece -1 or -2 = piece, adjacent piece higher DTF Marshal: 2 when bombed in 1 when DTF > when on flag side Bombs: 2 when bombed in 1 when DTF > when sergeant adjacent + 2 when lieutenant adjacent 1 when scout adjacent

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8 Sub-functions of the evaluation function: Material value Information value Near enemy piece value Near flag value Progressive bonus value Evaluation Function

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9 How it works: All the sub-functions return a value These values are then weighted and added to each other The higher the total added value, the better that move is for the player

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10 Evaluation Function Material Value: Used for comparing the two players' board strengths Each piece type has a value Total value of the opponent's board is subtracted from the player's board value Positive value means strong player board Negative value means weak player board

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11 Evaluation Function Information value: Stimulates the collection of opponent information and the keeping of personal piece information Each piece type has a certain information value All the values from each side are summed up and then substracted from each other A marshall being discovered is worse than a scout being discovered

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12 Evaluation Function Near enemy piece value Checks if a moveable piece can or cannot defeat a piece next to it If piece can be defeated, return positive score If not, return a negative one If piece unknown, return 0

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13 Evaluation Function Near flag value Stimulates the defence of own flag and the attacking of enemy's flag Constructs array with possible enemy flag locations If enemy near own flag, return negative number If own piece near possible enemy flag, return positive number

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14 Evaluation Function Progressive bonus value Stimulates the advancement of pieces towards enemy lines Returns a positive value if piece moves forward Negative if backward

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15 Monte Carlo A subset of all possible moves is played No strategy or weights used Evaluation value received after every move At the end a comparison of evaluation values determines the best move A depth limit is used so the tree doesn't grow to big and the algorithm will end at some point

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16 Monte Carlo Tree representation

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17 Monte Carlo Advantages: Simple implementation Can be changed quickly Easy observation of behavior Good documentation Good for partial information situations

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18 Monte Carlo Disadvantages: Generally not smart Dependents on the evaluation function Computationally slow Tree grows very fast A lot of memory required

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19 Genetic Algorithm Evolve weights of the terms in the evaluation functions AI uses standard expectiminimax search tree Evolution strategies (evolution paremeters are themselves evolved)

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20 Genetic Algorithm Genome: Mutation:

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21 Genetic Algorithm Crossover: σ and α of parents average weights: Averaged if difference < α Else randomly chosen from parents

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22 Genetic Algorithm Fitness function: Win bonus Number of own pieces left Number of turns spent

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23 Genetic Algorithm Reference AI: Monte Carlo AI Self-selecting reference genome Select average genome from each generation Pick winner between this genome and previous reference

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24 Opponent modeling Observing moves Ruling out pieces Stronger pieces are moved towards you Weaker pieces are moved away

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25 Opponent modeling Initial probability distribution Updating the probabilities Update the probability of the moving piece Update probabilities of free pieces nearby Bluffing Bluffing probability

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26 Strategy Split the game up into phases Exploration phase Elimination phase End-game phase Alter the evaluation function

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27 Results First generation GA against MC First generation GA wins 80,0% of the games Algorithmnr. of winsAverage nr. of turns Standard deviation First GA87990,684,5 MC163184,789,6 None (draw)60

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28 Results Newest generation (66th) GA against MC GA won 81,3 % of the games Algorithmnr. of winsAverage nr. of turns Standard deviation Newest GA42685,078,2 MC73181,490,8 None (draw)25

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29 Results First generation GA against newest generation of GA First GA wins 40,9 % of the games Newest generation GA wins only 25% Algorithmnr. of winsAverage nr. of turns Standard deviation First GA391080,665,4 Newest GA ,066,7 None (draw)3266

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30 Conclusion Monte Carlo is (still) weaker than GA Limited by begin piece setup Manual weight tweaking required GA gets weaker after training Non transitivity of references Should let it play against other AI's

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