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Dice Game IntroductionMiller TinkerhessUniversity of Michigan

Overview Two or more players Each player starts with five dice Each round, one player wins or loses a die– Usually loses Last player with dice left wins the game

Why is this interesting? Mixed symbolic / probabilistic reasoning– Heuristic reasoning vs. precise calculations Opponent modeling– Gleaning information from opponent's actions It's fun!– We're competitive; can Soar defeat us?

PerceptionDuring each player's turn, they perceive:–––––The dice under their own cupDice that any player has pushedHow many dice are under each player's cupMove historyLegal actions to take (affordances)

Actions BidBid and PushPassChallenge previous bid or passExact

Bids A bid has a face and a count– e.g. “Three sixes”, “Two fours”, “One one” The first player may make any bid Subsequent bids must increase either theface or the count If the count increases, the face may decrease The count may not decrease

Bids“One four”“One five”“One six”“Two twos”“Two threes” face face count, - face face

Ones Ones are wild To compensate, bids on ones may halve thecurrent count value (rounding up) Bids following bids on ones must double andadd one to the count

Ones“One two”“Two threes”“One one”“Two ones”“Five twos” face; count! count (ones) count2x 1 count; face

Push When a player bids, they may push some oftheir dice and re-roll their other dice Pushed dice are viewable by all players Advantage:– Higher probability of your bid being correct Disadvantage:– Opponents get to see some of your dice

Pass You may pass once per round By passing, you are asserting that all yourdice are showing the same face If you bluff a pass and are challenged, youlose a die

Exact Once per game, if you think the previous bidwas exactly correct, you may exact If you exact and the previous bid was exactlycorrect, you gain a die (limit 5) Otherwise, you lose a die

PlayerOpponent“Three sixes”“Four fours”“Five fours”Round1“Challenge”Result:Three fours two ones(Five fours)Opponent loses a die

PlayerOpponent“Three twos”“Three threes”“Four twos & push”(re-roll hidden dice)Round 2“Challenge”Result:Two twos two ones(Four twos)Player loses a die

Agent Perception il .players player * id (int) cup count (int) die * face (int)*multi-valued attribute il .state last-bid player player action (string) face (int) multiplier (int) next bid

Agent Actions il .affordances action * name (string) available (string) target player *multi-valued attribute ol bid face (int) multiplier (int) challenge target (int) exact pass push die * face (int) sleep