A Whist AI

1
A Whist AI

• Jason Fong
• CS261A, Spring 2005

2
What is Whist?

• Old card game, driven into obscurity by Bridge
• Similar to other trick taking games
• Bridge, Spades, Hearts
• Many variations no current official version
• Variation studied is the one I play
• Similar to Oh Hell!
• a.k.a. Perpetual Aggravation, Oh Jerusalem, Oh
  Pshaw, Blackout, Screw Your Neighbor, Nomination
  Whist, or Animal

3
Rules of Whist

• Game structure
• Played with 5 players
• No partnerships
• Rounds played with varying number of cards
• 10-9-8--3-2-1-1-2-3--8-9-10
• After hands dealt, next card turned face up and
  determines the trump suit
• Players take turns dealing
• Highest cumulative score wins

4
Rules of Whist

• Trick taking game
• Each player plays one card per round
• Suit of first card played is the lead suit
• Subsequent players must play same suit if
  possible
• If no cards of same suit, then play any card
• Highest card of lead suit wins the trick
• Trump suit
• One suit is designated as the trump for each deal
• Highest card of trump suit always wins a trick
• Can only play trumps if void of lead suit or if
  trump led

5
Rules of Whist

• Bidding
• Each player declares how many tricks they will
  take
• Goal is to take exact number of tricks bid
• Bidding starts at person following dealer
• Bids must not add up to number of cards dealt to
  each player
• Dealer bids last bid value restricted

6
Rules of Whist

• Scoring
• One point for each trick taken
• 10 points for making bid exactly
• No bonus for zero (nil) bids
• Making/missing bids most important part of score
• Stopping other players bids factors into
  strategy
• Also need to consider other players trying to
  stop you

7
Making an AI for Whist

• Perform some sort of search
• Each node is a particular play order
• Internal nodes are the order of play for a
  partial game
• Leaves are complete order of play
• Imperfect information

8
A Naïve Approach

• Assume opponents can have any card not seen yet
• Search tree quickly explodes
• Worse case when 10 cards dealt
• Depth of 50
• Opponent branching factor begins at 41
• Branching factor reduces by one with each
  opponent turn but tree still too big
• Number of leaves 41! x 10! 1056

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Reducing Branching Factor

• Assume we can cheat, and peek at opponents cards
• Branching factor becomes the number of cards in
  an opponents hand
• Tree still too large to search completely
• Number of leaves (10!)5 6 x 1032
• Cut off search depth and use a heuristic

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Heuristic

• Most important part of score is making bids
• How likely is it to make the bid?
• How many tricks can I win?
• How many tricks can I duck?
• Calculating a heuristic value
• Classify cards based on ability to win / duck a
  trick
• Consider tricks needed to make bid
• Estimate final number of tricks taken

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Heuristic

• Classify cards in your hand
• Absolute winners
• Have highest card of suit, and no players void of
  the suit has a trump
• Absolute losers
• At least one player has the suit and their lowest
  value is higher than this card
• Or some player has all trumps
• Likely winners / losers
• Consider whether an opponent wants to take the
  trick
• Consider opponent tricks left after absolute
  winners/losers
• Neutral cards
• Everything else

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Heuristic

• Calculating a heuristic value
• Tricks to make bid
• Subtract absolute winners
• Subtract some fraction of likely winners
• If under bid subtract some fraction of neutrals
• If over bid add some fraction of neutrals
• Gives an estimate of likelihood of making bid

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Heuristic

• Other considerations
• Each trick taken adds a point
• If you cant make your bid, might as well take as
  many tricks as possible
• Forcing opponents to miss a bid
• If everybody misses their bid, then scores dont
  change much
• If you cant make your bid, take as many others
  down with you

14
Search Methodology

• Maxn algorithm
• Similar to minimax, but for n players
• Evaluation of each node gives an n-tuple
• Each node maximizes the moving players element
  in the n-tuple
• Backup entire n-tuple to parent
• Best next move is best child of root

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An Honest Whist AI

• Nobody wants to play with a cheater
• But gamblers are fine use Monte-Carlo
  simulation
• Remember which cards have been seen
• Take unseen cards and randomly deal the
  opponents hands
• Peek at cards and find best move
• Do this many times and count how often each of
  your cards was chosen as the best move
• Play the card that came up most often
• Pseudo-perfect-information while searching, but
  does not need to see the actual cards in play

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Optimization Considerations

• Branching factor decreases as game progresses
• Search deeper later in game
• No choice of moves in last trick
• Automatically play last 5 cards
• Possible to have only one legal move
• Dont search, just play the card

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Improving Quality

• Depth vs. Iterations
• Thinking time can be spent on searching deeper or
  searching more iterations of deal variations
• Many cards in hand Favor iterations
• Many more possible variations need more samples
• Searching deeper not cost-effective
• Additional depth more expensive
• Heuristic values not as accurate
• Few cards in hand Favor depth
• Fewer possible variations need fewer samples
• Complete search more often
• Heuristic more accurate when fewer cards left to
  play
• Adjust depth and iterations based on cards left
  to play

18
Evaluation Methodology

• Non-standard game, so no existing programs to
  compare against
• A subjective evaluation
• Played against a focus group of four human
  players
• Took their comments on blunders made by the AI
• Observed percentage of games won
• Observed reasoning behind moves made
• Difficult to determine effect of each component
  of the system

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Results

• Play against the focus group suggests the AI
  plays acceptably well
• Does not play well enough to consistently win
• Plays well enough to not fall hopelessly behind
• Trials possibly effected by opponent bias
• Human players focused on defeating the AI player
• AI possibly hindered by not being paranoid enough

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Heuristic Improvements

• Weights of likely winners/losers
• Divide neutral card classification based on
  whether a card is more likely to win or lose
• Rank cards relative to other remaining cards with
  same suit
• Count how many cards of the same suit have been
  played likelihood of being trumped
• Consider protected high cards
• If you have low cards of the same suit as a high
  card, not as dangerous when close to getting too
  many tricks
• Adjust value of forcing missed bids
• Learned paranoia degree for each opponent

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Other Improvements

• Deal opponent hands based on their bids
• Need to consider bids being incorrect when a
  player misses with a winner/loser card
• Observe play and count possible missed
  winners/losers?
• Adds lots of complications

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Automating Bidding

• Possible algorithm
• Consider all bid possibilities and get backed up
  value at root
• Choose bid with best backed up value
• Results not very effective
• Missing other factors protected high cards,
  long/short suits, ability to keep / give away
  lead, etc.
• Bids entered manually
• Evaluation based on live games, so no need to
  quickly bid on a large number of games
• Focus on card play without being affected by bid
  quality

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Conclusions

• Produced a respectable Whist AI
• Not a dominating player, but still many
  possibilities for improvements
• Winner/loser card classifier effective for Whist
  possibly applicable to other trick taking games
• Suggests that Monte-Carlo / peek-at-cards method
  can be effective for other imperfect information
  card games

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Future Work

• Improve AI performance
• Graphical interface
• Online multiplayer version