A Whist AI

Jason FongCS261A, Spring 2005

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

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

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

Rules of Whist

BiddingEach player declares how many tricks they

will takeGoal is to take exact number of tricks bidBidding starts at person following dealerBids must not add up to number of cards dealt

to each playerDealer bids last– bid value restricted

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

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

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

Reducing Branching Factor

Assume we can cheat, and peek at opponents’ cards

Branching factor becomes the number of cards in an opponent’s hand

Tree still too large to search completelyNumber of leaves: (10!)5 ~ 6 x 1032

Cut off search depth and use a heuristic

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

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

Heuristic

Calculating a heuristic value:Tricks to make bidSubtract absolute winnersSubtract some fraction of likely winners If under bid: subtract some fraction of neutrals If over bid: add some fraction of neutralsGives an estimate of likelihood of making bid

Heuristic

Other considerationsEach trick taken adds a point

If you can’t 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 don’t

change much If you can’t make your bid, take as many others

down with you

Search Methodology

Maxn algorithm Similar to minimax, but for n players Evaluation of each node gives an n-tuple Each node maximizes the moving player’s

element in the n-tuple Backup entire n-tuple to parent Best next move is best child of root

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

Optimization Considerations

Branching factor decreases as game progressesSearch deeper later in game

No choice of moves in last trickAutomatically play last 5 cards

Possible to have only one legal moveDon’t search, just play the card

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

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

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

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

Other Improvements

Deal opponent hands based on their bidsNeed to consider bids being incorrect when a

player misses with a winner/loser cardObserve play and count possible missed

winners/losers?Adds lots of complications

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

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

Future Work

Improve AI performance Graphical interface Online multiplayer version