Where We Are Going

The Mental Models project at MITRE was initially funded (Internal R&D) from 2001-2003. We were recently awarded further funding to continue the research through 2006. The further research will focus on the game of "Poker TRACS", because: “The theory of games [von Neumann] originated in poker, and that game remains the ideal model of the basic strategic problem.” (McDonald, 1950).

 

 “What von Neumann and others were onto was that poker is distilled competition, a less deadly version of combat, and therefore a good way to practice for it. The best strategy involves probability, psychology, luck and budgetary acumen but is never transparent; it depends on the counterstrategies deployed by the enemy… Each poker session is a miniature global economy laid out on a baize oval table.” (McManus, 2003). 

 

 

Mathematically speaking, poker is a game of “imperfect information that better [compared to chess and other games] reflects the decision making challenges of real world domains” (Billings, et al., 2002). Psychologically speaking, “Poker contains a greater element of skill than any other card game including Contract Bridge… because poker is a game of money management in addition to card management. It is a game where there is a correct technical play in every situation. It is a game where the best possible hand need not win the pot, due to a bluff.” (Scarne, 1980). These features make poker an ideal tool for our research on how people make decisions and how systems might help people make better decisions.

Compared to poker played with standard (one-sided) cards, Poker TRACS (played with two-sided cards) offers additional advantages of both rigor and relevance (see Burns, 2004). With respect to rigor, the information given on the backs of the cards constrains the possible hands that other players (hiding the fronts of their cards) might hold, and this makes the game more tractable to mathematical analyses of normative strategies. Such analyses are needed to measure and model cognitive competence, and to design and assess support systems that can improve human performance. With respect to relevance, the clue/truth (back/front) structure of two-sided cards in TRACS replicates the track/target ID problem in Command and Control. This improves the analogy between poker and warfare, compared to standard poker played with one-sided cards (where information comes only from the betting behavior of opponents, or from face up cards that all players can see equally well).

Like standard poker, the possible hands in Poker TRACS are ranked according to rareness, with the most rare (best hand) winning in a showdown. But there are several differences that make Poker TRACS more useful for our research. First, the two-sided cards provide players with partial information about their opponents’ hands, which makes the game more similar to Command and Control in real-world domains (see above). Second, each hand in Poker TRACS has only 3 cards and there are only 10 possible rankings (by rareness) of each 3-card hand. Although standard poker also has 10 rankings by rareness (i.e., Royal Flush, Straight Flush, Four-of-a-Kind, Full House, Flush, Straight, Three-of-a-Kind, Two Pair, One Pair, No Pair), it also makes further distinctions within each rank (e.g., 4 Kings beats 4 Queens, even though each is equally rare). Poker TRACS makes distinctions based only on rareness, and this coupled with a 3-card versus a 5-card hand makes the game much more tractable to mathematical analysis (i.e., many fewer possibilities). As a side benefit, Poker TRACS is also more challenging for players because, with fewer possibilities, it becomes increasingly important to accurately assess the probability of each possibility.  

 

Poker In The Lab
Our research will involve human experiments (to build models) and agent simulations (to test models) in a synthetic environment (Poker TRACS) that replicates cognitive challenges of naturalistic environments. The research will focus on three topics that are fundamental to decision making in Command and Control (and poker). These three topics are summarized below.

 

Expected Value: “Resource Management” in Command and Control (like betting chips in poker) depends on the probability (P) and utility (Q) of possible outcomes (like winning the pot in poker) from possible options (like betting or folding in poker). Our thesis is that people make decisions based on their subjective (mental) representations and calculations of expected value such that they choose what looks like a good thing to them. Mathematically speaking, the expected value of an option (n) is the sum of P(n)*Q(n) over all possible outcomes, with losses having negative Q values. Psychologically speaking, the question is: How do people represent and calculate the Ps and Qs to make their choice (n)? Our theory is that human thinking is bounded by “mind sets” (mental categories) and “short cuts” (mental calculations), and our research seeks to measure and model the representational features of mind sets and computational rules of short cuts in order to explain and predict human judgments and decisions. We will do this by performing experiments on people (playing poker) and by collecting data on our subjects’ judgments of “confidence” (P) and “consequence” (Q), along with their betting choices (i.e., bet, raise, fold) in the context of these subjective beliefs.

Bayesian Inference: “Risk Assessment” in Command and Control (like judging odds in poker) depends on the ability to update probabilities (P) as situations unfold and information is gained. Our thesis is that people generally reason in accordance with the norms of “Bayesian” mathematics, but that their judgments are “bounded” by the mind sets that they use to represent possibilities and by the short cuts that they use to estimate probabilities. The question is: When and how can these mind sets and short cuts be aided by support systems? The problem is that aids are useful only if people want them and trust them, so a system must be able to “explain” (or at least display) information in a way that allows people to reconcile differences between an “objective” recommendation and their “subjective” intuition. Our research will address this question/problem by developing and evaluating prototype systems (like Bayesian Boxes, see A Measured Result) for aiding and automating diagnoses and decisions.   

Opponent Models: “Rational Engagement” in Command and Control (like knowing when to hold or fold in poker) depends on the ability to “model” (understand and anticipate) the behavior of one’s opponents (and teammates). Our thesis is that people construct detailed models of their opponents, and that they refine these models in light of observed behavior to predict future behavior. The question is: How do people construct and update their models of opponents, and how do they use these models to adjust their own decision making strategies? This problem is central to good poker playing, and in fact the problem of opponent modeling is the main reason that Artificial Intelligence has not achieved the same success in poker-playing programs that it has achieved in chess and other games of “perfect information” (which can be won by brute-force search algorithms that do not require sophisticated opponent models). The problem of opponent modeling is also critical to warfare, especially asymmetric warfare like the war on terror, where one’s self-image may not be a good model of one’s opponent.

References

Billings, D., Aaron, D., Schaeffer, J., & Szafron, D. (2002). The Challenge of Poker. Artificial Intelligence Journal, Volume 134, 201-240.  

Burns, K. (2004). Making TRACS: The Diagrammatic Design of a Double-Sided Deck. Proceedings of the 3rd International Conference on the Theory and Application of Diagrams.

McDonald, J. (1950). Strategy in Poker, Business and War (W. W. Norton).

McManus, J. (2003). Positively Firth Street: Murderers, Cheetahs and Binion’s World Series of Poker (Farrar, Straus, Giroux).

Scarne, J. (1980). Scarne’s Guide to Modern Poker (Simon & Schuster).


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