Knowledge acquisition and strategic action in “Mastermind” problems

Abstract

In two experiments, the strategies used by subjects playing the logical-deduction game, Mastermind, were examined. In the first experiment, subjects showed improvement resulting from the continued use of a particular strategic action, and the data suggested that the subjects learned the strategy from their transactions with the task. In the second experiment, the question of changes in underlying strategic knowledge of Mastermind was examined. The accuracy and complexity of the subjects' deductions and their use of the previously identified strategy were used to generate a model of the cognitive operations involved in Mastermind. Although there were improvements in the accuracy and complexity of the subjects' deductions resulting from continued play, these improvements were unrelated to the use of the strategy. Moreover, the likelihood of making accurate and complex deductions was well accounted for by a Markovian model, suggesting that the deployment of the strategy was not driven by any change in the subject's underlying knowledge structures. Rather, the subjects seemed to use the strategy to create Mastermind situations whose interpretation was fairly easy. The implications for previous work on the issue of Mastermind strategies and the development of logical-deduction strategies are discussed.