Abstract
Tetris is a complex task which taps into several human skills: among them perceptual learning, planning, motor skills, and sequential decision-making. Following a divide-and-conquer strategy, we adopt a machine modeling approach to isolate the contribution of sequential decision-making from the other three skills. In two studies, we test three sets of 1,771,561 feature-based machine players (MPs) (116, 11 weights for each of 6 features) of Tetris for both long-running (tortoise) and short-running (hare) MPs. Tortoise models run until they die. Hare models are stopped after 506 episodes. For both studies, we select the longest running tortoise model and compare its score and behavior with that of the best scoring hare model. The best tortoise models adopt an endurance strategy which emphasizes single-line over multi-line clears. The best hare models adopt an escalation strategy which stresses multi-line clears. In contrast, our human players tend to adopt the escalation strategy early in their game but switch to the endurance strategy as speed demands increase. Unexpectedly, across three model runs, each with a different random seed, we obtain three different sets of “best fitting” models, that is, the MPs overfit the data even though that data is generated by an essentially infinite random sequence. However, in each model run, the best tortoise adopted the endurance strategy and the best hare adopted escalation.
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Notes
Attempting to keep, say, the right-most column clear while completely filling up the first four rows of the other nine columns is a common, human tactic. This configuration allows the right-most column to be plugged by an I-beam zoid, clearing four lines at once, and is called “a Tetris.” However, building this configuration requires getting zoids that would leave pits (e.g., see Fig. 2) if placed in the first four rows out of the way, by placing them on the left-side of the top of the growing pile, while using other pieces to build the “four high wall,” then waiting for the I-beam to appear, and finally placing the I-beam into the (at least) 4 deep slot, after that wall is built.
The number of alternative possible placements for a zoid varies with the zoid type and with the current state of the board; however, for an empty board, there are 9 positions where the square zoid can be placed, 17 positions where the Z-, S-, and I-beam can be placed, and 34 positions where the L-, J-, and T- can be placed. Hence, the “average” zoid in an unconstrained board can be placed in any one of 23 locations.
Note that the authors disagree among themselves as to whether this use of the term “strategy” is strictly appropriate; however, at least for now, we cannot find a better one.
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Wayne Gray received grant (N00014-17-1-2943) from the Office of Naval Research, Dr. Ray Perez, Project Officer.
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Sibert and Gray conceived and designed the study and wrote the manuscript. Sibert did the modeling and data analyses. Gray and Sibert discussed the results and elaborated the theoretical implications of the results.
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Sibert, C., Gray, W.D. The Tortoise and the Hare: Understanding the Influence of Sequence Length and Variability on Decision-Making in Skilled Performance. Comput Brain Behav 1, 215–227 (2018). https://doi.org/10.1007/s42113-018-0014-4
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DOI: https://doi.org/10.1007/s42113-018-0014-4