1 Research Transparency Statement

1.1 General Disclosures

The authors declare no conflicts of interest. Funding: This study was supported by an NSF BCS grant #2021053 awarded to C.F. M.M is supported by a post-doctoral research fellowship at All Souls College. Artificial intelligence: No artificial intelligence assisted technologies were used in this research or the creation of this article. Ethics: The research complied with all relevant ethical regulations and was approved by the Institutional Review Board of Johns Hopkins University.

1.2 Experiment 1 (Battleship)

Preregistration: The hypotheses and methods were preregistered on 2021-12–21, prior to data collection, and following the analysis of an independent pilot sample. A detailed pre-registration can be accessed at https://osf.io/v9zsb. The pre-registration was time-locked using cryptographic randomisation-based time-locking (Mazor, Mazor, & Mukamel, 2019) (protocol sum: 60c270410375e8a192468fc1a0e9c93da60d5e203eb2760b621a8631a26f4c5c; link to relevant lines in experimental code, making experimental randomisation causally dependent on the content of the pre-registration and thus ensuring that all data were collected after pre-registration. All pre-registered analyses are publicly available, including the report-generating R script (https://self-model.github.io/pretendingNotToKnow/docs/exp.-1-battleship.html). Exploratory analyses are flagged as such. Materials: All study materials, including demos of analysis experiments, are publicly available (https://github.com/self-model/pretendingNotToKnow). Data: All primary data are publicly available (https://osf.io/zma9b). Analysis scripts: All analysis scripts are publicly available (https://osf.io/zma9b).

1.3 Experiment 2 (Hangman)

Preregistration: The hypotheses and methods were preregistered on 2022-06–22, prior to data collection, and following the analysis of an independent pilot sample. A detailed pre-registration can be accessed at osf.io/3thry. The pre-registration was time-locked using cryptographic randomisation-based time-locking, making experimental randomisation causally dependent on the content of the pre-registration and thus ensuring that all data were collected after pre-registration (Mazor, Mazor, and Mukamel 2019). Due to an error in the experiment code, time-locking took effect only from player number 221 (batch 3) and on (protocol sum: c4929c7fe33df1b7b52f15c789d98eab30a9cee09a8121807a3c59e28e7430a4;relevant lines in experimental code. All pre-registered analyses are publicly available, including the report-generating R script (https://self-model.github.io/pretendingNotToKnow/docs/exp.-2-hangman.html). Exploratory analyses are flagged as such. Materials: All study materials, including demos of the experiments, are publicly available (https://github.com/self-model/pretendingNotToKnow). Data: All primary data are publicly available (https://osf.io/zma9b). Analysis scripts: All analysis scripts are publicly available (https://osf.io/zma9b).