Appendix 3—table 12. Exploration-phase choices as a function of Δ-uncertainty, overall uncertainty, and side of repeat option.

	Pre-registered sample		Preliminary sample
	(146,766 trials, 194 participants)		(41,009 trials, 62 participants)
Term	Median	95% PI	Median	95% PI	Units
Predictors
Intercept	–0.04	[–0.10, 0.02]	–0.03	[–0.14, 0.07]	logit
Δ-uncertainty	1.01	[0.86, 1.14]	1.16	[0.87, 1.44]	logit / nat
Δ-uncertainty × overall uncertainty	–326.14	[-468.61,–245.18]	–349.54	[-691.47,–251.13]	logit / nat²
Transformed threshold	2.55	[2.40, 2.72]	2.36	[2.16, 2.67]	a.u.
Repeat choice on right	0.50	[0.42, 0.59]	0.57	[0.43, 0.72]	logit difference
Participant-wise variability
SD of intercept	0.40	[0.36, 0.44]	0.38	[0.31, 0.46]
SD of Δ-uncertainty	0.90	[0.80, 1.02]	1.05	[0.86, 1.31]
SD of Δ-uncertainty × overall uncertainty	14.21	[0.98, 41.45]	9.23	[0.46, 29.28]
SD of transformed threshold	0.44	[0.36, 0.54]	0.35	[0.22, 0.50]
SD of repeat choice	0.57	[0.51, 0.64]	0.53	[0.44, 0.66]
Correlation of intercept and Δ-uncertainty	–0.06	[–0.21, 0.10]	0.05	[–0.21, 0.32]
Correlation of intercept and Δ-uncertainty×overall uncertainty	–0.08	[–0.76, 0.72]	–0.01	[–0.76, 0.75]
Correlation of Δ-uncertainty and Δ-uncertainty×overall uncertainty	0.01	[–0.69, 0.69]	–0.10	[–0.78, 0.70]
Correlation of intercept and repeat choice	–0.16	[-0.30,–0.00]	–0.06	[–0.31, 0.22]
Correlation of Δ-uncertainty and repeat choice	0.32	[0.17, 0.46]	0.11	[–0.18, 0.38]
Correlation of Δ-uncertainty × overall uncertainty and repeat choice	0.38	[–0.67, 0.87]	0.00	[–0.76, 0.77]
Correlation of intercept and threshold	–0.03	[–0.26, 0.22]	0.31	[–0.09, 0.64]
Correlation of Δ-uncertainty and threshold	–0.35	[-0.52,–0.16]	0.09	[–0.27, 0.43]
Correlation of Δ-uncertainty × overall uncertainty and threshold	–0.42	[–0.88, 0.61]	–0.10	[–0.79, 0.70]
Correlation of repeat choice and threshold	–0.60	[-0.74,–0.43]	–0.38	[-0.64,–0.05]

This model can be summarized with the following formula: $logit(P(tableonrightchosen))=Intercept+$ $b1\cdot \mathrm{\Delta }-uncertainty+b2\cdot (overalluncertainty-\omega )$ $\cdot step(overalluncertainty-\omega )\cdot \mathrm{\Delta }-uncertainty+b3\cdot repeatonright$, where step is the step function, $\omega =-2ln(0.5)\cdot inv\mathrm{\_}logit(\alpha )$. The intercept and parameters b1, b2, b3, and α all vary by participant, and their correlations across participants are modeled. This model was fit as a logistic regression.