Table 1.

Set of studies and drifts used to generate optimal policies

Study	Paradigm	Conditions	Distribution	Drifts ({𝜖 1…𝜖 n})
PHS_05	Motion	$\left\{0\%,3.2\%,6.4\%,\right.$	Uniform	$\left\{0,0.03,0.05,\right.$
		$\left.12.8\%,25.6\%,51.2\%\right\}$		$\left.0.10,0.20,0.40\right\}$
RTM_01	Distance	32 values	Uniform	17 values
		Range: [1.7, 2.4] cm		Range: [0, 0.50]
R_07	Brightness	$\left\{\text{Bright}:2\%,35\%,45\%,\right.$	Uniform	{0.05, 0.10, 0.20}
		$\left.\text{Dark:}55\%,65\%,98\%\right\}$
RM_08	Motion	$\left\{5\%,10\%,15\%,\right.$	Uniform	$\left\{0.04,0.07,0.10\right.$
		$\left.25\%,35\%,50\%\right\}$		$\left.0.15,0.20,0.30\right\}$
MS_14	Color	$\left\{35\%,42\%,46\%,\right.$	Uniform	{0, 0.05, 0.10, 0.20}
		$\left.50\%,54\%,58\%,65\%\right\}$
VRS_16: E1	Numerosity	Range: [21, 80]	Piecewise	$\left\{0,0.02,0.04,0.06\right.$
			Uniform	$\left.0.30,0.32,0.34,0.36\right\}$
VRS_16: E2	Numerosity	Range: [3, 98]	Approximately	{0, 0.05,…, 0.50}
			Gaussian
VRS_16: E3	Numerosity	Range: [31, 70]	Uniform	{0, 0.02,…, 0.20}
VRS_16: E4	Numerosity	Range: [3, 98]	Uniform	{0, 0.02,…, 0.48}

Notes. Each row shows the set of conditions used in the experiment, the distribution of these conditions across trials and the set of drift parameters used to compute optimal policies in Fig. 11. The value given to a condition refers to the motion coherence for the motion discrimination task, to the separation of dots for the distance judgment task, to the proportion of black pixels for the brightness discrimination task, to the percentage of cyan to magenta checkers for the color judgment task and to the number of asterisks for the numerosity judgment task. For the computation

VRS_16: E2

, the probability of each drift value 𝜖 was equal to $\frac{1}{Z}\mathcal{N}(𝜖;\mu ,\sigma )$, where $\mathcal{N}(\cdot )$ is the probability density of the normal distribution with μ = 0, and standard deviation σ = 0.21 and Z is a normalization factor ensuring that the probabilities add up to 1. The names of studies are abbreviated as follows

PHS_05:

(Palmer, Huk, & Shadlen, 2005),

RTM_01:

(Ratcliff, Thapar, & McKoon, 2001),

R_07:

(Ratcliff, Hasegawa, Hasegawa, Smith, & Segraves, 2007),

RM_08:

(Ratcliff & McKoon, 2008),

MS_14:

(Middlebrooks & Schall, 2014),

VRS_16:

(Voskuilen et al., 2016) with

E1

…

E4

standing for Experiments 1 … 4, respectively.