Table 3.

The ATTC method. Each three-trial reward sequence results in a different variance estimate, depending on the contribution of exploration draws ($\eta$) and learning ($\alpha$) to the trials. Only sets C (corresponding to panels a, b in Fig. 8) and D (corresponding to panels c, d in Fig. 8) result in an estimate of exploration variance and are used in Eq. 12

Set	Post-failure sequences			Post-success sequences			Post-failure – post-success
	Sequence	Estimate	Trial-to-trial change ($\mathrm{\Delta }$)	Sequence	Estimate	Trial-to-trial change ($\mathrm{\Delta }$)	Exploration estimate ($\widehat{{\sigma }_{\eta }^2}$)	Weight
A	${\widetilde{{\mathrm{\Delta }}^2}}_{-,0\mathbf{0}0}$	${\sigma }_{\mathrm{\Delta }\eta }^2$	$\eta \left(t\right)-\eta \left(t-2\right)$	${\widetilde{{\mathrm{\Delta }}^2}}_{-,0\mathbf{0}0}$	${\sigma }_{\mathrm{\Delta }\eta }^2$	$\alpha \ast \eta \left(t-1\right)-\eta \left(t-2\right)$	${\widetilde{{\mathrm{\Delta }}^2}}_{-,0\mathbf{0}0}-{\widetilde{{\mathrm{\Delta }}^2}}_{+,0\mathbf{0}1}\stackrel{\wedge }{=}0$	0
B	${\widetilde{{\mathrm{\Delta }}^2}}_{-,1\mathbf{0}0}$	${\sigma }_{\eta }^2$	$\eta \left(t\right)$	${\widetilde{{\mathrm{\Delta }}^2}}_{+,1\mathbf{0}1}$	${\sigma }_{\eta }^2$	$\alpha \ast \eta \left(t-1\right)$	${\widetilde{{\mathrm{\Delta }}^2}}_{-,1\mathbf{1}0}-{\widetilde{{\mathrm{\Delta }}^2}}_{+,1\mathbf{0}1}\stackrel{\wedge }{=}0$	0
C	${\widetilde{{\mathrm{\Delta }}^2}}_{-,0\mathbf{1}0}$	${\sigma }_{\mathrm{\Delta }\eta }^2$	$\eta \left(t\right)-\left(1-\alpha \right)\ast \eta \left(t-2\right)$	${\widetilde{{\mathrm{\Delta }}^2}}_{+,0\mathbf{1}1}$	${\sigma }_{\eta }^2$	$\left(1-\alpha \right)\ast \eta \left(t-2\right)$	${\widetilde{{\mathrm{\Delta }}^2}}_{-,0\mathbf{1}0}-{\widetilde{{\mathrm{\Delta }}^2}}_{+,0\mathbf{1}1}$ $\stackrel{\wedge }{=}{\sigma }_{\eta }^2$	3
D	${\widetilde{{\mathrm{\Delta }}^2}}_{-,1\mathbf{1}0}$	${\sigma }_{\eta }^2$	$\eta \left(t\right)$	${\widetilde{{\mathrm{\Delta }}^2}}_{+,1\mathbf{1}1}$	0	$0$	${\widetilde{{\mathrm{\Delta }}^2}}_{-,1\mathbf{1}0}-{\widetilde{{\mathrm{\Delta }}^2}}_{+,1\mathbf{1}1}\stackrel{\wedge }{=}{\sigma }_{\eta }^2$	1