TurnTrout comments on Seeking Power is Often Convergently Instrumental in MDPs

[TurnTrout]

Yes. The full expansions (with no limit on the time horizon) are

$\frac{r_{\text{Candy}}}{1-\gamma },r_{\text{Wait!}}+\gamma \frac{r_{\text{Chocolate}}}{1-\gamma },\text{and}{r}_{\text{Wait!}}+\gamma \frac{r_{\text{Hug}}}{1-\gamma }$, where $r_{\text{Candy}},r_{\text{Wait!}},r_{\text{Chocolate}},r_{\text{Hug}}\sim \text{unif}(0,1)$.