Why a Random Reward in One-step Dynamics MDP? I am reading the 2018 book by Sutton &amp; Barto on Reinforcement Learning and I am wondering the benefit of defining the one-step dynamics of an MDP as
$$
  p(s',r|s,a) = Pr(S_{t+1},R_{t+1}|S_t=s, A_t=a)
$$
where $S_t$ is the state and $A_t$ the action at time $t$. $R_t$ is the reward.

This formulation would be useful if we were to allow different rewards when transitioning from $s$ to $s'$ by taking an action $a$, but this does not make sense. I am used to the definition based on $p(s'|s,a)$ and $r(s,a,s')$, which of course can be derived from the one-step dynamics above. 

Clearly, I am missing something. Any enlightenment would be really helpful. Thx!
In general, $R_{t+1}$ is is a random variable with conditional probability distribution $Pr(R_{t+1}=r|S_t=s,A_t=a)$. So it can potentially take on a different value each time action $a$ is taken in state $s$.

Some problems don't require any randomness in their reward function. Using the expected reward $r(s,a,s')$ is simpler in this case, since we don't have to worry about the reward's distribution. However, some problems do require randomness in their reward function. Consider the classic multi-armed bandit problem, for example. The payoff from a machine isn't generally deterministic. 

As the basis for RL, we want the MDP to be as general as possible. We model reward in MDPs as a random variable because it gives us that generality. And because it is useful to do so.