Intuition for Conditional Expectation

It seems like NNT aka Nero in The Black Swan (2007) is giving the law of iterated expectations that involve filtrations in a heuristic way by matching the everyday usage of the word 'expect' with the mathematical definition of expectation (a Riemann integral or sum in elementary probability theory; a Lebesgue or Riemann-Stieltjes integral in advanced probability theory).

I'm guessing the correspondence between the precise and the heuristic is as follows:

Heuristic:

$\text{If I expect to expect} \ \color{green}{\text{something}} \ \text{at} \ \color{red}{\text{some date in the future}},$

$\text{then I already expect that} \ \color{green}{\text{something}} \ \text{at} \ \color{purple}{\text{present}}.$

Precise in the case of one non-trivial $\sigma-$algebra,

$$E[E[\color{green}{X}|\color{red}{\mathscr F_t}]] = E[\color{green}{X}|\color{purple}{\mathscr F_0}] (= E[\color{green}{X}])$$

Or

Precise in the case of two non-trivial $\sigma-$algebras,

$$E[E[\color{green}{X}|\color{red}{\mathscr F_{t+1}}]|\color{purple}{\mathscr F_t}] = E[\color{green}{X}|\color{purple}{\mathscr F_t}]$$

where $\color{green}{X}$ is a random variable in $(\Omega, \mathscr F, \mathbb P)$ with filtration $\{\mathscr F_t\}_{t\in I}$ where $I \subseteq \mathbb R$

An example I thought of for second case

I currently expect to expect tomorrow at 1pm that someone will try to prank me tomorrow at 3pm if and only if I currently expect someone to prank me tomorrow at 3pm

Where 3pm refers to the larger $\mathscr F_{.}$ and 1pm refers to the smaller $\mathscr F_{.}$.

1. Anything wrong? If so, please explain why, and suggest how it may be improved.

2. How to similarly heuristically explain law of iterated expectation when we don't have filtrations?

For example

$$E[E[\color{green}{X}|\color{blue}{Y}]] = E[\color{green}{X}]$$

$\text{If I expect to expect} \ \color{green}{\text{something}}$ _____ $\color{blue}{(?)}$_____,

$\text{then I (?)expect that} \ \color{green}{\text{something}} $ _____ $(?)$ _____

What I tried:

I guess we can consider X as payoff of playing one game out of Y possible games.

So the amount we expect to win is equal to the (probabilistically) weighted average of the amounts we expect to win in each of the Y games.

But I wanted to use similar language to the one with filtrations so I'm looking for something like

If I expect to expect to win 5 dollars (something something) then I expect to win 5 dollars

Of course without the something something we have simply

$E[E[X]] = E[X]$