One Dial Instead of Two

A GRU is reading the review "Good screen, but battery dies within an hour."

One slot of its hidden state has learned to track how positive the review is so far. Just after "Good screen," that slot holds

$h_0 = 0.80$

A GRU carries one state, and mixes it with the candidate using a single update gate $z_t$. The gate is the share of the new candidate that gets written in; whatever is left over, $1 - z_t$, is the share of the old state that is kept:

$h_t = (1 - z_t)\, h_{t-1} + z_t\, \tilde{h}_t$

Follow that one slot through the next three tokens.

(The reset gate has already done its work inside each candidate shown — it governs how much of the old state the candidate is allowed to look at, and does not appear in the mix above.)

What does the slot hold after the third step, $h_3$?

Round your answer to 2 decimal places, carrying at least four decimals through the intermediate steps.