The interesting decision in this game is rarely which dice to keep. It is whether to settle for what you have or spend a roll chasing something better.
Count what is still open before you decide
A reroll is cheap when several boxes would accept the result. It is expensive when only one box is left that fits.
Look at the card, not just the dice. The same roll is a good result early and a poor one late.
Early on, chase the rare boxes
Five of a kind, the large straight and four of a kind are the hardest to fill. Going after them in the first few turns leaves you the rest of the game to recover if the roll does not come.
Leaving them until the end means needing a specific result under pressure, which is how cards end up with zeros in the expensive boxes.
Late on, protect the total you have
With three or four boxes left, a reroll that fails costs a real score. Taking 18 in Chance beats rerolling into a zero.
The exception is when every remaining box would score nothing anyway. Then the reroll is free and worth taking.
Keep Chance open as long as you sensibly can
Chance accepts any five dice, which makes it the only true safety net on the card. Spending it on a middling early roll removes that net for the rest of the game.
Use it when a turn has clearly failed and nothing else will take the result.
A zero is a decision, not a failure
Sometimes the right move is to write zero in a box you were never going to fill. Zeroing five of a kind late costs less than zeroing Sixes and losing the bonus.
Choose the box that costs the least rather than the one that feels worst.