Contrary to what Jim said I found that I don't have to be that generous, that my orders which are usually only 1/3 on the way from bid to ask will indeed remain open most of the day - but that a good part of them will be executed shortly before the market closes, in the last moment.

I've noted the same thing. The market maker software seems to be much easier to please in the last minute. Their little pea brains seem to be thinking "better to rack up even a small profit today than nothing at all".

But during the day, for major stocks with wide gaps, I usually budget on getting a fill at about 3/4 the way across the gap.
For Berkshire options I do a little bit better than that on average, but I prefer pleasant surprises to unpleasant ones.

I suspect there is a difference between securities with one market maker (presumably a bot) versus securities with two or more players. For example, when single stock futures were available, it wasn't possible to shave a single penny off the asking price. I think that's because there was only a single player in the game.

Jim