I spent 2 evenings surfing crochet sites, some many years old and lost in the deep web. If my browser history is correct i looked at 237 different hat patterns, not counting all the sites that turned out to be a waste of time. Out of those I chose a small number that I might actually make and wear. Here they are.

This hat is worked in spiraling rounds through rnd 16. Don't join rounds. Use a stitch marker to indicate first stitch in round, move it up at beginning of each round.

This cap is based on the red cap from the movie "The Professional". However, I have changed my original pattern a bit (added a row of shells) in order to make it longer. To obtain a more movie-consistent cap, omit one row of shells. In order to make the hat more like a beanie in length, add two rows of shells.