Picket count is run length divided by the coverage of one picket. A nominal 6 inch board covers 5.5 inches laid tight — about 2.2 pickets per foot, so the default here is a solid privacy layout.
Solid, spaced, or board-on-board
A solid privacy fence butts every picket tight to the next. That is 2.2 boards per foot for a 5.5 inch board.
A spaced picket fence with an inch and a half between boards drops to about 1.7 per foot. Board-on-board, where a second layer covers the gaps, runs closer to 3 per foot and is the only layout that stays private after the wood shrinks.
Shrinkage decides the look
Pressure-treated lumber leaves the yard saturated. Each 5.5 inch board can lose a quarter to a half inch of width as it dries.
Built tight, a solid fence becomes a spaced fence by the following summer. There is no fix after the fact — the decision is made at build time.
Rails and fasteners
Two rails is the minimum for a four-foot fence, three for six feet. Pickets are fastened with two ring-shank nails or screws per rail.
Galvanised or stainless only. Plain steel fasteners in treated lumber corrode fast and leave black streaks down every board.
Gates are not part of the fence run
Gate openings come out of the picket count, but a gate is not simply a section of fence on hinges. It needs its own frame, diagonal bracing, and posts heavier than the line posts.
Gate posts carry a swinging load that line posts never see, and they are the posts that lean first. They want to be larger, set deeper, and set in concrete even where the line posts are not.
Work out gates separately from the run. The hardware alone is a meaningful line item and it is the part that determines whether the gate still closes in three years.
Which side faces out, and the rules about it
A board fence has a good side and a frame side. Convention, and in many places an ordinance or an association rule, puts the finished side toward the neighbour and the street.
Board-on-board and shadowbox designs sidestep the argument by looking the same from both sides, which is why they are common on shared boundaries.
Check the rules before building, and check where the property line actually is. A fence built a foot inside the line is a foot of yard given away; a fence built a foot over it is a legal problem.