You also have to consider rail contour. I’ve had hard-railed, narrowed round pins that felt like 2+1’s with the right single fin because they got so much ‘bite’ off the rails. I’ve also had W I D E square-tailed boards which slid-a$$ almost no matter what fin was in them if I got too far up to the front.
In general, I’d say think first about what shape or radius of turn you can do with a given tail. Like how a square can kick through a tighter turn, but pushing it too far or leaning out too far over the rail, you can get a couple spots of instability as you go past the corners. A round pin has no such ‘break point’ - you can lean it all the way over and it will feel smooth - just your turn will be longer-radius.
So - and this is only one school of thought, there are dozens when it comes to single fin selection - I’ve always preferred a thicker, more upright fin on the squares & squashes to smooth out that ‘break point’ in the turn. Round pins get a little more raked fins. An upright fin needs a foot right over it to turn it with a snap - you can’t rail-turn a pivot fin (read about the hulls in the current SJ for the exact opposite of a rear-placed pivot fin and you’ll see that the full-rail turn goes with the thin, whippy, up-from-the-tail fin instead) so foot placement is more critical - so a nice wide tail allows more heel-toe adjustment over a big pivot, so you can go frontside or back.
A round pin, you can be up a step or two with a raked fin. That’s good too, because on the drop-in, you get less tail lift from less tail surface area and you want to be up a bit anyway. Not exactly a rail turn, but closer. So more rake in the fin lets you turn it from where you want to be surfing it.
This is pretty much all about the initial bottom turn/setup. After you’ve picked a line & you’re in trim, the combinations are a bit less critical. But to get a big log going, you’ve got to be able to match all the variables together in that very first turn to push you up to speed…
And after you’ve covered the above with matching tail shape to rake amount you have to check off about rails & rocker. More rocker will make it more turnable. So if you want to drive big s-turns, a combo of tail rocker & a smaller fin will maximise that. On the other hand, if you’re in a noseriding contest at 2’ Malibu, and your board has a lot of tail rocker, you might want a less turny fin to smooth it out - so pick one more upright with a wider base.
Harder rails = quicker planing, less control; softer rails = more drag & more control. So your fin choice has to do with if you want to enhance what the rails are giving you or counterract it
And then there’s the wave itself. If it’s slow & mushy or small, you want big fin area to drive you along and get stability. If its big & fast, the wave will drive you along on its own and you’ll get stability from the rail line & the speed, so you can go with a smaller fin for less drive and remain in control.
Who needs multiple fins when there’s so many choices you can make with just one ?