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I often find it interesting talking to people about concave, because most people refer more to the angle of the kicks, compared to the side to side between the bolts, which is more what I think of when I talk about concave. Also given most people are not quite as product "nerdy" as I am, or the average person on here either, but there are also some boards that might have medium to steep kicks that have very little concave through the middle of the deck.
Not to say that kicks can always be flattened - parking on an upside down board will usually flatten out most kicks without any issues with the wood, glue or board construction - but if I am feeling out concave on the average BBS deck, I know I can mellow out the kicks, but I can't mellow out the concave.
From almost all the boards I have had the chance to stand on, the blanks / PGI distributed decks have been the flattest, but are often difficult to find or get many of, depending on brands or what is going on with certain distros.
Maybe the DLX boards with IV being the ones most common to find, but even then, the 8.38 or 8.5 are usually way more mellow than the 8.25 or 8.12 shapes, so it also depends on what size or shape you are looking for as to whether or not it will be better in that regard.
Other brands that use that same 8.38 shape I have bought, including DGK, Element, Baker, Birdhouse, Deathwish and more are all middle of the field, some more mellow and some not so mellow, regardless of how they are advertised, eg Baker mellow mold seems like it is the same board from the same press as all these others.
Most Passport decks (BBS) have also been very flat in the concave with medium to steep kicks, which also flatten out really well, as per some that I have done, but also some that come like that too, one 8.38 needed nothing whatsoever. Other Passport boards have been quite deep / steep in kicks and concave, as per an 8.5 I got recently, but from half a dozen of each, some were steeper (top of the press) and some more mellow (bottom of the press).
I have also found quite a few PS Stix decks from brands like GX1000 or Quasi to be some of the steepest decks around, but then some other PS Stix boards have been very flat and very mellow in both kicks and concave.
The hardest thing with all this is if you can't go into a shop that has multiples of each board, or can't get someone to go through boards to find the most mellow, it is a bit of a lucky dip with those brands that use boards that come from woodshops that have four or five to a press.
As per those Passport boards, multiples of each have very different concave, for the same graphic on the same shape in the same run, as I have seen whenever I have bought up to half a dozen of the same boards.
I can pick and choose what I want to ride and put the rest in the shop / pass on to others, but it makes it harder for anyone else without those sort of options to find exactly what they are looking for.