I forgive you. You didn't play Primal when it came out on PS2 in 2003, but I forgive you, because it looks like you'll get another chance. An ESRB rating (opens in new tab) suggests that the tale of shapeshifting, demon-slaying Jennifer Tate and her gargoyle sidekick Scree is among the next PS2 games on PS4 (opens in new tab).
If Primal still doesn't sound like your type of game, don't worry. Several other PS2 games were rated for PS4 by the ESRB recently: Ape Escape 3, Okage: Shadow King, Siren, and Wild Arms 3 can all be found on the organization's archives. Fireworks puzzle game FantaVision also made its PS4 debut earlier this week.
These are quality titles (okay, maybe my thoughts on Fantavision are rooted in nostalgia for it being a launch title more than anything), though there still seems to be no real rhyme or reason as to which games are being made available. But hey, if the selection process exposes people to the quirkier, more overlooked side of PS2 history - as it has so far - I'm okay with that. And if you're listening, Sony: we've got a list of suggestions (opens in new tab) here.
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