My friend bought the same system a year after me and can only play ps1 games on his.
I also own a ps1 and a ps2 both of which look better playing their games than they look on my ps3 for some reason.
maybe the ps3 is too advanced for the ps1/ps2 games and since you can still find those systems for very little money, maybe it was not such a bad thing for Sony to exclude the compatibility on the newer models. that way they could use the space taken up by compatibility for some other use.
PS2 games work perfectly on it, all my various third party PS3 controllers work too, and I haven't had a problem with the console in the year that I've had it.
I have no problem running ps2 or ps1 games. I can even use the Codebreaker disc, and other models tend to have problems with it.
The first ones: The 60GB "phat" PS3's could run Other OS and PS2 discs, they are bigger and had SD card etc slots in the front. Oh and 4 USB ports.
Sony thought they needed to strip down them to save some cash, they did, upgraded the CPU etc with smaller components (goes faster) and removed the SD card slots in the front and took away 20GB of HDD space and removed 2 of the USB ports.. The 40GB phat was born
Then they removed Other OS via a Firmware update because people had hacked it...
Later they made a slim version with more HDD space, up to 250 (I think there's a 320GB on the way too) and then of course you can still remove that one and put in a new HDD if you prefer
That's about it... I got a phat 40GB when it was released in late 2007 and then a slim 120GB the day it was released (my 40GB's disc reader died :uhh
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