Thanks for the info - I've amended my listing.
I must confess I don’t play on PC and don't know much about it. Most English "mahjong" computer games seem to be tile-matching solitaire ones with the notable exceptions being
Four Winds which offers a wide range of configurable rule-sets and this nice
free Flash game. For online play with Japanese rules (and text) I guess the obvious sites are
Tenhou,
Janryūmon and the JPML's
Ron2.I'm sure other posters could give you more info, either here or in a new thread.
All three retail (non-download) games for the PS3 have their merits. Mahjong Fight Club is a quality title with the best range of options and stats. Mahjong Taikai IV has a nice table display and historical characters for opponents. If you want to play online then go with Janline-R. Look over my guides to get an idea of the options and modes available in each. Mahjong Dream Club is released next week and will include online play (worldwide access TBC), authentic 3D table view and cheat functions.
I don’t own a PSP but MFC has to be a safe bet again. The Saki game should be a lot of fun too if you're familiar with the anime plus it has a solid 4-star rating on Amazon Japan and there's an English guide for it on GameFAQs. If I had a PSP those are the first two I'd pick up. I'd say the screen layout is a key factor on a portable device so check the links in this thread for screenshots.
EDIT: I just noticed that Saki Portable for the PSP (originally released in 2010) was reissued just yesterday! It's a "Best" budget release - half the price of the original and even cheaper as a download - with new bikini cover art.