Platform: Sony PSP (which is region free for games, not so for UMD movies)
Publisher/Developer page: http://products.alchemist-net.co.jp/products/saki/
Released only in Japan in March 2010 and then re-released in 'The Best' format (I gather this is a bit like Sony's Greatest Hits here in the USA).
Sadly, the price on this hasn't come down much... I found a few in the US$60 range and more commonly US$70 and up for a new copy. Used copies are only slightly cheaper.
I apologize for the screenshots. The game looks nicer on a real PSP and PSP emulation still has a little ways to go. I had to add a little filtering to get the shots to look good.
For those who love all things Saki, this is a portable Mahjong game with Saki and friends firmly entrenched within. The game does more than just past in animation and art from the OVA but instead does much further in trying to re-create some of the real feel from the series. Actual tournament matches. Lengthy story mode. Challenge situations where you are given a starting hand and starting points as if the game was already mid-match and you have to work your way to victory. There is plenty of gallery options and Saki music here to satisfy even the most dedicated fan. Let's see how it all looks...
Yes, the PSP has load-times as the PSP disc spins and reads. They aren't too bad - and you get treated to a little chibi animation.
The main menu gives you a number of choices. STORY mode, CHALLENGE mode, FREE BATTLE mode, SOME OTHER Battle Mode I don't quite understand, GALLERY MODE and OPTIONS.
In story mode you unlock stages as you go through the story and play out the mahjong matches. In many cases you are thrust into the middle of a match and need to work your way out. The story mode is available in three levels: Easy, Normal and Hard.
You can bypass the animation and text/voice by pressing START. But it's really kinda fun to watch.
Just before the story-mode mahjong challenge takes place, you get a little chibi animation that represents the summary of the chapter.
The main mahjong game screen. Familiar to anyone who has played Video Mahjong before. A nice touch here is that due to the PSP having a reasonably wide screen we get the portraits of the players along with their seat/wind indicators and a few other useful bits of information. You can see that the scores are not equal - this is the starting hand and points for Saki at the beginning of Story-Mode (Normal).
When you win a hand, it counts the points in standard fashion. Nothing too flashy - and suitable Saki music to count points by.
In challenge mode, you pick a character and it pits you against opponents that are meaningful to that character and puts you in certain situations you need to battle back from. There are at least 21 different challenges - and several involve Saki as the main character. More challenges become available as you work through the story-mode.
In the free battle mode, you can pick which 4 players are sitting at the table - and which character you want to play.
For the story mode, you can't change the rules... but in free battle mode you can. There are, however, only a small handful of things you can change here - most of the actual Mahjong rules are fixed (and match the rule-set used on the Saki Animation... Four Red Akadora tiles, Double Riichi / Iipatsu enabled, etc, etc.).
One of the best modes in the game - Team/Tourney mode! You pick your school (team of 5 characters) and your team starts with 100000 points and just like in the Saki OVA you battle it out tournament style! You get to pick the order your characters battle in - the team captains are shown in the middle.
Every character (including all of the Rival schools) have their signature moves animated (mostly in terms of a sliding image across the screen with some voice acting). Good stuff.
In gallery mode you unlock character portraits, music, and mini-animations.
And finally there are a few overall game options that you can configure. Mostly in terms of music and sound effects. You can enter your name for one of the Battle modes.
There are unlockable characters - including my favorite Fujita Pro! Some unlockable costume swaps. A host of little touches that really make this feel like a well tuned Saki game and not just a paste-on of Saki art onto a standard mahjong game. I'd like a few more tweakable options, but really that's a minor point.
A brand new PSP would set you back US$130 (maybe closer to US$70 for used). Saki Portable would run another US$60-$70. It's not cheap, but there are worse ways to spend your money!
The new PS Vita doesn't have a slot for PSP games and, while you can download PSP games for the Vita, you'd need a Japanese PSN account and I believe you can't switch between accounts without resetting the device to factory defaults. 
There's also a really nice 'safe tile indicator' function - you pick a player and the game will highlight all the tiles in your hand that are safe discards against that player.