Youmu I know you are an airhead but please think about Akyuu's ability more!
Im an airhead and dont get it! Help!
She's remembering the exact movements of each tile as they were shuffled so she knows where all the face-down tiles are, I presume.
But that doesnt make sense... Abilities like Shou/Hina/Kaguya do not make the tiles more likely to be drawn by them, but they change the value of the face down tiles/how people play tiles, as seen by marisas failed attempts at cheating. Unless actually knowing the tiles changes that? I mean, Marisa certainly did not need perfect memory to know where her tiles where, since she arranged them as such.
One, I don't think you should conflate Kaguya's ability with the other two really. Kaguya's affect the whole table in a lot of subtler ways, causing a draw by any means possible, while the other two strictly affect the tiles they pick up.
As for how they do it, it's actually probably closer to Marisa. It seems like in this version of Mahjong, each player draws their tiles from a "wall", basically an individual deck. Hina's and Shou's abilities seem to be that they draw far more of their personal tiles into their hand and their wall when setting up the round. Marisa does the same, just by sleight of hand rather than an ability. I don't think anyone has the ability to actually change what a tile's value is - if they could, it'd be far more suitable for a character like Mamizou... but even Mamizou's abilities only deceive people on what the card actually says, rather than change what it actually is.
Akyuu is actually a great counter to this, for basically her memory skills. Like the person above said, she can remember the exact movements of tiles.
Shou's power draws in the Pin, (aka the coins). there are 36 Pin tiles, and a hand is 13 tiles big. So just by showing her hand, Shou's already given Akyuu a marker on about a third of her core gameplan. With even that much, as well as the ones in her own hands, Akyuu's probably aware of about half the Pin cards by round 2.
by extension, if she remembers the exact movements of tiles, she can infer information on even a small amount of them (as the various trios and quads that make up a Mahjong hand are fairly consistently pre-arranged by everyone, if she knows, for example, that Shou has arranged two of the same tile with another tile between them, she can be pretty confident that there's at least three of a kind there.)
Note exactly what she did in this round - she didn't go for a big win, she went for a seemingly riskier AND smaller one that none the less paid off. The reason isn't because she's dumb, it's probably because either she knew she couldn't get the better hand or that someone else would win first if she tried.
I'm reminded of a discworld story, where a game like poker is being played with an undercover witch. The one time the main scumbag on the table has what could be the best hand in the game, the witch folds early, sacrificing a grand total of... one dollar. Akyuu's doing something similar here - accepting smaller wins and losses to prevent other players from capitalising on their good hands.
She's basically the world's best card-counter, with an eye for the very long game. Like she said, not knocking her out in the first round was a big mistake, as now she has a lot of information on Shou.
So their majhong just has different rules? Normally, you dont set up your own wall, thats actually really stupid, cos anyone could just mix up the tiles to their advantage, no ingenious tricks needed (just move desired tiles closer to you) Another thing I feel like is completely off the mark is how perfect memory works. Yeah, sure she can remember each tile movement, but only if she actually can see them. For instance, how many tiles do you think can one perceive reasonably? Unless she has a bird view and hawk eyes, she would only ever have information on a fractiom of tiles, and since they are hopefully indistinguishable by human (and yokai) eye she would always lose all information the moment the tiles get mixed.
Its like, perfect memory does not help you in this "where is the prize under the cup" (forgot its name) game, The problem in this game is not your memory (since you only ever need to remember one number), its the fact that you cant perceive what happens fast enough. Even if akyuu has perfect memory here, her playback would just be as unhelpful. Same with mixing tiles, just a million times more difficult.