Which Touhou Character is the best at Chess?

I ran a Touhou Sort with my audience and sorted every character from worst to best. For top five best we had:

1. Miko
2. Eirin
3. Momiji
4. Alice
4 (Was a Tie). Mamizou

For five worst we had:

5. Rumia
4. Futo (Always falls for the 4 move checkmate)
3. Koishi
2. Fortuneteller (is dead)
1. Shion

What Touhou characters do you all think are the best and worst at Chess?

pretty sure ran would also make the cut, shes literally a super robot. its like stockfish but now its shikigamifish.

yukaris also pretty smart and does scheme a lot, and patchy is not only smart but could probably also memorize every grandmaster game ever played. 

and one last question is whether were factoring in abilities. im assuming not since that isnt exactly whos the best at chess but rather who can manipulate chess in their favour, but if we are running abilities into the mix, a few characters i can think of are sakuya, seija, and keine. 

I immediately thought of patchouli

Eiki

Abilities factor in to a certain degree. For example, Satori can still read minds (the reason I don't have her at the top is because I think despite being able to know what her opponent would play, she wouldn't always know the proper counter), but Cirno can't freeze her opponent to win.

its a bit blurry over here, but doesnt that mean keine can technically 'eat' history and create a new one, effectively removing certain blunders shes made during a game and playing new moves under that? and sakuyas whole time stop thing does give her infinite time but it depends on her intelligence after that, so i suppose shes off the board. and does seija's ability of 'flipping anything' also apply to chess? could she 'turn' a losing game to a winning one? its a bit vague so abilities might not be the best judging factor in this type of discussion 

Keine probably could, but I feel like it's in her personality not to. Sakuya you've got the right idea, and then Seija is such a wild card that she'd be winning and losing all over the place.

i have a feeling seija would just lose on purpose cause she hates winning, cause everybody else loves winning. and yeah, keine would play fair 

the worst?

Yeah, when you guys are typing words, cirno has already lost 10 chess games.

Cirno is the best in chess

I'd say Ran and Momiji would be pretty good at chess.

Why would Momiji be good? There's little information about her intelligence as she only shows up as a sprite in MoF and cameos in the mangas. I get Ran since she's literally a supercomputer but there's not enough info about Momiji. 

in one of megapig9001's touhou byte shorts, its said that momiji is really good at a board game (that i forgor the name of) that is similar to style in chess (as you move pieces to the enemy side of the board, attempt to capture the king, yadada yadada)

The specific board game is Shogi, which evolved from the same game as Chess and is really similar (with the main differences being different piece movement, permanent CrazyHouse rules, and almost all pieces can promote into a set piece). Momiji's so invested into Shogi that she creates her own version by fusing Gensokyo's version with the one from the Outside World.

I think Shion would actually be decent at chess because she would only draw due to her bad luck

Eirin and  Ran.

Eirin has a title "Brain of the moon". Besides, Eirin is based on Ame no Yagokoro Omoikane no Mikoto, the god of wisdom in Japan. 

"Ran has a very high intelligence, especially good at mathematics. It is said that even calculations to a degree unimaginable by humans can be completed in an instant." Akyuu mentioned in Perfect Memento in Strict Sense.

Patchouli. She has the books.

Cirno is 9x stronger than Mittens confirmed