If the fate of the two Sakamoto sisters is like a coin, Satsu and Chiyo are on opposite sides—heads you win, tails you lose. And Chiyo definitely wins best out of three.
Satsu is older than Chiyo, less attractive than Chiyo, and born in the year of the cow. Not a flattering sign for a young girl. As a result, she is sold into prostitution instead of geisha-hood. It's a similar fate, but offers no glamour, no respect, and way less cash.
However, unlike Chiyo, Satsu is able to break her bonds of fate and escapes...and then ceases to be a character because Sayuri never sees her again. How sad.
One of the reasons that the two sisters never reconnect is because Sayuri never again tries to escape the bonds of being a geisha. Even in the end, when she moves to New York, she's still the Chairman's mistress. You can take the girl out of Gion, but you can't take the geisha out of the girl.