The Game of Fate world is an Earth much like "the real world". The biggest difference is that this world secretly has magic. Magical society is a well guarded secret because there are people out there that would not hesitate to slaughter magic users in cruel witch hunts-- a fact evidenced by this world's history. Magic users do all in their power to not attract attention; they co-exist side by side with "the normal world", holding normal jobs and having normal identities. There is no "Hogwarts" for magical children and there are no full-time magical jobs.

There is, however, the MASQ. A magical government that monitors magical society and protects it. The MASQ is responsible for maintaining the secret of magic by arresting magical criminals and cleaning up any magic-related messes. They also assign all grown magic users a "Title", which is a secret identity of sorts that allows their magical life to be separated from their normal life. The MASQ's second most notable job, for this summary anyway, is clearing magic prices.

Because magic in this world is not for free. All magic users have a "curse" on their DNA that is passed down from generation to generation. It limits how much magic they can use freely. If they go over their set limit then they pay a "price", which is something very important to them. It varies from magic user to magic user. If a person accidentally gets priced and loses a lot of important stuff then they can turn to the MASQ. In exchange for community service the MASQ will slowly reverse the effects of the pricing and return lost things to those who lost them.

This world also acknowledges most if not all historical events in the "real world". However, they typically happened anywhere between five to ten years sooner than in actual history. This is because magic has allowed inventions to be invented faster and for society to therefore develop faster. Magic is based around emotions and willpower and essentially allows things you want to have happen to happen almost immediately. For example, inventing the light bulb no longer took a thousand mistakes; it could have been invented almost instantly. Satou's canon takes place in the 2000s, but technology is almost more advanced than even in 2011 of "our world".

At the time of Satou's canon-- technically starting decades before it-- the founders of the MASQ got into a fight. The price of magic did indeed keep bad magic users in line, but it also caused create suffering for good and innocent people. Founder Felicity Dystini requested that Founder Benita Goodon nullify the curse. In the panic of the resulting fight, Benita sealed Felicity in a single moment in time so that she could not interfere with the magic pricing system. Even though she is sealed, Felicity-- who now calls herself "Fate"-- has found ways to manipulate the present time. She continues to plot and plan a way to bring the system down, while her old friend Benita (now calling herself "Vinita") searches for a way to ensure that the system lasts forever.

Their lasting conflict pulls the strings in the Game of Fate, with Satou as one of their tools.

A longer, more detailed version of the World History can be found here.

Satou's history begins before she was born. Her mother, Horie, lived in Germany during World War II. In the chaos of the war her entire family was lost; her husband died on the battlefront and her daughter, Samantha, died when their hometown was bombed. While a normal woman might grieve and then pick herself up again, Horie was a witch. She didn't feel she needed to move on. Instead, Horie decided to revive her dead family with magic.

This plot would require a lot of magical power, more than Horie could safely use at once. She needed to put the magic in a separate container. This container was her new daughter, Samantha Kuroneko. Samantha was born from Horie and Yosuke Kuroneko, over forty years after Horie stopped her aging and went on a husband search. Born from two strong mages, Samantha had incredible magic potential.
Horie manipulated Vinita to bless her daughter with the ability to reap magical power from sins and virtues, and then manipulated Fate (who she discovered through her friendship with Vinita) to bless Samantha with the highest magical capacity of her time. Both the girls wanted Samantha's power as well and openingly admitted that they hoped to use her before Horie. When Samantha reached her maximum potential it would be a race to see who could use her first. Vinita hoped to immortalize the magic price system, Fate hoped to destroy that same system, and Horie wanted to revive her husband and daughter.

Yosuke did not know about magic for the longest time, but when he discovered it he confronted Horie on her past and the pair decided to move on from Horie's past. They moved from America to Japan, hoping to escape Vinita and Fate, and renamed their daughter "Satou". Though she did not understand why she had to get a new name and move, Samantha agreed to the switch and struggled to adapt. She was given a new little sister, her adopted cousin Masume Sakura, who was created from the remains a girl by the same name that had almost died in a car accident. Satou's powers were split between Masume and herself, making her harder to detect.

But that did not last for long. Not only was Satou relocated by Fate, but she was introduced to magic. Masume and Satou began a magical girl of justice spree and racked up a lot of magical debt-- Satou paid the price of her "existence" and Masume lost memories of her old family. Their father tried to step in and bail them out, but a fatal injury unlocked a "fail safe" in Satou. She was compelled by the fail safe that Fate put in her to save herself by putting her fatal injuries on his father. This devastated her mother, who vowed to ruin the lives of everyone who had ruined hers (that's Fate, Vinita, and Satou).

Vinita stepped in to wipe Satou's memory of murdering her father and tried to be a mentor to the two girls. Masume and Satou entered a competition to win a "Title", which would allow them to get more access to their magic and begin repaying their debt. Since, as far as they knew, their family had disappeared as a price of their magic.

This competition gave eleven and twelve year old Masume and Satou the chance to meet many new friends. Fate manipulated these meetings so that Masume and Satou ended up with "harems". Their friends were so smitten with them that they would protect them from any threat and keep her two tools alive until she used them.
Satou in particular met her best friend and fellow competitor Touka Takamachi, her friend and future knight Shugo Yumeno, and her stalker friend Mikale Godono.

Masume and Satou even won. But everything went to hell on their way to the awards ceremony. They were separated and Satou seemed to vanish off of the face of the planet. Touka took her place as the second winner, and it was Masume and her that won the competition. They tried to relocate Satou, but all proof of her existence seemed to have disappeared.

That was the price of her magic. Satou was forgotten by society. Vinita found her and lied, telling her that everyone she knew had forgotten about her. In truth, those who loved Satou still had memory of her but had no way to find her. Satou was given the title "Witch of Sins" out of pity and allowed to take of jobs with the MASQ to "repay her debt and earn her existence". All the while, Vinita hoped that Satou would be killed on one of her jobs-- her magical potential was dangerous if Fate got her hands on her, and Vinita had decided it would be easier to destroy her.

For years, Satou lived on her own. She had trouble finding food and shelter and would probably have died from starvation or illness, if not for Mikale Godono. Though Vinita had hired her adopted brother to kill Satou, he was too smitten with her and would instead arrange for her to have access to food and lodgings during her three years on her own.

When Satou was 15 she got a job that brought her to Willowing City, where Shugo Yumeno lived, and she was quickly adopted by his mothers. Charlotta Yumeno and Yui Tamura gave Satou a room and meals in exchange for her being Shugo and Usao's magic tutor. Satou trained them accordingly and Shugo even went on to apply for and recieve a job at the MASQ, while Usao was content to just have a new hobby to share with her half-brother.
During this time, Satou even managed to get Mikale to switch sides and become her permanent ally, and was relocated by Touka Takamachi when her friend came to interview Shugo on Satou's whereabouts. They all stayed together at the Yumeno-Tamura residence and began to unravel the plot that swirled around Satou's existence.

However, Shugo came to learn too much. Afraid that he was going to tell Satou, Fate arranged for Satou to be fatally injured on a job and to seemingly murder Shugo. He was silenced, not even leaving a body behind, and though she would have liked to be punished for murdering the boy that she loved it was impossible to put a girl who did not exist on trial. There was no one to arrest her. Shugo's murder was forever a mystery and attempts to find the culprit would go without results.

Perhaps a normal reaction in this sort of story would have been for Yui and Charlotta to toss Satou out of their house, but it was quite the opposite. They knew Satou was the culprit but also knew she could not have committed such a crime willingly. Rather than toss her out, the women asked Satou if she would like to be officially adopted into their family, as best they could when no one knew she existed. Satou's heartache over Shugo remained, but the new family-to-be clung to their hope of having a future together, the kind Shugo would have wanted. Satou pulled herself together and returned to school, determined to keep living her life for the boy she loved, but that would not happen.

Now Yui and Charlotta were learning more about Satou than Fate wanted them to know. They were giving Satou a safe place to live and grow stronger, which Vinita did not want either. To end this, Fate tricked Usao Tamura into believing she could revive her dead brother. The large quanities of magic Usao used in her scheme to sacrfice some classmates caused her to go over her magic limit and pay the price most dear to her; her love for her family. Usao was blinded by magic and came to hate her mothers for accepting Shugo's murderer, enough so that she stormed home while Satou was at school and not only burnt her house to the ground but murdered her own parents.

Satou was horrified. Mikale and Touka helped her piece together what had happened and she accepted that the horrible things happening were somehow linked to her. Touka returned to the MASQ and pretended to cut ties with Satou, so that she could help her best friend and conduct research with the MASQ's resources. Mikale swore himself to Satou and they also began researching the plot and trying to decide how to solve it.
Vinita alerted the entire magical community that an elusive witch called "The Witch of Sins" was on the run and encouraged those that could to hunt her down and kill her. In particular, she assigned Satou's own sister, Masume Sakura, to the task of locating The Witch of Sins and ending her supposed "reign of terror". Oblivious to the fact this girl was her sister, Masume accepted the task and started her hunt.

That said... this is a condensed version of her history. A more detailed version is over here. Satou is coming from the update labeled " End of the Happy Days ". She has been on the run for a few months now.