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As most of here also already know, way before FGO, it was actually an idea proposed by Type Moon to be created as an MMORPG, the Fate online project. The planning fell apart and broken halfway, but most of it setting was scavenged, reimagined and used in Fate/Apocrypha. This doesn't wave away the bitterness Type-Moon had at the time. (Page 200, 201)
The proposal to built FGO was sent out by Iwakami Atsuhiro of Aniplex. This gave both Nasu and Takeuchi "a chance of revenge". (Page 201)
However there was a problem: FGO was meant to be developed for smartphones, this became a problem for Nasu - the difference of platforms, that and mainly, Nasu did not own smartphones prior to this project, so he had no experience in smartphone games. Nasu's reason behind this was because smartphones are so convenient, that if he started using it he will then "turn useless as a result". So to change his mindset, Takeuchi bought him a smartphone, and one day when Nasu goes to work as usual, he saw a smartphone being placed on his desk, with games installed for him. The games Nasu then used to refer for the project would be "Chain Chronicles" and "Brave Frontier". It was then Nasu discover the potential of smartphone games. This would then aligned with the vision Takeuchi wanted as well since Type-Moon wanted to catch up with the times, the times where a visual novel games for the niched would then shuffled and moved into current times - where people can access and game and anywhere, anytime. Additionally, the reason why Type-Moon chose to start by creating R18 game was because they felt it was "the most interesting thing likely to happen at the most interest place", so it managed to became the forefront brand recognizable by most otakus, therefore to Takeuchi, who always have been looking for interesting places, to be able to delve into the potential of smartphone games, a new horizon for him, was an experience worth exploring. (Page 202, 203)