I wonder how long it would take to start diverging. There's a maximum volume of trades you can make before you start having an impact on the prices yourself. Knowing the future perfectly means eventually you would be the most dominant force on the market unless you tempered yourself. But having a book is just having a snapshot of a single reality that your reality will start diverging from.
The show The Travelers addresses this a bit, but I think even that one underestimates how much a new player will full knowledge of the future market would affect that future market.