"The fact that it was live when I won it altered the experience."
That is so, subjectively for them, but no more, and the one fact does not alter the other.
The fact that she was free didn't alter Fen's situation.
This fact does not alter the ratio of the aristocracy to the doctor.
By the time the two met, he was well aware of Minor's past, and that fact did not alter their relationship.
The fact that I took it as a matter of course did not alter that any.
Everybody gambled, and the fact that it might be against the law would never alter human nature.
The fact that Iraq was attacked, the experts continued, does not alter its legal obligations.
This little fact now altered the entire course of events.
The fact of their service does not alter their nature.