I have few questions.
I would consistently create new accounts; once a 4BTC bank doubled, I typically withdrew; moved into a new account and started again.
That would imply that provably fair site is cheating

I don't think he meant that. I also use a strategy that allows me to eliminate almost all the percentage of loss. Among the various things I do there is also: "change often accounts".
Create new account, bet, withdraw, create new account etc ...
I do not know why it works, but if I keep the same account sooner or later I lose everything
How can this be explained?
with new accounts, I don't see any other reason to move to new account.