Are the odds of winning the same on a new and old account?
I don't think there is any effect between the old account and the new account. It's just a feeling when playing using an old account rarely wins or often wins when playing with a new account.
Perhaps this is also the reason many casinos prohibit the use of multiple accounts.
The ban on users using more than one account is not for that reason, but the casino has its own rules why they prohibit such actions. After all, why would one person use more than one account. If it's to chase bonuses, that's not the way to go.