Also gambling houses should stop the users initially, when they come for withdrawal stating you've got multiple accounts doesn't look to be a fair thing.
It is fair in all sense. They cannot freeze your accounts when their ToS has no mention about multiple accounts or anything about abusing their system (usually bonus/give-away) using more than one account. So, they reserve the rights to lock a suspected account at any time they catch. Houses go freezing out mostly at the time of withdraw due to the obvious reason of their last check point where they lose all the control over a gambler.
In some other perspective, a gambler opens more than one account and may deposit or not but plays for some time and develop some gambling interest and may get eligible to withdraw but house catch them and lock all the accounts. Now, house helped a person to be a new gambler.
If that gambler deposit some money to gambling bankroll with one of their multiple account and plays and lose some portion of it, again houses welcome that until they opt for withdrawing. These are the reasons why all the houses are locking out at the point of withdrawing and until then allows gamblers to enjoy.
Gamblers usually have two accounts only, 1 for betting and the other one as bank account.
As bank account? It is a news to me
. Probably OP wants to have more number of bank accounts
. Are you using any gambling houses as your web-wallet? Are you saving tx fees by doing so?