It depends on both sides you mentioned and on the specific payment method.
If you request a withdrawal, then it needs to be processed by the casino. According to my experience, this can take few minutes, days, but sometimes even weeks.
When the casino approves the withdrawal, they send this information to the payment provider. Then it exclusively depends on the payment provider and the speed of transferring the money between the provider's bank and your bank.
According to my experience, when we for example approved a withdrawal to Skrill, the customer received the money within 15 minutes since it's not necessary to transfer the money from one bank to another. If you have an account in the same bank as the casino, then of course, it will be much faster as well. Unfortunately, most of the times, the casino won't tell you which banks they use for security reasons.
Then you've got the cases where the casino claims they sent the money weeks ago, but the player never received it. Then the issue is usually on the payment provider's side or on your bank's side. It can actually happen that your bank refuses to accept the money from the foreign entity (because the amount is too high, the money is transferred from a 3rd world country, the sender is unknown etc). That often applies to the US players. Most of the times, you can't simply send them an amount they would normally earn after 6 months or more. It looks suspicious.
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