I don't hear of any gambling sites that have fast withdrawals unless you talking about a lightning transaction or other coins/token that doesn't need confirmation?
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Fast Withdrawals other than having to increase the Gas fee can use the Lightning Network.
I know an online casino that applies Lightning Network to withdrawals and deposits, such as
https://betplay.io.
Withdrawals and deposits will be made quickly and at a reduced cost.
my question is what is the process of withdrawal on most of the sites, which is so fast and without any double spending or issue like that?
It depends on the site. Some take slightly long, while others take 1–3 minutes to broadcast the transaction. For example, when I am sending funds from exchanges like Binance, MEXC, Phemex. The transaction gets approved very fast as soon as i am done with approving the 2FA and email confirmation.
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That is the normal time, withdrawals take time to confirm and as I mentioned it also depends on how much Gas Fee is used.
If using an Exchange the confirmation time is usually 1-3 minutes and it could be longer depending on how the Bitcoin network is doing.
If there is a spike in transactions like a few months ago then confirmation will take longer and can even be more than 24 hours.
However, instant transactions can be made using the P2P feature between internal exchanges.