Exchanges are not going to necessarily to look at "taint" percentages (which are often wildly inaccurate). If the exchange has good reason to believe that you are depositing money from certain prohibited sources (as outlined in their agreement with you), they will reject the deposit and/or close your account.
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I don´t think that they will reject the deposit. At most exchanges cryptocurrency deposits are fully automated.
Therefore the funds will be credited to your exchange account even if they are tainted.
It is more likely that the account will get frozen after the deposit or they will at least ask you
to prove that you obtained the cryptocurrency from a legitimate source.
The process for checking for deposits from prohibited sources is also largely automated.
Exchanges may seek additional information from the customer if it appears a deposit is from a prohibited source.
It is unlikely that exchanges have any legal basis to freeze coin indefinitely without some kind of court order.
The exchange wouldn't know that the coins have changed hands here.
This is one of the reasons why I argue that taint is completely meaningless. As soon as coins are involved in a transaction - any transaction - then they could have changed hands in a perfectly legal transaction such as the purchase of some goods from a vendor or a peer to peer trade.
Of course it makes no sense. Even a direct transaction between a gambling platform and a centralized exchange can involve two different people and doesn't mean that the same person owns both addresses. It's quite possible that person A has sold Bitcoin to person B, and person A made that transaction from a casino they use. Person B received the coins in their exchange account on a CEX. Accusing person B of illegal activities or having tainted coins is out of order.
If I am not mistaken, most exchanges have TOS that direct people to only deposit their own coin onto their exchange account.
If the exchange has good reason to believe that you are depositing money from certain prohibited sources (as outlined in their agreement with you), they will reject the deposit and/or close your account.
Those Terms and Conditions are written in such a way that gives them the right to freeze or block your accounts for whatever reasons they think are necessary. After that, they can request from you whatever proof they deem necessary, including KYC. You have a choice to play ball and do what they say, or give them your coins. A third choice is never depositing there in the first place.
I think it is probably a good idea to assume you will need to provide KYC to any exchange you deposit coin onto.
I would also point out that it is very common for various crypto businesses to ask for KYC when they have what they believe to be stolen property. Multiple reputable casinos have done this in the past to those they have evidence of substantial cheating/hacking.
Regardless of what is in any TOS, there is no legal basis for an exchange to "freeze" an account indefinitely without a court order. If an exchange were to do this, the customer should take the exchange to court.