Arbusers

Do bookies track BTC?  I use Coinbase, can they say if BTC come from the same Coinbase account? I also use Blockchain of course and I don't send money directly from Coinbase account to bookies. But I think it's not possible, because Coinbase don't use the same adress when they send BTC, right?

Technically if they want they can. But i dont think they have advanced in this. Most bookies use third parties for btc deposits.

I¨m not sure how Coinbase works with BTC addresses. But I think if I received BTC then convert it to currency and then again to BTC, then there is always different btc address for those BTC, right?

They have the same private wallet but only different receiving addresses, one for each user. If you notice your public receiving address in an exchange always stays the same. This is different when you use a wallet where you can create different receiving address for each payment if you want. Because you are provided with a wallet but not the keys. While in exchange you are provided with only a public address, in different terms a label. Even in a wallet it can be seen that some addresses belong to the same user, when the user sends coins.