When you use a change address he sees another address you own because he can relatively sure the second sending address is no other payment but the sending to a change address. So he knows the second address.
Yes, the party you are transacting with can make a reasonable guess about change— though multiple destinations in a single transaction is something regular users use. But one person knowing about your change is still much better than the whole world knowing.
If youre unlucky he can see that this change address already had other changes inside (change addresses are used more than once)
They are not reused in correctly written software.
Im really not sure that its regularly happening that one transaction contains more than one real transaction and its not a change-address involved. That is, because many wallets till now dont allow more than one transaction in one transaction (i dont know how to name a whole transaction). And its very uncommon anyway because how often do one want to send 2 transactions or more in one? Till now i didnt even meet the requirement to do so. Only theoretically... in case i have to pay back my groupbuyers it would make sense to make this at once.
But it doesnt matter much anyway because when a transaction means to send one part to the recipient and the whole rest that lies at this address is going to another address its even more likely that a change address is involved, because 2 transactions to 2 persons nearly never will lead to exactly zero at the sending address.
Ok, not reusing them is better. I see. In fact the whole change addresses makes much more sense with single used change addresses. Ill check this with the dev of my wallet. When i think about change addresses that arent reused then the whole effekt could at least be a bit better but not really a gain in anonymity. I mean when someone gets a transaction from a change-address he only needs to check where the money came from. If its a transaction where the sending address is empty afterwards and the second recipient address in the list is the address that sent now, then its relatively sure that its a change address. And that can be connected to the previous address again. So its not really very much more anonymous.
Can you give me a reason, why its better to use change addresses, i didnt found yet? I mean when one dont want that the recipient knows that an address is yours, you simply have to send the btc to a clean address in your wallet. The recipient cant tell then if the previous sending address is yours or if the sender is another person. Or wherent there a website that loops bitcoins through a couple of addresses, splitting it and so on, so that its not know at the end where the bitcoins came from?
So if there is a reason, i didnt get yet, to use change addresses please let me know.
What do you mean with "But one person knowing about your change is still much better than the whole world knowing."