To protect your privacy, it is commonly recommended to send change to a new freshly generated address. It is argued that this makes it impossible to distinguish the payment from the change which makes it harder to group the transactions that belong to you.
Anyone that argues the underlined passage above is either intentionally misleading you or misunderstands what they've read.
It does however make it significantly more difficult.
Correct me if I'm wrong, I'm afraid it doesn't help in many cases. The reason is simple: payment value is usually smaller than the change.
When I spend money from my debit card, the payment amount is usually much smaller than the remaining balance. That's because I don't want to refill my card as often as I spend. The same spending habits applied to Bitcoin make transactions traceable.
Not exactly. Bitcoin transactions don't work with a wallet "balance" or even an address "balance", they work with individual unspent outputs. This is an important concept to understand well if you are going to try to discuss "change" at the transaction level.
If you have 10 BTC (say, you received it from an exchange) and want to pay 1 BTC, your transaction will have two outputs:
1 BTC - the payment,
9 BTC - the change to another your address.
And what if you have 10 BTC (say you received it from an exchange) and you want to pay 6 BTC? Then how much will your change be? Will it still be the largest output?
What if you received your 10 BTC in 3 separate transactions to 3 different addresses, first a transaction for 1.1 BTC, then a second transaction for 3.5 BTC, and finally a transaction for 5.4 BTC?
Without any other knowledge, just by looking at the output values, it is usually safe to say that 1 BTC is the payment and 9 BTC is the change, and the address where the 9 BTC landed is again your address.
No it really isn't. Especially if you are using a new address for every transaction you receive (as you should be). Then that 10 BTC "balance" could be made up of a dozen or more smaller individual outputs. The total of any combination of those outputs might be less than 2 BTC, meaning any output will be
LESS THAN half of the transaction value (the actual payment will be the
BIGGER output).
Any thoughts how this situation is really often and how to protect one's privacy?
It is only possible if you are receiving your bitcoins in single large transactions and are then spending less than half of what you received every time you spend it. Even then, the amount will eventually dwindle to the point where you can no longer assume that the larger output is the change.
To significantly improve your privacy, receive your transactions as smaller amounts and use a new address for every transaction.