Basic theory of Bitcoin mixing, part 2<<< part 1
This part is about types of mixing and how do they work.
Mixing it yourself
Doing it yourself is great when you want to learn how it works. Lets start with our 10 mBTC example. You have received it from Bob and you do not want him to know how you will spend it. You create transaction spending your 10 mBTC sending 5 mBTC to address A and change (4.99 mBTC) to address B. Bob knows you sent it and assumes address B is also your (because it is rare to pay uneven amount like 4.99 and get round 5 as change). He may suspect address A is yours but he is not sure. If you pay for coffee with 4.99 mBTC address barista will not know if you also own 5 mBTC.
This single transaction increases your blockchain privacy and you can repeat it many times. Problem arises when you want to pay 6 mBTC as this transaction will join address A and address B allowing both Bob and barista to know. You can read more about this problem at our advanced Bitcoin mixing theory.
Using mixing software
Basic Bitcoin wallet allows you to send and receive Bitcoins. Some wallets (Samurai, Wasabi) have mixing capabilities using CoinJoin. This means your wallet may contact with other people wallets and create transaction that links them together. If 10 wallets create this transaction then Bob will know that 1 of 10 outputs is yours but will not know which.
This method is better than doing transactions by yourself and you can repeat it many times to achieve better privacy. CoinJoin is trustless and you trust only wallet developer (who also coordinates how wallet contacts each other). Bad part is that all transactions are on-chain and your privacy is one-of-some.
Using mixing service
There are multiple types of services:
First - magic services. You deposit some funds, you receive some funds. "Our special algorithm mixes best" and "quantum AI cleans your coins". Good part is your Bitcoin transacts off-chain by magic. Bad part is magic does not exist and only thing you can be sure is that you sent your Bitcoin to liars.
Second - newly minted coins. You deposit some funds and you receive "clean, newly minted coins fresh from miners genesis block". Good part is newly minted coins out of coinbase (not this one) should have no history and should be accepted by anyone accepting Bitcoins. Bad part is that none of services that advertises by that does that. If you can use blockchain explorers and try their service you can prove it.
Third - pool mixers. You deposit some funds, you receive some funds out of the same wallet. Bigger the pool, better the privacy. Good part is that it worked for years and works now. It is off-chain and owners does not lie about it. Bad part is you can do better.
Fourth - ChipMixer. You deposit some funds, pick size of outputs and receive private keys for funds deposited days or weeks ago. All same-sized chips are the same and sizes allows your wallet to create transactions without joining multiple inputs. Your mixing output transaction is recorded only when spending chips so you may increase your privacy by keeping chips unspent longer. You can read how it works and pick between privacy and comfort yourself.
Next part is about using ChipMixer to mix your coins.