I hope everybody here knows about BitcoinFog, Shared Send, and other mixers. And uses them for random transactions now and then to give the rest of us plausible deniability.
Most mixers introduce points of centralization, which allow a party to steal your coins or allow them to break privacy. JoinMarket is a good solution that works on Bitcoin today. Monero is a good altcoin which will automatically mix your coins using crypto. I believe it is more powerful than JM but requires using an altcoin. Zcash offers unmatched anonymity powered by fancy new crypto (less tested, less certainty on…
Assuming no mixer reputation, they allow a party to steal your coins. Note that breaking a large transaction into small pieces allows you to determine a sort of short-term reputation while only risking one piece at a time.
My standard first two steps used to be SharedCoin->BitcoinFog, for example.