It is a big pleasure of Monero to be mentioned publicly by theymos on its anonymity. The guide of admin on decent mixing methods and Monero is one of the best two options with cheap fees to use is a good recognition on the anonymous transaction of Monero. However, the key is to maintain anonymity totally depends on each person in the way of using internet and moving funds. Monero, Wasabi, or any other kinds of mixer services are not able to guarentee 100% of anonymity.
Most "tumblers", like the now-defunct bestmixer.io or even ChipMixer, aren't great because they are needlessly expensive, you're trusting the service not to run away with your coins, and you're trusting the service not to keep logs. Maybe they're the best current solution for small amounts where lasting anonymity isn't mission-critical, but in most cases you shouldn't use them.
Anonymity is very difficult, especially with blockchain-based systems where so much data has to be public, but also in other areas (eg. there are several known weaknesses with Tor). You should always operate with the expectation that any anonymity system you use will eventually fail you. If you're ever confident in your anonymity, then you're wrong.
That said, there are two halfway-decent mixing methods currently:
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#2 - Monero
Monero is not a magic black box which provides perfect anonymity! If you use eg. flyp.me to buy XMR and then quickly sell this XMR on flyp.me again, it is blatantly obvious to flyp.me what you've done (if they keep logs), both due to the amounts and the specific Monero inputs used. In order to get decent privacy, you have to do something like this:
1. Convert BTC to XMR (using your own Monero wallet, not a hosted wallet).
2. In two or more transactions of random amounts, move XMR from that wallet to a different wallet/account.
3. Optionally, you can repeat the above step with additional wallets/accounts for greater anonymity.
4. Preferably in two or more transactions of random amounts, convert the XMR in your last wallet in the chain to BTC.
Ideally, all of the above should be performed over as long a period of time as you can tolerate.
- Pros: Possibly the best anonymity, especially if you're able to stay within the XMR ecosystem to some extent
- Cons: You should use Tor with Monero, but you have to set this up manually; it's all more difficult; you're exposed to exchange rate risk; transaction fees may be significant
Anonymity comparison between the two
Both Wasabi and Monero can be thought of in terms of "anonymity sets". If you're spending some BTC with an anonymity set of 50, this means that an observer can see that the sender is one of 50 people, but they can't tell which. So someone investigating a particular transaction you sent would have you "in their sights" to a certain extent from the start since you're among the 50, but in order to prove that you sent it, they'd have to either eliminate 49 other people from consideration or find some other evidence linking you to it.
Wasabi always aims for an anonymity set of 50 when mixing. Monero has an anonymity set of 11 per transaction. If you cascade transactions as I suggest above, then this multiplies, so after two transactions you have an anonymity set of 11*11=121, and after a cascade of three you'd have an anonymity set of 1331.
The quality of each member in the anonymity set isn't quite comparable, though. Monero is able to hide transaction amounts, which is helpful, but I tend to consider the quality of Monero anonymity-set-members to be lower on average, since many are probably owned by hosted wallets or other possible global adversaries.
