How do mixers work and how can they provide untraceability of transactions?
I'm curious about it because i'd like to provide a similar service


As far as i know they are middle-man wallets where outbound transactions are performed only when there are many to be done at the same time and at different addresses, otherwise the mixers just waits.

Maybe because if you, Alice, send 5 BTC to Bob through the mixer Mallory, and Mallory just redirects the 5 BTC to Bob as soon as it gets them, it is obvious that "Alice sent 5 BTC to Bob" isn't it?

But it's not enough: even if it waits until many outbound transaction have to be done, there are still those 2 5BTC transactions that have the exact same amount...what a coincidence.
It is almost obvious that those 5BTC from Alice were intended to be sent to Bob......

i'm missing something here, how do they solve that issue?

Perhaps the mixer is not a wallet but a group of several wallets (100 or 1000+??) that

1- split the incoming amount between them
2- each of them sends BTC to Bob a little at a time, while sending BTC to other several thousands destination addresses at the same time

In this way an analyst will have an hard time to track hunderds/thousands of transactions and sum them toghether, or maybe he does not know all the wallets that belong to the mixer.