How can you be sure the mixing service isn't a honey pot? And how do you know the gambling site (or a clever 3rd party) isn't fingerprinting every transaction?
I've seen a lot of suggestions for using very weak 3rd party solutions ITT but not a single trustless solution. I believe someone here (CIYAM?) is working on cross-chain atomic transactions that would effectively "scrub" links to past transactions, but that's in development (AFAIK).
That's a good idea. Do you know/trust anyone that operates a gambling/mixing site, and what are the odds that they are truly indifferent or interested in protecting user privacy? I ask just to get a feel for the odds of success.
I'd guess that just due to the nature of the problem 75% of all of these sites are either intentional honeypots or actors that could not be trusted.
If that's accurate, then the probability of being successfully tracked through two mixers (two independent events) is:
(.75) * (.75) = .5625
And tracked through three mixers (few people would take the time to do this):
(.75) * (.75) * (.75) = .421875
Four mixers:
(.75) * (.75) * (.75) * (.75) = .3164
So after using four mixers/gambling sites you still only have a 68% chance of reasonable privacy.