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).
mixers are very probably safe. If you want to be safer, use two 3rd party websites then two different mixers.
i think the most trust mixer just bitmixer.
But what is he function to hide your bitcoin ?