I see some gambling sites mention that they are provably fair. They provide some seed and ask to check some hash or whatever. My question is, can this fairness really be checked from outside ? Where are they twisting to make sure the house's win ?
Yes, it can.
I can explain it on simple example, (just the principle)
BTCRock - it's game where you have a grid 20x20 and you have 6 attempts to find gold vein.
Their proof is that immediately after solving captcha you can see hash of "gold vein coordinates ".
After you made your 6 tries, a result is shown to you:
Proof is that from begining the coordinates gold vein was [11,9], and was not moved if you luckily hit it ( it would change the hash)
You can check it using: http://www.xorbin.com/tools/sha256-hash-calculator
1 - enter: 65879c50984f5b9ede009960e6efa3c6|[11,9] (proof of location, shown after game end)
2 - hash it (using sha2586)
3 - you'll get: c0344a8d187371c671d9e16cb27190a74caef8fe32ab66be7287ed050fca2b12 (this is what you know from begining)
tip: for clarity try to change one coordinate and hash it again, will see you got completely different hash.
P.S. This's only principle, and can be used in various way. You should check description on particular site.