What's a TTP? Do you mean "trusted third party"?
SatoshiDice can certainly place bets against themselves, and can tell whether any given bet will win or not before publishing the transaction. In that way they can defraud their shareholders by "winning" their profits for themselves.
A) Nothing stops a casino from disconnecting from a player in the event of the player receiving a hand which is likely to win.
Any decent casino will save the state of the game. If you get disconnected you just reconnect and carry on where you left off.
B) Nothing stops the casino from bruteforcing different keys incase a TTP is used to get an outcome which is the most profitable for the TTP.
Yes, it does. Use a big enough hash and bruteforcing becomes untenable. sha256 is big enough if you hash a long enough secret.
C) Even such casinos which are considered 100% secure and use the last transaction or the hash of all transactions as means of determing a winning hand/number/player can still bruteforce the outcome by sending small amounts to themselves.
I don't care about bets they make against themselves. So long as they can prove that their interactions with me are fair that's enough. I know SatoshiDice could be cooking their books to defraud their investors. I also know that when I make the "lessthan 32768" bet with them I have
exactly 50% chance of winning. I'm not an investor of theirs. As a customer I
know I'm getting a fair deal.
D) People that own shares of any competing casino don't state that clearly in their posts when bashing us to not make their personal gain obvious which is unethical in the real business world.
Thus any casino which claims to be fair/provably fair while having a TTP are liars at best and we are at least as trustworthy as them if not more since we are more serious regarding the matter and ready to invest a lot more funds into our casino.
Provable fairness (as used by satoshidice and bitzino.com for example) doesn't require a trusted third party. The randomness comes from the customer providing some data that the house can't know in advance. In the case of satoshidice the customer provides the txid. At bitzino the customer provides an arbitrary "client seed". In both cases the data provided by the customer determines the result of the bet, but so does the secret known only by the house. The hash of the secret is provided before the customer provides their data, which ensures fairness.