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Are all trades stored in block chain?

Are all trades, like mtgox exchange, gambling, etc. stored in block chain? Or, few trades could have been skipped / ignored?

Consider this case, 'a' transfers 10btc to 'b', and then 'b' transfers 10btc to 'c'. Is it possible to store this as single trade, as 'a' transfers 10btc to 'c'?

Is it possible for an exchange to include fake bid/ask orders for it's own benefit?

Is it really possible to differentiate between two transfers, where in one transfer is between single user accounts and another one is between two users?

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Within an exchange's ledger system, value may be moved between accounts without creating actual transactions in the public Bitcoin ledger, the blockchain. Exchanges that use this method keep all of their reserves in one set of accounts and simply debit and credit user accounts as necessary. Only when a Bitcoin transaction is necessary to move value from one account to another outside of the system will a Bitcoin transaction be created and broadcast.

In other systems, an exchange or other entity may actually create a new Bitcoin transaction for every trade. This method is more inline with the ideals of Bitcoin, but costs more because of the transaction fees necessary to expedite/facilitate processing.

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Any transaction stored in the Block Chain are money transfers between two Addresses. However, if one controls both of the Addresses in question and runs some accounting system on top of the Address balances (such as bitcoind and the use of Accounts), one does not need to create Transactions in order to move bitcoins between two accounts. They can just update their personal ledger of the different Accounts. This option creates less noise in the Block Chain and makes the money transfers instantaneous, but requires extra effort to make sure each Account can only spend only the bitcoins they own.

Many systems can and do behave like this. I'm guessing all of the exchanges do this, as well as some eWallets and probably some casinos.

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