There is already such a system. Send a transaction with 1 BTC in fees. Since a miner can collect the fee of any transaction they include in a block, the fees would then, like you say, "be given as a reward with coins entering circulation, making it a lottery".
That's very different from what I am proposing because in my proposed system you don't have to be a miner and the probability of winning is completely separated from the likelihood of miners to win the mining rewards.
That part was a joke, I was only pointing out that the quoted paragraph is fulfilled by mining fee.
The failure with your system (besides zero interest) is that miners make the blocks and decide what goes into them. Transactions are stateless, they have no order in which to be processed. The miner can order them however they wish, and can quickly determine a transaction solution that would make their entry always win.
Besides you are missing my point because it doesn't matter the order of the transactions that goes into the block because the hash of the block will be random and unpredictable and so the result is completely unpredictable. There is no way the miners could determine the outcome.
What you describe is so different from the way that Bitcoin works it is hard to fathom in technical details what you are saying. Bitcoin is only comprised of transactions with ECDSA-signed spends, and UXTOs to a new address. A generate transaction is the only unique one, because Bitcoin allows for an additional transaction per block with no inputs, which pays to an address(es) or a public key, and the maximum that payment can be is MAX_REWARD + FEES.
You seem to be proposing another kind of "virtual" transaction as unique as the generate transaction, where Bitcoin sees another amount as spendable from the calculated lottery winner. The winner would be able to spend the "won" amount with the same privkey as entered. A whole new way of referring to this transaction number when spending would need to be thought of though, if you know how UXTOs are specified in transactions. The "entrant" transactions would only be unusual in that they are sending normal bitcoins to a new type of unspendable address, recognizable as being a lottery entrance, say any address with a network byte of 77.
The first critique is that hash % number of tickets = winning ticket is not fair. There are solutions to this, in fact I wrote them:
http://we.lovebitco.in/raffle.htmlNow the second inaccuracy - you say that entries will be made "during that 10 minutes in between block creation" - that's not how bitcoin works. Entering the contest takes a spending transaction. Miners choose what transactions to include in a block, and transactions must be included in a block in order to be spent or burnt. Transactions may have a large queue, miners may ignore some or all lottery transactions, etc. They might not be included in the next block, nor is there really a promise that they would be included in any particular order or in any block at all if miners all conspire to ignore them.
Then it all breaks down when you say
"last hash" which I interpret to be the hash of the previous block.
So now we know that miners can pick and choose transactions, can include them in the Merkle tree in any order that they want, and that the "picking mechanism", the hash, is already known. It is a simple matter to gather up as many entrant transactions as possible, add one more transaction as the miner's entrance to get N, and determine the "winning ticket number". The miner just moves around the transactions until his is the winning number. If there is no solution, the miner just adds more satoshis or BTC to re-sort things until there is. Then he starts hashing that block.
Let's say you weren't so naive and that "last hash" meant the top hash of the current block, the one including the entrance transactions. This is not so manipulable in Bitcoin, because the hashed data includes the Merkle tree including the entrant transactions. This would still be subject to miner attack. The miner can include 9999 BTC of his own entrance transaction, vs the 1 BTC he includes from other entrants, so he will win 99.99% of the time and collect the 1 BTC. If a block is mined where he's not the winner, it can be discarded and he continues mining. He will never lose because his lottery entry is not published on the rest of the network.