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I'm not entirely sure how the reward system in Bitcoin works.

So, every 10 minutes a block is solved and 25 bitcoins are rewarded to a miner (or group). This happens in proportion to the amount of total computation power that miner has invested in solving the block. So a miner that has 30% of the total network power has a 30% chance of getting the 25 bitcoins and so gets roughly 8 bitcoins every 10 minutes right? If it was a group of 4 miners, average payout would be 2 bitcoins per minder I think.

How do transaction fees work with this? So a block consists of transactions. Are all fees for all transactions summed up and added to the basic 25 bitcoin reward and hence rewarded according to the same probability as above?

In addition, does this mean that a certain block can be worth much more than another one, should somebody be particularly generous in his transaction fee?

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The amount of Bitcoin a successful miner can claim for himself is currentBlockReward + transaction fees. If there are a lot of fees, a block can be worth more than others.

When users send transactions, they can attach a transaction fee by assigning less to the transactions' recipients than the inputs' total. The unassigned amount can be claimed as transaction fee: Inputs - outputs = Transaction Fee

Example: In: 0.005BTC, Out: 0.004BTC ⇒ Transaction Fee: 0.001BTC

When miners work to confirm a block, they include their individual Coinbase Transaction in the transaction data that they are trying to confirm. This Coinbase Transaction spends the block reward and transaction fees to an address of the miner's choosing. This means that a miner assigns his own reward when he successfully finds a block.

However, after a block is found, every node will check whether the block adheres to the rules: The sum of all transaction outputs in a block must be smaller than all transaction inputs and the block reward, i.e. the miner may only assign the free floating transaction fees and the current block reward to himself.

sum(BlockOutputs) ≤ sum(BlockInputs) + BlockReward

It has happened in the past that a miner claimed less than he could have. In that case the remainder is lost to the network.

Also see the related questions:

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