( 30th August 2019 )
Assuming sufficient quality of the hash function in the protocol and the pseudo-random number generator used in the construction of the block header, whether a given calculated hash leads to a valid block can be considered for all purposes a random event, independent of the validity of any other calculated hash. A quantity known as the difficulty (which we will denote D) is adjusted periodically by the network and determines, as the name suggests, the difficulty of finding a valid block. The target value is chosen so that every computed hash will lead to a valid block with probability 1 / (2 powered 32 * D).
A miner with hashrate h mining for a period of time t, will calculate a total of ht hashes, and so will find on average ht / (powered 32 * D) blocks. Our expected payout is thus htB /(2 powered 32 * D). Example. We dedicated mining computer which can perform a billion hash calculations per second, h = 1Ghash/s = 109 hash/s. If he uses it to mine continuously for a day (86,400 seconds) when the difficulty is D = 1690906 and the block reward is B = 50BTC, we will find on average
and receive payment of 0 .0119B = 0.595BTC on average.
Poisson process on Mining pool
Mining is hence analogous to gold mining. Just like a gold miner who spends manpower and energy to dig the ground in search of gold, a miner spends computing powers (known as hash rates) and related electricity/cooling/network expenses in search of solutions to some difficult cryptography puzzles. Technology rules that the probability of finding a solution is not affected by the number of trials attempted. This well-known memory less property implies that the event of finding a solution is captured by a Poisson process with the arrival rate proportional to a miner’s share of hash rates globally. Precisely, given a unit hash cost c and unit dollar award R for each block, the payoff to the miner who has a hash rate of λA operating over a period T is:
Here, N solo is number of blocks the miner finds within T, Λ denotes global hash rate (i.e., the sum of all hash rates employed by miners during T, D = 60 × 10 is a constant so that on average one block is created every 10 minutes. The Poisson distributed random variable N solo captures the risks that a miner faces in this mining game. Because mining is highly risky, miners have strong incentives to find ways to reduce risk. While theoretically there are various ways to reduce risk, a common practice is to have miners mutually insure each other by creating a (proportional) mining pool. The next section describes how such a mining pool works.
Cryptocurrency wallet
A cryptocurrency wallet stores the public and private "keys" or "addresses" which can be used to receive or spend the cryptocurrency. With the private key, it is possible to write in the public ledger, effectively spending the associated cryptocurrency. With the public key, it is possible for others to send currency to the wallet.
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