Bitcoin Mining Probability

Estimate the probability of finding a Bitcoin block from hashrate, network difficulty, and time, with a live simulated mining visualization.

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PoW cryptographic security and Poisson probability 🖖

Bitcoin mining utilizes a Proof-of-Work consensus mechanism based on finding a double-SHA256 hash below a target difficulty threshold. The process behaves as a memoryless Poisson process, where the time to mine a block is exponentially distributed: P(T > t) = e^{-t/λ}, with λ typically target-adjusted to 10 minutes. This difficulty adjustment ensures network security independent of total global hashing power.

Mining is a lottery, not a race 🖖

Every hash attempt is a lottery ticket with astronomically bad odds — the winning number is any hash below the target. You cannot 'work toward' a block; you simply buy more tickets per second by adding hashrate. Your chance of finding the next block is roughly your share of the total network hashrate, so a miner with 1% of the power wins about 1% of blocks over the long run.

The 32-bit nonce runs out in microseconds 🖖

A Bitcoin block header has only a 32-bit nonce — about 4.29 billion (2³²) values. A modern ASIC doing 100 TH/s burns through that entire range in roughly 43 microseconds, far too few tickets to find a block that now needs around 10²³ hashes. So miners keep generating fresh headers by tweaking the coinbase transaction's extra-nonce and the timestamp, quietly expanding the search space the header alone cannot provide.

Example problems

  • Easy - Low difficulty (20), 2000 TH/s → blocks arrive frequently — large target zone
  • Balanced - Balanced defaults: 800 TH/s, difficulty 160 → moderate block frequency
  • Hard - Hard mode: difficulty 850, 300 TH/s → tiny target, very rare blocks