Mining and Proof of Work

# Probability of finding a block in N hash attempts:
# P(find) = 1 - (1 - 1/D)^N ≈ N/D when N << D

# Target = 2^256 / difficulty (roughly)
# Current network difficulty: ~80 trillion (as of 2025)

current_difficulty = 80_000_000_000_000  # 80T
network_hashrate_eh_per_sec = 600         # 600 EH/s = 6e20 H/s
network_hashrate = 600e18

# Expected time for the entire network to find a block:
target = 2**256 / current_difficulty
expected_attempts = 2**256 / target  # = current_difficulty * 2^32 approximately
expected_seconds = expected_attempts / network_hashrate
print(f"Expected block time: {expected_seconds:.1f}s (target: 600s)")

# Probability a single 100 PH/s miner finds the next block:
miner_hashrate = 100e15  # 100 PH/s
share = miner_hashrate / network_hashrate
print(f"Miner share: {share*100:.4f}%")
print(f"Expected blocks per day: {share * 144:.4f}")
# 144 blocks/day (10-min target) * share = expected blocks/day for this miner

# Variance is huge: a 100 PH/s miner gets ~0.024 blocks/day on average,
# but might go weeks without one. Pools exist for variance reduction.

# Why 51% attack is expensive:
# - Need >50% of network hashrate sustained for the attack window
# - 600 EH/s * 30 J/TH * 24h * 30d * $0.05/kWh ≈ $1.5B/month in electricity alone
# - Plus ASIC opex/capex; total cost easily $5-10B/month for sustained attack