abnormalrate.py

"""
Simulation to estimate the rate of occurrences of the event
'>= 48 blocks in 4 hours'.
"""
from random import expovariate

BLOCKRATE = 1. / 600  # Once per 10 min, the equilibrium block rate
NUMBLOCKS = 144*365*1000  # 1000 years of simulation

# Event constants
BLKTHRESH = 48  # 48 blocks
INTERVALTHRESH = 4*3600  # 4 hours

blocktimes = [None]*BLKTHRESH  # The blocktimes of the most recent 48 blocks

t = 0
numexceeded = 0
for n in range(NUMBLOCKS):
    curr = n % BLKTHRESH
    blocktimes[curr] = t
    tbegin = blocktimes[(curr+1) % BLKTHRESH]
    if tbegin is not None:
        interval = t - tbegin
        if interval <= INTERVALTHRESH:
            # Last BLKTHRESH blocks took <= INTERVALTHRESH.
            # Equivalent to there being >= BLKTHRESH blocks in the past
            # INTERVALTHRESH.
            numexceeded += 1
            # Reset blocktimes; we want independent events
            blocktimes = [None]*BLKTHRESH
    t += expovariate(BLOCKRATE)
    if not n % (1051200):
        print("{}% complete".format(n*100./NUMBLOCKS))

print("The event '>= {} blocks in {} hours' happened {} times in {} years.".
      format(BLKTHRESH, INTERVALTHRESH/3600, numexceeded, NUMBLOCKS/144/365))
print("This is roughly once every {} years.".
      format(NUMBLOCKS/144/365/float(numexceeded)))