# A quick Python code that goes through all possibilities calculates the odds of Gurubashi survival at 84.247%.
 
minions = [1,2,2,2,3,7]
cache = {}
def f(minions, volcano):
  code = tuple(minions + [volcano])
  if code in cache:
    return cache[code]
  if volcano == 0:
    return float(minions[-1] == 1)
  num_alive = sum([x>0 for x in minions])
  chance = 0.0
  for idx, minion in enumerate(minions):
    if minion > 0:
      one_tick = minions[:]
      one_tick[idx] -= 1
      chance += f(one_tick, volcano-1)/float(num_alive)
  cache[code] = chance
  return chance
print(f(minions, 16))

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