##Python (2.6) Extremely simple, but still I'm curious how it will perform compared to the other approaches.
import sys, random
try:
s = sys.stdin.readlines()[-2]
m = min(int(x) for x in s.split())
except IndexError:
m = random.choice([1,1,1,2,2,3,3,4])
a = random.choice([-2,-1,0,1,1,2,2,3,3])
print max(m + a, 1)
Just pipe in the bids via stdin, e.g. python testbid.py < bids.txt.
EDIT: changed for the 'first round all zeros'
EDIT: changed the 'magic numbers' a bit (a second time)