##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])
    a = random.choice([-2,-1,0,1,1,2])
    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.