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#Eidetic, Python 2

import random, math, sys, json

total_degrees, degrees_left, total_people, people_left = map(int, sys.argv[1:])
try:
    inp_f = open("./data/Eidetic.json", "r")
    out = json.load(inp_f)
except (IOError, ValueError):
    out = {"last_cake": 0,
           "runs": 0,
           "total_runs": 0,
           "total_rounds": 0,
           "training":  [0.0, 0.0, 0.0, 4.0, 400.0, 426.0, 720.0, 1042.0, 1042.3129032258064, 1044.0, 1044.0, 1044.0, 1044.9741935483871, 1045.3129032258064, 1051.3677419354838, 1056.4022617124394, 1264.1534733441033, 1378.663974151858, 1451.5218093699516, 1473.0856219709208, 1662.069466882068, 1828.9919224555736, 2671.3430420711975, 4423.720064724919, 3625.3333333333335, 2619.4789644012944, 1270.9288025889969, 741.2718446601941, 480.4757281553398, 122.66990291262135, 27.54736842105263]}

else: inp_f.close()

def write_out():
    out_f = open("./data/Eidetic.json", "w")
    out_f.write(json.dumps(out))
    out_f.close()

def get_last_winner(): # Find the bid of the last winner
    bid = out["last_cake"]
    return max(bid, degrees_left) - degrees_left

def train():
#    print degrees_left # If you get that much, your probably safe.
#    sys.stderr.write("\nEidetic - Training len %s, no runs: %s, no_rounds: %s, last winner: %s\n"%(len(out["training"]), out["runs"], out["total_rounds"], get_last_winner()))
    if len(out["training"]) <= out["runs"]: out["training"].append([])
    out["training"][out["runs"]].append(get_last_winner())

def get_best_round():
    data = out["training"][out["runs"]+1:]
    mean = [sum(i)/(float(len(i)) or 1) for i in data]
    bid = max(mean+[0]) - 0.5
    #sys.stderr.write("\nEidetic - mean %s\n"%mean)
    return bid

def main():
    reset = total_people == people_left
    if reset:
        out["total_rounds"] += 1
        out["runs"] = 0
    train()
    bid = get_best_round()
    print bid
#    sys.stderr.write('\nEidetic Bid: '+str(bid)+'\n')
    out["total_runs"] += 1
    out["runs"] += 1
    out["last_cake"] = degrees_left
    write_out()

main()

I ran this bot in the controller a couple of times to train it up a bit, it remembers the bids required to win each round and then once trained, it goes out into the real world and votes with the rest of them.