FIRST LEGO League coding help for US teams

# Our model: which run plan wins when only the highest of three matches counts?
# Mission points and success rates are invented for teaching.
from itertools import product

def outcomes(missions):
    """Every possible score for one match, with its probability."""
    table = {}
    for result in product([0, 1], repeat=len(missions)):
        prob, score = 1.0, 0
        for (points, p), hit in zip(missions, result):
            prob *= p if hit else 1 - p
            score += points if hit else 0
        table[score] = table.get(score, 0) + prob
    return table

def expected_top_of(table, n=3):
    """Expected value of the highest score in n independent matches."""
    total, below = 0.0, 0.0
    for score in sorted(table):
        at_or_below = below + table[score]
        total += score * (at_or_below ** n - below ** n)
        below = at_or_below
    return total

plan_a = [(20, 0.90)] * 5                  # five steady missions
plan_b = [(20, 0.90)] * 3 + [(60, 0.45)]   # three steady, one bold

for name, plan in [("A", plan_a), ("B", plan_b)]:
    t = outcomes(plan)
    one = sum(s * p for s, p in t.items())
    print(name, round(one, 1), round(expected_top_of(t), 1))

# prints:  A 90.0 98.6
#          B 81.0 107.0

Our own teaching program, standard Python with no robot library. It lists every way a match can go, then works out the expected highest score across three matches.