problem-dice.py

N = 2022

primes = [i for i in range(2, N) if len([d for d in range(2, i) if i % d == 0]) == 0]

# Expected additonal rolls needed if I have d_k (k-sided dice) already determined
# 0-index is hit when we 
EAR = [10.0] * N
EAR[0] = 0.0

for it in range(20):
    def best_ear(k, ear):
        if k == 0:
            return 0.0
        min_ear = 10.0
        for p in primes:
            r = p * k
            over = r % N
            p_over = over / r
            min_ear = min(min_ear, (1.0 - p_over) * 1.0 + p_over * (1.0 + EAR[over]))
        return min_ear

    EAR = [best_ear(k, ear) for k, ear in enumerate(EAR)]
    print(it, EAR[:5])