import random

# A "jagged frontier": on 60 % of tasks the AI is right 90 % of the time; on the rest, 40 %.
# The human alone is right 70 % of the time everywhere. In the team, the human decides
# whether to accept the AI's answer or use their own, and recognises which kind of task
# it is with some accuracy ("discernment").
random.seed(5)
def team(discernment, n=100000):
    right = 0
    for _ in range(n):
        inside = random.random() < 0.6
        ai_ok = random.random() < (0.9 if inside else 0.4)
        human_ok = random.random() < 0.7
        thinks_inside = inside if random.random() < discernment else not inside
        right += ai_ok if thinks_inside else human_ok
    return right / n

ai_alone = 0.6 * 0.9 + 0.4 * 0.4
print(f"AI alone {ai_alone:.2f}, human alone 0.70")
for d in (0.5, 0.7, 0.85, 1.0):
    print(f"discernment {d:4.2f}: team accuracy {team(d):.3f}")
# AI alone 0.70, human alone 0.70
# discernment 0.50: team accuracy 0.697
# discernment 0.70: team accuracy 0.746
# discernment 0.85: team accuracy 0.784
# discernment 1.00: team accuracy 0.820