EV is a lie

gamble.py

import random
import statistics

random.seed("FOOBAR")


def won_round():
    return random.choice([True, False])


START = 10
WIN = 1.5
LOSE = 0.6
PER_TRIAL = 1000
TRIALS = 100


def trial(win=WIN, lose=LOSE):
    bankroll = START
    for _ in range(0, PER_TRIAL):
        if won_round():
            bankroll *= win
        else:
            bankroll *= lose
    return bankroll


print(f"running 50/50 bet with win={WIN}, lose={LOSE}, bankroll starting at {START}")
ev = .5 * (WIN + LOSE)
print(f"EV per round = .5 * {WIN} + .5 * {LOSE} = {ev}")
print(f"EV across {PER_TRIAL} rounds = start * {ev}**{PER_TRIAL} = {START * ev**PER_TRIAL}")
print("")

last_mean = -1
num_trials = TRIALS
trials = []

while last_mean < 0:
    trials = trials + [trial() for _ in range(0, num_trials - len(trials))]

    print(f"after {num_trials} trials")
    print(f" min = {min(trials)}, max = {max(trials)}")
    last_mean = statistics.mean(trials)
    print(f" mean = {last_mean}, median = {statistics.median(trials)}")
    try:
        print(f" mode = {statistics.mode(trials)}")
    except statistics.StatisticsError:
        pass
    print("")

    num_trials *= 10