Expected value

import random
from math import comb

WIN_PCT, AVG_WIN, AVG_LOSS = 35, 200, 100

def simulate(n_trades, rng):
    equity, path = 0, [0]
    for _ in range(n_trades):
        equity += AVG_WIN if rng.random() < WIN_PCT / 100 else -AVG_LOSS
        path.append(equity)
    return path

rng = random.Random(11)
paths = [simulate(1000, rng) for _ in range(100)]
print(sum(path[-1] < 0 for path in paths))   # people who are down after 1,000 trades in this run: 10

def prob_still_losing(n_trades):
    """Probability that the account is down after n_trades trades."""
    losing = sum(
        comb(n_trades, wins) * WIN_PCT**wins * (100 - WIN_PCT) ** (n_trades - wins)
        for wins in range(n_trades + 1)
        if wins * AVG_WIN - (n_trades - wins) * AVG_LOSS < 0
    )
    return losing / 100**n_trades

for n in (100, 1000, 4400):
    print(n, round(prob_still_losing(n) * 100, 2))   # probability of being down (%): 38.03, 13.68, 0.99