Roulette What are the odds of flat betting randomly on even chances and losing 7 units before winning 3?

what are the odds of flat betting randomly on red black odd even high low and losing seven units before winning three

 

Masaniello?

 

The probability of either losing seven units before winning three, or winning three units before losing seven, when flat betting randomly on even-money bets like red, black, odd, even, high, or low in roulette, is approximately 97.96%. This high probability indicates that reaching either outcome is very likely in this scenario.

from scipy.stats import binom

# Define the probability of losing a single even-money bet (e.g., red, black, odd, even, high, low)
p_lose = 0.486 # Approximate probability of losing an even-money bet in roulette
n_games = 10 # Total games played until either losing 7 units or winning 3 units

# Calculate the probability of losing 7 units before winning 3 units
# This means we lose 7 games before winning 3, out of 10 games (as losing 7 units ends the trial)
games_to_lose = 7 # Number of losses required to lose 7 units
prob_losing_first = binom.cdf(games_to_lose - 1, n_games, p_lose) # P(X < 7), where X is number of losses

# Calculate the probability of winning 3 units before losing 7 units
# This means winning 3 games before losing 7, out of 9 games or less
p_win = 1 - p_lose # Probability of winning a single game
games_to_win = 3 # Number of wins required to win 3 units
prob_winning_first = binom.cdf(games_to_win - 1, n_games - games_to_lose, p_win) # P(X < 3)

# Probability of either losing 7 units before winning 3 or winning 3 units before losing 7
prob = prob_losing_first + (1 - prob_losing_first) * prob_winning_first

prob =
0.9796481492548674​