D’Alembert simulation

D’Alembert simulation#

Created by a French mathematician in the 1800s, this strategy stands the test of time. It’s often likened to the Martingale strategy, only less risky.

from roulette import Roulette
from core import *
from simulations_core import *
from simulations_plots_core import *
roulette = Roulette()

def transformation_on_win(bet_history):
    next_bet = bet_history[-1] - 1 if (bet_history[-1] - 1) > 0 else bet_history[-1]
    return next_bet, bet_history

def transformation_on_loss(bet_history):
    return bet_history[-1] + 1, bet_history

The D’Alembert strategy follows a simple structure that only works on even bets, like red or black. Before you play, decide on a set amount of money to act as a unit, for example $1. If you win the bet, decrease the next bet by one unit, and if you lose, increase the next bet by one unit.

def dalembert_betting(goal_money_won, bet = 1, money_limit = None):
    return goal_money_betting_even_bet(roulette, goal_money_won, bet, transformation_on_loss, 
                                        transformation_on_win, money_limit)

money_goals = [10, 100, 500, 1000]

Starting bet = 1, Allowed money lost = -10#

bet = 1
money_histories = simulate_different_goal_money(
                    betting_type = dalembert_betting, 
                    goal_money_list = money_goals, 
                    number_histories = 10000,
                    start_bet= bet,
                    money_limit= -10*bet)

successful_histories = get_successful_histories(money_histories, money_goals)

for goal in money_goals:
    print(f"For goal {goal} mean money won:")
    print(get_mean_money_won(money_histories, goal))
    print(f"For goal {goal} mean money lost:")
    print(get_mean_money_lost(money_histories, goal))

For goal 10 mean money won:
10.323592441067602
For goal 10 mean money lost:
-13.281487569344565
For goal 100 mean money won:
101.08658008658008
For goal 100 mean money lost:
-14.070054797464275
For goal 500 mean money won:
502.969696969697
For goal 500 mean money lost:
-14.516609623515201
For goal 1000 mean money won:
1003.75
For goal 1000 mean money lost:
-14.584969939879759

Analysis when the goal is to win 10 units#

UNITS = 10

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 100 units#

UNITS = 100

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 500 units#

UNITS = 500

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 1000 units#

UNITS = 1000

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Starting bet = goal, Allowed money lost = -10*goal#

money_histories = dict()
for goal in money_goals:
    bet = goal
    tmp_money_histories = simulate_different_goal_money(
                        betting_type = dalembert_betting, 
                        goal_money_list = [goal], 
                        number_histories = 10000,
                        start_bet= bet,
                        money_limit= -10*bet)
    money_histories = money_histories | tmp_money_histories

successful_histories = get_successful_histories(money_histories, money_goals)

for goal in money_goals:
    print(f"For goal {goal} mean money won:")
    print(get_mean_money_won(money_histories, goal))
    print(f"For goal {goal} mean money lost:")
    print(get_mean_money_lost(money_histories, goal))

For goal 10 mean money won:
11.321283325802078
For goal 10 mean money lost:
-107.20731707317073
For goal 100 mean money won:
103.07509033423668
For goal 100 mean money lost:
-1033.479020979021
For goal 500 mean money won:
502.9665835976439
For goal 500 mean money lost:
-5045.529010238908
For goal 1000 mean money won:
1003.0391511575125
For goal 1000 mean money lost:
-10054.299663299664

Analysis when the goal is to win 10 units#

UNITS = 10

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 100 units#

UNITS = 100

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 500 units#

UNITS = 500

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 1000 units#

UNITS = 1000

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Starting bet = goal, Allowed money lost = -20*goal#

money_histories = dict()
for goal in money_goals:
    bet = goal
    tmp_money_histories = simulate_different_goal_money(
                        betting_type = dalembert_betting, 
                        goal_money_list = [goal], 
                        number_histories = 10000,
                        start_bet= bet,
                        money_limit= -20*bet)
    money_histories = money_histories | tmp_money_histories

successful_histories = get_successful_histories(money_histories, money_goals)

for goal in money_goals:
    print(f"For goal {goal} mean money won:")
    print(get_mean_money_won(money_histories, goal))
    print(f"For goal {goal} mean money lost:")
    print(get_mean_money_lost(money_histories, goal))

For goal 10 mean money won:
11.494012299061387
For goal 10 mean money lost:
-211.54172366621066
For goal 100 mean money won:
105.11465106198526
For goal 100 mean money lost:
-2047.300518134715
For goal 500 mean money won:
505.957669108143
For goal 500 mean money lost:
-10138.343575418994
For goal 1000 mean money won:
1006.0268624252311
For goal 1000 mean money lost:
-20148.766459627328

Analysis when the goal is to win 10 units#

UNITS = 10

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 100 units#

UNITS = 100

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 500 units#

UNITS = 500

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 1000 units#

UNITS = 1000

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Starting bet = goal, Allowed money lost = -30*goal#

money_histories = dict()
for goal in money_goals:
    bet = goal
    tmp_money_histories = simulate_different_goal_money(
                        betting_type = dalembert_betting, 
                        goal_money_list = [goal], 
                        number_histories = 10000,
                        start_bet= bet,
                        money_limit= -30*bet)
    money_histories = money_histories | tmp_money_histories

successful_histories = get_successful_histories(money_histories, money_goals)

for goal in money_goals:
    print(f"For goal {goal} mean money won:")
    print(get_mean_money_won(money_histories, goal))
    print(f"For goal {goal} mean money lost:")
    print(get_mean_money_lost(money_histories, goal))

For goal 10 mean money won:
11.576980093180856
For goal 10 mean money lost:
-313.58992805755395
For goal 100 mean money won:
105.50802997858672
For goal 100 mean money lost:
-3067.1954545454546
For goal 500 mean money won:
509.08187259512613
For goal 500 mean money lost:
-15306.826086956522
For goal 1000 mean money won:
1008.6657402458578
For goal 1000 mean money lost:
-30315.883720930233

Analysis when the goal is to win 10 units#

UNITS = 10

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 100 units#

UNITS = 100

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 500 units#

UNITS = 500

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

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plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 1000 units#

UNITS = 1000

plot_successful_bets(money_histories[UNITS], UNITS, title=f"Successful bets for {UNITS}")

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mean_money_list, std_money_list = get_mean_and_std_of_histories(successful_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title=f'Successful simulations mean and std for {UNITS} units')

../_images/225a2815c2b1b72ec66205d1aaceaed42e3d27f50e3c99ec2f5810aa3b995c54.png

plot_money_histories(successful_histories, UNITS)

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D’Alembert simulation

Contents

D’Alembert simulation#

Starting bet = 1, Allowed money lost = -10#

Analysis when the goal is to win 10 units#

Analysis when the goal is to win 100 units#

Analysis when the goal is to win 500 units#

Analysis when the goal is to win 1000 units#

Starting bet = goal, Allowed money lost = -10*goal#

Analysis when the goal is to win 10 units#

Analysis when the goal is to win 100 units#

Analysis when the goal is to win 500 units#

Analysis when the goal is to win 1000 units#

Starting bet = goal, Allowed money lost = -20*goal#

Analysis when the goal is to win 10 units#

Analysis when the goal is to win 100 units#

Analysis when the goal is to win 500 units#

Analysis when the goal is to win 1000 units#

Starting bet = goal, Allowed money lost = -30*goal#

Analysis when the goal is to win 10 units#

Analysis when the goal is to win 100 units#

Analysis when the goal is to win 500 units#

Analysis when the goal is to win 1000 units#