Paroli simulation

Paroli simulation#

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

The Paroli system is the reverse of the Martingale strategy. If you lose a round, you keep your stake the same. And if you win, you double your stake – this is known as ‘positive progression staking’. The overall aim of Paroli is to double your stake for three winning spins in a row. Once that happens, you go back to your starting stake.

def paroli_betting(goal_money_won, start, money_limit):
    money = 0
    money_history = [money]
    streak = 0
    bet = start
    while money < goal_money_won:
        if money_limit is not None and money < money_limit:
            return money_history
        
        prev_money = money 
        money += roulette.make_even_bet(bet)
        money_history.append(money)
        if money < prev_money:
            streak = 0
            bet = start
        else:
            streak += 1
            bet *= 2
            if streak == 3:
                streak = 0
                bet = start

    return money_history

money_goals = [10, 100, 500, 1000]

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

bet = 1
money_histories = simulate_different_goal_money(
                    betting_type = paroli_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:
10.883047707271885
For goal 10 mean money lost:
-11.0
For goal 100 mean money won:
100.81865284974093
For goal 100 mean money lost:
-11.0
For goal 500 mean money won:
0
For goal 500 mean money lost:
-11.0
For goal 1000 mean money won:
0
For goal 1000 mean money lost:
-11.0

Analysis when the goal is to win 10 units#

UNITS = 10

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

../_images/083dd69b31697cfb2fe3863faf0749843402ff7f4016d9710bc8b0a393ac27b5.png

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/cdaf5b9fd9929b0c6dfb56a61098705021a51bed930e3885045dfd8435e093be.png

plot_money_histories(successful_histories, UNITS)

../_images/209406939c79b37fb0a43c84eb1257d34b3eea71151d22b1976347adcf1d1c03.png

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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}")

../_images/3e0a68569793a6b0a5b58de5ae06917582c647765c461c537e98a26aa814a71c.png

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/45b5144ee281cccff1a58c18486e16e43e887798319bd7508dd3c9e67c3e2c7d.png

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}")

../_images/6e45b101e6c7227a3bae84fac468b33b0d94e96c45b5eddc448cfef39f252c86.png

Analysis when the goal is to win 1000 units#

UNITS = 1000

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

../_images/e5bd2ef79a3c5f435fa221e24f7fc319ec81e679ec869df51653ca99b6b7944e.png

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 = paroli_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))

For goal 10 mean money won:
14.086405529953916
For goal 100 mean money won:
140.79963129392786
For goal 500 mean money won:
704.3913093459018
For goal 1000 mean money won:
1408.0831408775982

Analysis when the goal is to win 10 units#

UNITS = 10

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/6b55fc71833bfeea5ff91b80483c49696d648a94c5f7f998c0899874b811365f.png

mean_money_list, std_money_list = get_mean_and_std_of_histories(money_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title='Simulations mean and std')

../_images/9edcbc47d532a61807fd66e472ba636cb44e009ac8e8e68d4efb5924649e5d38.png

plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 100 units#

UNITS = 100

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/0f5b2aa32aadbb97ac68df5c2cebb93d4b8b1ec116ffb4823cad3a76fa6b45df.png

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/52dae0b0fc98d025abe37bc7955e604c3a498bee50e1924d15bd51b21d65a010.png

plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 500 units#

UNITS = 500

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/f76c00a3b298ccb4aab6743743ba3e263732b21fef8d00bf6bda19b92d30b90b.png

mean_money_list, std_money_list = get_mean_and_std_of_histories(money_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title='Simulations mean and std')

../_images/957ea9d1c35b36b953dbefa468162eaba9dcfb48919918fc59bf7c1e3f811b30.png

plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 1000 units#

UNITS = 1000

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/4e739af7c5fecac1232b134801cc2955341ceba60e0cf9d400879fc19ad586c2.png

mean_money_list, std_money_list = get_mean_and_std_of_histories(money_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title='Simulations mean and std')

../_images/c50c38434965f5f23f8f73630bc0b15dcac86b9a1c028a05a30954d0c1625a46.png

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 = paroli_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))

For goal 10 mean money won:
14.155121631940657
For goal 100 mean money won:
142.35922012852632
For goal 500 mean money won:
720.9731725860759
For goal 1000 mean money won:
1435.7942807437207

Analysis when the goal is to win 10 units#

UNITS = 10

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/d0bf1f62723b7e0f73b09b0b52bc22b547b5ea18c12127891a520fab3cd59bb8.png

mean_money_list, std_money_list = get_mean_and_std_of_histories(money_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title='Simulations mean and std')

../_images/5348f71aec53a8dd3ac6a26a30839d382ab2e06c836d4fbc1c7b0a14971fba08.png

plot_money_histories(successful_histories, UNITS)

../_images/0390dd5eeef21412b3eb3e8f8a32f2b15826dc40ccd57c9601786c6e8e726fcd.png

Analysis when the goal is to win 100 units#

UNITS = 100

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/ee09a8c0f81ddbb90d1305357996e12cde19203dd82e2261d0f54364577a6a9f.png

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/f957578ea546cfac0489dba353d31e3c8b86fe46b686851e4e93e1b03f934426.png

plot_money_histories(successful_histories, UNITS)

../_images/6017c57bbf732ebc543207b48b63b05eb5f6410239111ec8097c5f21f439aef5.png

Analysis when the goal is to win 500 units#

UNITS = 500

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/54e430b4ed98f5472249c4d294b7e00d3bc99e803ca74ed61bfcb0074c248c3f.png

mean_money_list, std_money_list = get_mean_and_std_of_histories(money_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title='Simulations mean and std')

../_images/a25341062d542bb0759d614af8627327a762d7960c43ea28076d5bff923be3d2.png

plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 1000 units#

UNITS = 1000

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/8330299e1a6d1b84bd7430f77488896c69952de91ef23dd65cdc86e196f1aa75.png

mean_money_list, std_money_list = get_mean_and_std_of_histories(money_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title='Simulations mean and std')

../_images/8c2336240935c1d93227d6c561e0ab4aa09500f9d1b307a2acdcfb4bff794be8.png

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 = paroli_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))

For goal 10 mean money won:
14.34000642329515
For goal 100 mean money won:
144.52640581569383
For goal 500 mean money won:
724.7149099435148
For goal 1000 mean money won:
1439.1494817822418

Analysis when the goal is to win 10 units#

UNITS = 10

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/9a05f0740dd0d3eb1679eb60df3726d57200d6db801457143b47fb06caba4101.png

mean_money_list, std_money_list = get_mean_and_std_of_histories(money_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title='Simulations mean and std')

../_images/7a51bfbc6b6d085eb3db60552529f551b71d99f6b56172078a616f6b9c5a9695.png

plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 100 units#

UNITS = 100

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/ba68f2099293968e8daa90b3af365a486bae594df4578aaf4ff0b776daa01255.png

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/e033f554f68b675c9a57a6bf09c640f77ddcda83e77c351ae495293be10a8d39.png

plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 500 units#

UNITS = 500

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/8d80c533bce0acd6136742592b2512d37daa50f519dc581baca28dc8322f1200.png

mean_money_list, std_money_list = get_mean_and_std_of_histories(money_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title='Simulations mean and std')

../_images/58c052615f87481775b0fd0229ea954ac3db9fe05b9b91bebcc10b57d41f458e.png

plot_money_histories(successful_histories, UNITS)

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Analysis when the goal is to win 1000 units#

UNITS = 1000

len(successful_histories[UNITS])

plot_successful_bets(money_histories[UNITS], UNITS)

../_images/18d2d78585b5edc04d2cc8e6df81a02fa3f804c30945cce77ff777723d97bc5b.png

mean_money_list, std_money_list = get_mean_and_std_of_histories(money_histories, UNITS)
plot_money_history(mean_money_list, std_dev=std_money_list, title='Simulations mean and std')

../_images/9b6fe4148ea33e68c7bcc295c9a9012fedccacddfca283b199688daad1f1aac0.png

plot_money_histories(successful_histories, UNITS)

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Paroli simulation

Contents

Paroli 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#