I dont like it when there is something random like "GS" and it is not explained anywhere.

Awesome, you yould derive so much insight from this data. Heartrate charte definitly says a lot about how amazingly you orogressed!

I never really used GitHub but it seems that it would be a good investment to look at it if I want to do some more mini projects. Thanks!

Its not about finding out that you lose when playing roulette which is absolutely obvious... You also dont need any kind of formula to conclude that, you could just look at a P&L of a casino ;)

It was about approaching a problem from a different angle and have some fun with a simulation :)

Fortunately the code is easy adaptable, here are the numbers from the simulations (all for 5'000 bets):

Single zero: 74%

Double zero: 83%

Tripple zero: 90%

European table where you dont get your money back when hitting green.

I first thought exactly the same but keep in mind that 26% winning does not mean that its a quarter of the total "pool" of money that changed hands. In the simulation the sum of all winners equals 3'195'425 $ while the sum of all losers (profit for the casino) is 16'524'025 $ which is 5x larger (despite "only" 74% of total losers). This is because there are far more large losses than large gains.

First of all thanks for acknowledging the simulation!

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>My math friend says it doesn't matter but it's so unintuitive to me.

I try to give you an intuitive answer for this one. if I would ask you which of the following two options has a higher probability to roll a six:

(a) Roll ten dices at the same time.
(b) Roll one dice ten times.

It would be very obvious (I hope) that (a) and (b) are exactly the same because in the end you rolled ten dice and each outcome is independent of each other no matter if rolled all at once ore one by one. Now applied to our roulette scenario (a) would be betting multiple numbers on the table and (b) would be betting only one number at the time. So, it really doesn't matter how you approach that.

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>What I wanna see is how to maximize the chance for not playing like an idiot.

Well if you play to win than there is no hope because you cannot win as I am quite sure you already know. What we could do is minimize our expected loss by finding the least worst strategy (we can also call it the best but you are still not winning). I am no guru when it comes to roulette but you could easily simulate that e.g. if you want to know whats your expected chance of walking away by betting on red all the time over X amount of bets.

=> If you are interested in gambling strategies read about Martingale strategy which is quite interesting but spoiler: it doesn't work either. Here is an example: Hyperlink

If you cannot simulate it yourself I might be able to do so but you find my Python code in another comment I replied to.

I am not sure if there is any good way to do that other than paste it in here but here you go.

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FYI: I first had some serious ugly for loops to simulate it which was extremely slow so I coded it more efficiently as you can find below (probably it's a bit less intuitive though, I don't know).

######### Simulation #########

import random

import numpy as np

k = 50000000

returns = [-5 for i in range(0,36)]+[170]

return_arr = np.array(random.choices(returns, k = k)).reshape(int(k/5000),5000)

return_arr_sum = np.sum(return_arr, axis=1)

return_arr_cumsum = np.cumsum(return_arr,axis=1)

return_arr_aux = np.ones((10000,5000), dtype=int)*10000

return_path = return_arr_cumsum + return_arr_aux

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######### Chart #########

​

import matplotlib.pyplot as plt

from matplotlib.pyplot import figure

figure(figsize=(15, 7), dpi=100)

# plot 1

plt.subplot(1, 2, 1)

plt.plot(return_path.T, linewidth = 0.2)

plt.title("Roulette Simulation of " + str(5000) + " Bets \n Start = 10'000 \$, 5 $ per Bet \n ("+str(int(k/5000))+" Player Paths Simulated)")

plt.xlabel("# Bets", fontsize=12)

plt.ylabel("Total Money Left", fontsize=12)

# plot 2

plt.subplot(1, 2, 2)

pos = [i for i in [return_path[i][-1]-10000 for i in range(0,len(return_path))] if i>=0]

neg = [i for i in [return_path[i][-1]-10000 for i in range(0,len(return_path))] if i<0]

plt.hist(pos, bins = 100, orientation="horizontal", color="green")

plt.hist( neg, bins = 100, orientation="horizontal", color= "red")

plt.title("Distribution of Player Returns After " + str(5000)+ " Bets")

plt.xlabel("# People", fontsize=12)

plt.ylabel("\n Player Profit/Loss", fontsize=12)

plt.show()

Haha the joke is pure quality, I needed to make sure everybody understands that one. Thanks!

Well in this case I do not generate a number but I chose from a predetermined list (which I defined to match the actual probabilities of roulette). random.choices() choses per default uniformely.

I used 35x payout and a normal table.

I would have to look into the rules of this game but I am pretty sure I could do that. Let me know.

This is the standard form where I am from. I know its not that usual around the world, most of the time it's either a comma or a period.

Ah it should be # of people you're absolutely correct.

I was also surprised that almost 25% walked away with a profit. Always good to run a simulation to detect such counterintuitive things.

&#x200B;

FYI: I ran the simulation with 25'000 bets per person and there is still a probability of above 6% to walk away with a positive return.

There is a "Monte Carlo simulation" used to model stochastic processes but there is also a casino called Monte Carlo. The joke is perfect because Roulette is played in a casino and I modeled a stochastic process.

Ah I like that comment on so many levels haha Nice that sb knows the simulation and the casino ;)

Would be interesting to know, I am sure sb has already done that.

Thanks for pointing out, single numbers only.

Tool: The two charts were generated in Python using the Matplotlib library.

Source: Also generated in Python unsing the random.choices() function onto a hard coded list of the respective Roulette numbers.

Edit: The simulation was done under the assumption that all players use a single number betting strategy.