why casinos have maximum (and strategically relative minimum) bets (you would need a pretty hefty bankroll for this even if you start with a $5 base bet)

roulette.cs

using System;

namespace Roulette
{
    class Program
    {
        static void Main(string[] args)
        {
            var r = new Random();
            double highestCumulativeLossPointOfAnySimulation = 0;
            double totalCumulativeProfit = 0;
            int highestConsecutiveLossesInAllSimulations = 0;

            for (int i = 0; i < 1000; i++)
            {
                // if you have billions of dollars you can maybe set n a little higher
                // n must be >= 1
                double n = 1.1;

                int maxIterations = 1000;
                double currentProfit = 0;
                double baseBet = 10;
                double highestBet = baseBet;
                double probabilityPercentOfWin = 16.0 / 38.0 * 100;
                //double probabilityPercentOfLoss = 1 - (probabilityPercentOfWin/100);
                double highestCumulativeLossPoint = currentProfit;
                // same as the odds you would get this far without losing if you don't play
                // essentially showing in simple mathematical terms that "you gotta pay to play"
                int mostConsecutiveLossesInCurrentSimulation = 0;

                for (int j = 0; j < maxIterations; j++)
                {
                    // reset
                    bool won = false;
                    double currentBet = baseBet;
                    int consecutiveLosses = 0;

                    while (!won)
                    {
                        if (currentBet > highestBet)
                        {
                            highestBet = currentBet;
                        }

                        currentProfit -= currentBet;

                        if (currentProfit < highestCumulativeLossPoint)
                        {
                            highestCumulativeLossPoint = currentProfit;

                            if (highestCumulativeLossPoint < highestCumulativeLossPointOfAnySimulation)
                            {
                                highestCumulativeLossPointOfAnySimulation = highestCumulativeLossPoint;
                            }
                        }

                        double outcome = r.Next(0, 100);
                        outcome += (Convert.ToDouble(r.Next(0, 1000000)) / 1000000);

                        if (outcome <= probabilityPercentOfWin)
                        {
                            currentProfit += 2 * currentBet;
                            totalCumulativeProfit += currentProfit;
                            won = true;
                        }
                        else
                        {
                            consecutiveLosses++;
                            if (consecutiveLosses > mostConsecutiveLossesInCurrentSimulation)
                            {
                                mostConsecutiveLossesInCurrentSimulation =  consecutiveLosses;
                            }

                            currentBet = currentBet + n * currentBet;
                        }
                    }
                }

                if (mostConsecutiveLossesInCurrentSimulation > highestConsecutiveLossesInAllSimulations)
                {
                    highestConsecutiveLossesInAllSimulations = mostConsecutiveLossesInCurrentSimulation;
                }

                Console.WriteLine("Simulation #{0}", i);
                Console.WriteLine("______________________________");
                Console.WriteLine("Total profit: {0}", currentProfit.ToString("C"));
                Console.WriteLine("Highest bet: {0}", highestBet.ToString("C"));
                Console.WriteLine("Highest cumulative loss (total amount of money you would need to \"beat the system\"): {0}", highestCumulativeLossPoint.ToString("C"));
                Console.WriteLine( "Most consecutive losses (assume you keep betting black, but only red or green come up consecutively): {0}", mostConsecutiveLossesInCurrentSimulation );
                Console.WriteLine(String.Empty);
            }

            Console.WriteLine("Highest cumulative loss in all the simulations that were run: {0}", highestCumulativeLossPointOfAnySimulation.ToString("C"));
            Console.WriteLine("Total cumulative profit: {0}", totalCumulativeProfit.ToString("C"));
            Console.WriteLine("Highest consecutive losses in all simulations: {0}", highestConsecutiveLossesInAllSimulations);

            Console.ReadKey();
        }

        /*

        Result of 20 simulations at n = 1.1 (note that the highest bet 
        is just shown to illustrate the kind of risk you're dealing with),
        but either way the point is that each of the below simulations
        result in a profit granted the volatility suggests if you have
        the bankroll to stomach the risk you probably don't need to take the risk
        
        In a thousand simulations, the highest cumulative loss got up to $1,032,974,407.67
        That said, the total cumulative profit was $172,400,244,529.76
        ... but if you have the money to fund those kinds of losses, Bernoulli's Marginal
        Utility comes into play: http://en.wikipedia.org/wiki/Marginal_utility

        Simulation #0
        ______________________________
        Total profit: $154,551.00
        Highest bet: $1,430,568.69
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($2,721,654.21)

        Simulation #1
        ______________________________
        Total profit: $21,526.50
        Highest bet: $16,679.88
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($14,634.25)

        Simulation #2
        ______________________________
        Total profit: $87,237.33
        Highest bet: $681,223.19
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($1,289,454.15)

        Simulation #3
        ______________________________
        Total profit: $41,405.91
        Highest bet: $154,472.38
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($275,364.42)

        Simulation #4
        ______________________________
        Total profit: $35,295.87
        Highest bet: $35,027.75
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($55,094.02)

        Simulation #5
        ______________________________
        Total profit: $44,652.44
        Highest bet: $154,472.38
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($285,481.48)

        Simulation #6
        ______________________________
        Total profit: $25,132.10
        Highest bet: $35,027.75
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($59,000.10)

        Simulation #7
        ______________________________
        Total profit: $24,764.42
        Highest bet: $35,027.75
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($58,111.16)

        Simulation #8
        ______________________________
        Total profit: $41,576.30
        Highest bet: $154,472.38
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($287,352.82)

        Simulation #9
        ______________________________
        Total profit: $78,780.55
        Highest bet: $324,391.99
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($618,858.16)

        Simulation #10
        ______________________________
        Total profit: $33,159.77
        Highest bet: $73,558.28
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($117,927.22)

        Simulation #11
        ______________________________
        Total profit: $33,356.50
        Highest bet: $35,027.75
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($47,784.42)

        Simulation #12
        ______________________________
        Total profit: $43,539.77
        Highest bet: $73,558.28
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($123,657.28)

        Simulation #13
        ______________________________
        Total profit: $45,424.23
        Highest bet: $154,472.38
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($284,748.21)

        Simulation #14
        ______________________________
        Total profit: $38,620.49
        Highest bet: $154,472.38
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($291,360.24)

        Simulation #15
        ______________________________
        Total profit: $169,231.62
        Highest bet: $1,430,568.69
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($2,706,170.98)

        Simulation #16
        ______________________________
        Total profit: $28,443.49
        Highest bet: $73,558.28
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($135,534.03)

        Simulation #17
        ______________________________
        Total profit: $69,819.12
        Highest bet: $324,391.99
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($586,217.03)

        Simulation #18
        ______________________________
        Total profit: $24,632.33
        Highest bet: $16,679.88
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($29,136.90)

        Simulation #19
        ______________________________
        Total profit: $48,867.44
        Highest bet: $154,472.38
        Highest cumulative loss (total amount of money you would need to "beat the system"): ($294,835.50)


        */
    }
}