I was reading an introduction to probability, and it discussed the game roulette.(adsbygoogle = window.adsbygoogle || []).push({});

The book recommended the strategy of always betting on a color or odd/even, which gives you 18/38 odds, and to double your bid after every loss. This way you will continue to gain--assuming that you had infinite money to gamble. :)

However, in real roulette there are two constraints on this: 1. there is a maximum bid limit. 2. you don't have unlimited funds.

Based on this, I was trying to figure out how to determine the:

1. Optimum amount of money a person should begin with to maximize his chances.

2. The best amount to wager per round (low amounts allows for longer losing strings, higher amount increases rate of growth).

3. What is the optimum amount of profit to shoot for before walking away. (Because the more you play, the greater your chance of seeing a loosing streak that you can't afford.)

I started the problem by assuming that I had about 1000 units to bet, so that I could double it 10 times. I calculated (perhaps incorrectly) that the chance of wining at least once in 10 rolls (ensuring that a profit, assuming that you start over after each win) is about 99.9%

But that also means that in order to double my money, betting 1 unit a round, will take over 1000 rounds, which makes a 10 losing streak a significant chance (I think).

How would I figure out the best balance of betting amount and the amount of profit that is optimal to call it quits, before the chances of a long losing streak becomes significant?

(By the way, I'm not planning to really gamble or anything, I was just intrigued by the problem. I also have nothing beyond high school level mathematics training, although I was good at math.)

To start with a simple example: Someone has $1,000 to bet. He can bet in denominations of 1, 5, 25, or 100. The maximum bid amount is 500. What is the biggest profit (largest winning string) that he can expect to see before seeing a losing string too long. And what denomination would he use to bid. Again, this is assuming that he doubles his bid after every loss.

You could also simplify further, by assuming an even probability of 50/50 like a coin toss.

I tried looking for equations for some of this, but got stuck and didn't understand the math.

Thanks

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# Probability and Roulette

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