# Strategy for beating roulette using simple probability

1. Aug 18, 2011

### cardicorona

I think that I have figured out a way to beat the game of roulette with simple probability and a very useful equality...

The bet is either red, black, odd, even, low, or high.

Each of these bets have a probability of 18/38 and the payout is double the bet.

The strategy is to increase the bet such that the payout is more than the additive losses and then after each win cycle back to the first bet.

For instance: first bet is a dollar, second bet is 2 dollars, third bet is 4 dollars, fourth bet is 8 dollars. In mathematical terms, we have

[tex]\sum_{0}^{n}2^{n}=2^{n+1}-1[\tex]

This way, with each winning, bet the gain is more than the loss.

Now, say you lose 4 times in a row betting red, the fifth bet will be 32 dollars probability that you will win the fifth time is already

1-(18/38)^5-2/38=.923

In which the 2/38 represents the 0 and double 0 squares.

Once you win then you start back with bidding a dollar.

Granted this particular choice in cycle would take a long amount of time to earn money since the net gain is only a dollar. But there are obviously an infinite amount of other choices in which the net is larger.

The fall back is that long losing streaks would amount to ridiculously large sums of money with 2^20 being just over a million dollars.

Thoughts?

2. Aug 18, 2011

### obafgkmrns

The strategy you describe is called a "martingale." You'll eventually go broke unless you start with an infinite amount of cash, in which case you probably wouldn't be bothering with roulette to begin with.

3. Aug 18, 2011

### skeptic2

The amount of cash you start with determines how many consecutive losses you can sustain without going broke. Once you know how many consecutive losses you can survive, you can calculate the odds of that happening. I think you will find that you will win remarkably little money compared to the amount you start with before you go broke.

4. Aug 21, 2011

### mrspeedybob

There is one ridiculously simple way to win at roulette, be the house. 0 and 00 give you a real mathematical advantage. As far as I am aware that is the only way.