# How to win Roulette every time?

Whenever someone tells you, that you can not beat roulette, because it is a negative expectation game or because of the house edge, please point him to this page.

### The concept of house advantage

The main idea behind the house advantage (or house edge or player dis-advantage or average expectation – they all refer to the same thing) is that the casinos need to make money. Therefore every casino game has a specific house advantage, depending on the type of the game (roulette, blackjack, craps, Texas Holdem etc.). Theoretically, the house advantage is the amount of money the casino is making for itself, while the rest of the money is given back to the players by paying out their wins. Another way to describe the house edge is that from all the bets that take place on a roulette table, the casino will pay-out to the players all the money played minus a small percentage, that percentage is called House Edge.

### Roulette house edge explained

Let’s be more specific. As you know roulette has, on the table layout and on the actual roulette wheel, the 37 numbers from 0 to 36.[*] Of these 37 numbers the 36 (1-36) are colored black or red and the Zero is colored green. The Green zero symbolizes the house edge. And I say “it symbolizes” and not “it is” the house edge, because if we want we can freely bet on zero and get a profit from it. But the point is that although the roulette wheel and table have 37 numbers and 37 discrete possible outcomes, we are paid as if it had only 36. This means that our payout in case of win is 1/37 = 2, 7% lower than it should.

When you bet on RED even chance, it is actually not exactly an even chance, since on the wheel there are 18 red numbers, 18 black numbers and 1 zero. So you have 18/37 = 48, 7% chance of winning (and not 50%), therefore your payout should have been (37-18)/18= 19/18= 102, 7% of your bet. But you are paid only 100% of your bet.

When you bet a single number, your chance of winning is 1/37 = 2, 7% and your payout should have been (37-1)/1=36= 360% or 36 times your bet. But you are paid only 350% or 35 times your bet. This is a 2, 7% difference of the ideal payout.

There is no doubt: although the roulette wheel has 37 numbers, casinos pay us as if roulette only had 36 numbers and this means they pay us 2, 7% less than it is “fair”. This “unfair” 2, 7% goes to the casino, to pay their bills and this is the so called the House Edge or House Advantage.

### The (bad) mathematician speaks: average expectation

The mathematicians take the concept of the house edge to a whole new level and they conclude that it is impossible to win at roulette in the long run. Their reasoning is as follows:

No matter what is your roulette strategy, the house advantage can not be negated. It is always there no matter what combination of bets you choose. Let’s say for example that you bet \$5 on zero (0) and \$20 on two dozens. This is 68% probability of winning. But let’s calculate the risk/reward relation. You have 1/37 chance of winning \$135 (for the zero), 24/37 chance of winning \$15 (for the 2 dozens), and 12/37 chance of losing \$45 (for the third dozen). The overall expected return (or expected value) is:

((1/37)*135 + (24/37)*15 – (12/37)*45)) /45 = -2.7%

Then they go a bit further and they say, arbitrarily again, that since every bet on the roulette table has a negative average value (-2, 7%), then in the end (in the long run), one will inevitably lose an amount of money, on the average, equal to 2, 7% of all his life bets. They call that average expectation.

Their verdict: You can not win at roulette, because it is a negative expectation game.
Now let’s see why they are wrong. Why this is too much narrow-minded mathematics and too little real life.

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