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Roulette Strategy

A roulette strategy is basically a smart way to go about playing the game. This page has a look at the expectancy of the game of roulette, that is, what defines the house edge and how it works. We also look a little bit about what variables other than systematic play might help to improve your odds in roulette.

The expectancy of a game is a number that defines how much you should expect to win or lose in the long run of bets. In the realm of gambling expectancy is often called the house edge, namely because it's rare if ever possible for the expectancy of a game to be a positive number. If that were the case the player would stand to win more than they lose in the long run, which wouldn't help the casino stay open for very long.

The mathematical formula for calculating expectancy is surprisingly intuitive. You take the money you could win on a bet multiplied by the odds of winning, and add that to the money you could lose on a bet multiplied by the odds of losing. In math, that looks like this:

Expectancy = [odds of winning X money won] + [odds of losing X money lost]

Now we'll plug some numbers into this equation. Say we're betting one dollar on an inside number on the roulette wheel.

Expectancy = [1/38 X 35] + [37/38 X -1]

Our odds of winning that bet are 1 in 38 on an American roulette wheel, and we would win 35 dollars if we did win. Our odds of losing that bet are 37 out of 38, and we will lose one dollar if we lose.

Expectancy = [1/38 X 35] + [37/38 X -1]
= [0.921] + [-0.9736]
= -0.526
This can be read as a 5.26% negative expectation for the player. Or you could simply say, the bet has a 5.26% house edge.

What makes it difficult to cultivate a good roulette strategy is the simplicity of this math. Say we were betting on two individual numbers on the table.

Expectancy = {[1/38 X 35] + [37/38 X -1]} and {[1/38 X 35] + [37/38 X -1]}
= -5.26% and -5.26%

What if we put $10 down on red, $10 down on the number 8, and $10 on the third column, what would the house edge be?

E = {[18/38 X $10] + [20/38 X -$10]} and {[1/38 X $350] + [37/38 X -$10]} and {[12/38 X $20] + [26/38 X -$10]}

E = [47.368 + (-52.631)] and [9.210 + (-9.7368)] and [6.3157 + (-6.8421)]
= -5.263 and -5.268 and -5.264

Combined, the house edge for these bets overall is, you guessed it, -5.26%. We can't escape it, and that makes it awfully difficult to say what we should bet on, or to define a roulette strategy based on the numbers.

So what do we have to do to improve our odds in roulette if it has a static house edge? In a game like blackjack that has a variable house edge, we can literally make different decisions as to hit or stand that we have calculated out to be better choices than another decision. But in roulette, there are no decisions to be made other than where to bet and what to bet on, and as we've already expressed with our math, it doesn't matter which bet you choose, and it doesn't matter which combination of bets you choose, each of the bets has the same house edge. We're left then, with determining a roulette strategy based on other variables.

For instance, if we set loss limits for ourselves and keep a strict bankroll (not allowing yourself to go back to the bank machine in a certain amount of time, even if you run out) then we can decrease the odds of losing all of our money, simply because we're taking less risk overall. Win limits are also a good idea, though not as intuitive. A good player knows that a winning streak cannot last forever, and when it ends, you're likely going to chase your winnings to try to get back up to your best point. The only way to combat this is to have a certain amount of money in your head, that if your bankroll reaches, you walk away. Sure you'll always be feeling as though you might have won a little more had you kept going, but knowing the odds of the game, the reality is that you've likely saved yourself from losing what you just won.
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