Roulette Odds - Mathematics
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Let's look a little into the not so complicated mathematics of roulette, and
talk about the expected outcome for the bets you like to place. To begin with
let's look at the classic equation that defines the house edge for American
roulette. The house edge for all bets except the five number bet on American
roulette is 5.26%.
Picture a $1 bet on an individual number. The probability of hitting that
particular number is 1 in 38, or 37 to 1. Of course the casinos only pay you 35
to 1, robbing you a bit of what's rightfully yours. With this shortfall, you
know that in 38 spins you will lose $2. Two dollars just happens to be 5.26% of
the $38 you put into those spins.
The mathematical formula for expectation reads as follows:
Expectancy = [probability of a winning outcome X the amount you would win] +
[probability of a losing outcome X the amount you would lose]
Which kind of makes sense. What you would expect to win on the bet, combined
with what you would expect to lose, should tell you what you're expected outcome
For the single dollar bet in roulette mentioned above:
E = [1/38 x 35] + [37/38 x (-1)] = 0.921 + (-0.97368) = -0.0526 = -5.26%
The negative simply shows you that you are expected to walk away down, as
expectation is calculated as 'player expectation'. Reversing this to a positive
gives you the 'casino expectation' or house edge. So now you can see where the
house edge in American roulette comes from, and how it weighs in at 5.26%.
You'll find that the roulette odds behind every single bet on the table work out
to the same incontrovertible house edge, with the exception of the five number
bet, which doesn't pay it's odds back as well as the other bets on the table,
and works out to an even worse house edge of 7.89%.
The sad thing about American roulette is that this house edge is
unalterable. Each and every bet, and every combination of bets, and every way
you can think to hedge your bets, all work out to a 5.26% house edge. That's why
your strategy should include a host of ways to play games that are a slightly
altered form of American roulette, and seek out rules that are beneficial.
Roulette odds, as unalterable as they are, provide a sense of stability to the
game. Hey, at least we know the casino isn't ripping us off with some trickery
we don't understand!
Roulette Betting Odds:
You can place the following Roulette bets, and receive payouts in accordance:
Bet on a single number for a 35:1 payout.
Bet on 2 adjacent numbers for a 17:1 payout.
Bet on 3 numbers in a horizontal line for a 11:1 payout.
Bet on a block of 4 numbers for a 8:1 payout.
Bet on 6 numbers in 2 adjacent rows for a 5:1 payout.
Bet on 1 of 3 vertical columns for a 2:1 payout.
Bet on 12 numbers, low (1-12), middle (13 - 24) or high (25 - 36) for a 2:1
Bet on even or odd, red or black, low (1 - 18) or high (19-36) pays 1:1.
Place any number of bets on each spin of the Roulette wheel up to the Roulette
In some casinos, the "en prison" rule applies to even money bets in
Roulette. This means that you lose half your bet, when the ball hits a zero or
double zero. Alternatively, if you let the bet stay in play, the results are
according to the next spin.
In American roulette, the house has a 5.26% edge (when 0 or 00 is hit, all bets
There is no (mathematically proved) system that can "beat the casino".
The game of roulette is a game of chance, and mathematics won't help you in this
situation. Don't believe people who state that they can break the law of
probability using some system "tested over 10 years".
All we can do is to calculate the probability for every bet, which doesn't
even reach 50/50 because of the zeros. Refer to roulette odds if you want to
know what determines the house edge.
The only system which allows to make money playing roulette was invented in
19th century by casino owners. It's quite simple - if you want to make money in
the long run - start your own casino.
So, don't take roulette systems seriously. Systems are for the blackjack and
video poker, where intelligent gambler can get a slight edge over casino. But
roulette is a game of chance, play for fun.
So, if we deny any system, what do we suggest for a roulette strategy?
In the games of chance your chance to win depends on your luck and common
sense. Intelligent gambler always tries to chose rules that give him the better
The best strategy in the game of roulette is to know the aspects of a game
that can give your better odds, and aspects that increase the casino edge. So,
the first thing we can do is to play in casinos that offer better rules.