Here we'll talk about the odds of winning each time that rulette wheel is spun and you have put a bet down. As always with any casino game, the house has an edge. In rulette, that edge is 5.26% or so, with slightly worse odds if one were to play a 5 number bet. At online casinos such as Casino King, your odds are improved slightly by the fact that you are given cash bonuses while playing.
When you read the different types of bets, you probably wondered to yourself: if there are 38 numbers on the roulete wheel, how come the payoff is only 35 to 1 if I bet on one number and it lands on the rulette wheel? This is called the house edge, and this is how casinos make their money. So if you bet $100 on every spin, mathematically speaking you will be losing $200 for every 38 spins of the wheel. This is how the casinos make money and stay in business.
It is a funny game though; people know that the house has an edge going in, but still, people win all the time. Most people are drawn to the simplicity of the game; sure, a great blackjack player might have an edge on the house, but it takes quite a bit of knowledge to become proficient in blackjack. In roulete, you can just walk up and place a bet on red . nothing too difficult about that. Sure, there are ways to hedge yourself in roulete and come up with different strategies, but most people are drawn to rulette for the simple rules and social aspect of the game.
Let's assume the American roulete rules, so we have 38 numbered wheel (1-36, 0, 00) and 11 possible bets. We can bet on a number, a group of numbers, or a color which we hope will be a winning choice.
The outcome of every spin is independent, that is not determined by prior spins. Even if you have ten black numbers after ten spins, the chance of getting red in the next spin is the same as to get black.
The probability of hitting the single number is 1 in 38, or 37 to 1. In other words, if you bet $1 chip on this number 38 times you will win only once. The payoff for this bet is 35:1. So, the dealer will give you $35 and you also keep the dollar you bet. In total, after 38 spins you will lose two dollars that is 5.26% of 38 wagered dollars. So, the house edge on the single bet is 5.26%.
The house edges on all possible bets for American roulette are in the table below, it details expected gains and losses per 38 games for $1 bet. Each number has a probability of 1/38 of being a winner.
With one exception, the casino edge is 5.26%. It is the five-number bet, where the casino has an edge of 7.89%.
We can, of course, calculate it in another way. The mathematical formula for expectation:
Expectation = [Number of the favorable results / Total number of the possible results] X The payoff for the favorable result + [Number of the unfavorable results / Total number of the possible results] X The bet
So, if you wager $1, your expectation, in terms of dollars, is:
Straight up (one number bet) = (1/38) x 35 + (37/38) x (-1) = -2/38 = -0.0526 or (-5.26%)
Five numbers = (5/38) x 6 + (33/38) x (-1) = -3/38 = -0.0789 or (-7.89%)
Red bet (18 numbers) = (18/38) x 1 + (20/38) x (-1) = -2/38 = -0.0526 or (-5.26%)
The results above are negative because we calculated the "player expectation". Revers these to positive and you will get the "casino expectation" or "house edge".
What does the expectation (house edge mean)? For every wagered dollar (we can say "invested" by the player) the casino expects to get at least 5.26%. And it's no wonder that casinos want their dealers to play as many games as possible during a specific time period.