Probabilities in Roulette Gambling

Roulette is one of the world’s most beloved casino games, enjoyed in casinos all around the globe. This thrilling game involves a spinning wheel with numbered slots and a small ball that spins around it – players betting on where they believe the ball will land, with payouts determined by odds for that particular bet. In this article, we’ll take a closer look at roulette gambling probabilities through examples and mathematical formulas.

Roulette Wheel and Betting Options

Are you looking to bet on roulette? Look no further – here is all the information you need!

The roulette wheel consists of 38 slots, numbered from 1 to 36, plus an additional 0 (European Roulette) and 00 slot (American Roulette). These numbers are colored green while all other numbers alternate between red and black. As the wheel spins in one direction, a small ball is spun around its outer edge in an opposite direction until it comes to rest in one of the numbered slots and determines who wins.

roulette table

Roulette offers two primary forms of bets: inside bets and outside bets. Inside bets involve specific numbers or combinations on the roulette table, while outside bets involve larger groups or characteristics of numbers like odd/even or red/black.

Inside Bets

  • Straight Up Bet – A wager on one number pays out at 35 to 1 odds.
  • Split Bet – Bets on two numbers will payout at 17 to 1 odds.
  • Street Bet – A bet on three numbers pays out at 11 to 1 odds.
  • Corner Bet – Bets on four numbers pay out at 8 to 1 odds.
  • Five Bet – Bet on the numbers 0, 00, 1, and 3 at 6 to 1 odds.
  • Six Line Bet – A bet on six numbers pays out at 5 to 1 odds.

Outside Bets

  • Red/Black – Bet on the color of the winning number pays out at odds of 1 to 1.
  • Odd/Even – Bet on whether the winning number will be odd or even and win at odds of one to one.
  • High/Low – Bets placed on whether the winning number will fall between 1-18 or 19-36 pay out at odds of one to one.

Probabilities in Roulette

To calculate the probabilities in roulette gambling, we can use mathematical formulas. The probability of a specific outcome is calculated by dividing the number of ways that outcome can occur by the total number of possible outcomes.

For instance, the probability of a straight up bet (a bet on one number) winning is calculated by dividing 1 (the number of ways this outcome can occur) by 38 (the total number of possible outcomes). This gives us an odds ratio of 0.026 or approximately 2.6%.

Similar to an inside bet (such as red/black), the probability of it winning is calculated by dividing the number of possible outcomes by 2. For instance, 18/38 gives us a probability of 0.473 or 47.3% for this scenario: there are 18 red slots and 18 black slots out of 38 total slots – giving us 18/38.

Expected Value

The expected value (EV) of a bet is the amount that we can expect to win or lose over the long term. It is calculated by multiplying the probability of winning by the potential payout and subtracting the probability of losing multiplied by the wagered. The expected value increases when more players join in.

Take, for instance, a straight up bet on the number 7 which pays out at 35 to 1 odds. The probability of winning this bet is 1/38, or approximately 0.026; consequently, its expected value can be calculated as follows:

EV = (Probability of Winning x Potential Payout) – (Probability of Losing x Amount Wagered)
EV = (0.026 x 35) – (0.974 x 1)
EV = 0.91 – 0.974
EV = -0.064

In the long run, we can expect to lose an average of $0.064 for every dollar wagered on this bet. This indicates a negative expected value, meaning the casino has the edge over players on this particular wager.

However, if we place an outside bet on red that pays out at 1 to 1 odds, the expected value would differ. In this instance, the probability of winning this bet is 18/38 – or approximately 0.473. Therefore, the expected value can be calculated as follows:

EV = (Probability of Winning x Potential Payout) – (Probability of Losing x Amount Wagered)
EV = (0.473 x 1) – (0.527 x 1)
EV = 0.473 – 0.527
EV = -0.054

On average, we can expect to lose approximately $0.054 for every dollar wagered on this bet over the long term. While this still represents a negative expected value, it is less severe than the one associated with straight up bets on single numbers.

Risk and Reward

It is essential to comprehend the relationship between risk and reward when placing bets in roulette gambling. Higher-risk bets, like straight up bets on one number, have a higher potential payout but a lower probability of success; lower-risk alternatives like outside bets on red/black or odd/even have lower potential payouts but higher chances for success.

When selecting the ideal betting strategy for each individual, we must take into account our risk tolerance and desired level of potential payout. Some players may prefer taking larger risks with the potential for larger rewards while others might opt for lower stakes but more frequent winnings.


Roulette gambling requires understanding the probabilities and potential payouts for different bets, as well as their expected values. By applying mathematical formulas, we can calculate these probabilities and expected values, enabling us to make informed decisions about which bets should be placed. It’s essential to remember that gambling always carries some risk, regardless if it done at the local casino or any online casinos; there is no guaranteed strategy for success; however, by understanding probabilities and making educated guesses, our chances for making profitable wagers in roulette gambling increases considerably.

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