Calculate the roulette odds, probabilities, payouts, number of spins for the player to be ahead and quit, leave the casino table as a winner. Probability, Odds to Win at Roulette in N Number of Spins To Be Ahead and Leave the Casino as a Winner By Ion Saliu, Founder of Roulette Mathematics.
- Odds On Roulette
- Best Odds At Winning Roulette
- Best Odds In Roulette
- Roulette Bets And Odds
- Best Odds Roulette Strategy
The roulette odds of you winning a single number bet are much lower than the odds of winning a bet on the red, as you are covering much less of the table. That much is obvious. We can also talk about your overall roulette odds- more commonly referred to as the payout. This will depend on the house edge. The odds of you winning by betting on any number in roulette are 37 to 1, since there are 37 numbers on the typical roulette wheel. However, the house will only reward you with 35 to 1 if you do get lucky and pick the right number.
Having explained the basic terms and the variations of the game, we move forward to discuss the mathematical side of roulette. Although some of you may ignore this topic, we should underscore that knowledge of such concepts as probability and odds is crucial before one digs deeper into the various strategic approaches to the game.
What do we mean by the term ”probability”?
If we are to offer a formal definition of the term ”probability”, it may sound as follows: ”The probability of the occurrence of an event is defined as the number of cases favorable to the event, divided by the number of equally-likely possible cases.”
In case we presume that all possible outcomes have an equal chance to occur, as they are a result of a random device (the roulette wheel), and for every single outcome there are only two possible scenarios (a success or a loss), the definition pinpointed above may be transformed into the following: ”The probability of winning equals the number of ways to win, divided by the number of possible outcomes.”
The number of possible outcomes includes the possible ways to win and the possible ways to lose. Having said this, the probability of success may be presented with a simple formula:
PROBABILITY OF SUCCESS = Ways to Win / Ways to Win + Ways to Lose
Probability always belongs within the range between 0 and 1 and can be expressed as a fraction or a decimal. If one is to present probability as a percentage, then the decimal needs to be multiplied by 100.
Let us take the simple example, when tossing a coin. As the coin is two-sided, it has one way to win and one way to lose. Therefore, in this case the probability of success will be as follows:
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PROBABILITY OF SUCCESS = 1 / 1 + 1 = 1 / 2 = 0.5, or 50%
An expert in statistics would interpret the probability of success when tossing a well-balanced coin as one half. An expert in gambling, however, would interpret it as 1 chance out of 2. We would interpret it as 50 percent.
Let us have another example – the tossing of an ordinary six-sided die. As there is one way to win and five ways to lose, the probability of success (rolling a specific number) will be as follows:
PROBABILITY OF SUCCESS = 1 / 1 + 5 = 1 / 6 = 0.1667, or 16.67%
The expert in statistics would now interpret the probability of rolling the particular number as one sixth, while the expert in gambling would say it is 1 chance out of 6. We would interpret it as 16.67 percent.
If we take the French roulette wheel, having 37 numbers, and we place a straight-up bet, then we have 1 way to win and 36 ways to lose. Therefore, the probability of success (the number we selected to win) will be as follows:
Classic Roulette Bets
French Roulette
Double Ball Roulette
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Probability and Odds in Roulette
PROBABILITY OF SUCCESS = 1 / 1 + 36 = 1 / 37 = 0.0270, or 2.70%
If we take the French wheel again and place a street bet on a row of three numbers, then we have 3 ways to win and 34 ways to lose. Thus, the probability of success (one of the three numbers to win) will be as follows:
PROBABILITY OF SUCCESS = 3 / 3 + 34 = 3 / 37 = 0.0810, or 8.10%
And lastly, if we place a dozens bet on the French wheel, then we have 12 ways to win and 25 ways to lose.
PROBABILITY OF SUCCESS = 12 / 12 + 25 = 12 / 37 = 0.3243, or 32.43%
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| Bet | Payout | Probability(American) | Probability(European) |
|---|---|---|---|
| Straight Up | 35 to 1 | 2.63% | 2.7% |
| Split | 17 to 1 | 5.26% | 5.41% |
| Street | 11 to 1 | 7.89% | 8.1% |
| Corner | 8 to 1 | 10.53% | 10.81% |
| Line | 5 to 1 | 15.79% | 16.22% |
| Dozens | 2 to 1 | 31.58% | 32.43% |
| Columns | 2 to 1 | 31.58% | 32.43% |
| Red/Black | 1 to 1 | 47.37% | 48.65% |
| Even/Odd | 1 to 1 | 47.37% | 48.65% |
| Low/High | 1 to 1 | 47.37% | 48.65% |
What do we mean by the term ”odds”?
The majority of players at a casino will use the term ”odds” instead of ”probability”. There is a certain difference between odds and probability and it lies in the way the two terms are mathematically expressed. Once we have calculated the probability of success, we can easily estimate the odds for success by using the following formula:
ODDS FOR SUCCESS = Ps / 1 – Ps, where
Ps equals the probability of success.
If we go back to the coin tossing example, then we will get the following result:
ODDS FOR SUCCESS = 0.5 / 1 – 0.5 = 0.5 / 0.5 = 1 / 1
Odds are usually not transformed into a decimal, but are rather presented as a ratio of whole numbers. In the case above we simply multiplied the numerator and denominator by 2, so that we come up with the result we wanted. Odds are presented as 1:1 and pronounced as ”one-to-one”, or ”even odds”.
We should note that there is another way to calculate the odds for success. There is no need to estimate the probability first and then the odds. We can get straight to the desired result by using the following simple formula:
ODDS FOR SUCCESS = Ways to Win / Ways to Lose
If we go back to the die tossing example and use the above mentioned formula, we will get:
Mississippi state tax on gambling winnings. ODDS FOR SUCCESS = 1 / 5, or
the odds are 1:5 (one chance to be successful and five chances to lose). This is different from the probability of success, which, as we estimated, is 1 chance out of 6. And it is what causes confusion.
| Bets | Payout | Probability |
|---|---|---|
| Even | 1:1 | 48.6% |
| Odd | 1:1 | 48.6% |
| Black | 1:1 | 48.6% |
| Red | 1:1 | 48.6% |
| 1-18 | 1:1 | 48.6% |
| 19-36 | 1:1 | 48.6% |
| 1-12 | 2:1 | 32.4% |
| 13-24 | 2:1 | 32.4% |
| 25-36 | 2:1 | 32.4% |
| Single Number | 35:1 | 2.7% |
| Combination of two numbers | 17:1 | 5.4% |
| Combo of three numbers | 11:1 | 8.1% |
| Combo of four numbers | 8:1 | 10.8% |
| Combo of six numbers | 5:1 | 16.2% |
People may end up confused, also when the odds are presented in reverse. If the odds for success are 1:5, then the odds against success are 5:1. It is so, because we have the following formula:
Best Odds At Winning Roulette
ODDS AGAINST SUCCESS = Ways to Lose / Ways to Win
If the two above mentioned odds are closer to even, it becomes a more delicate situation. If we have odds for success of 5:6, then the odds against success will be 6:5. An experienced player will surely see the difference, while the beginner may easily be misled.
House odds (odds paid) represent the opposite of odds for success. This explains why the lower the chance of success is, the higher the payout is. As the house is playing against the player, the odds paid equal the odds against success, if, of course, we presume that the casino does not take a share. The reality is that house odds are always set a bit lower than the odds against success, which provides casinos with a profit margin.
Best Odds In Roulette
Let us get back to the examples concerning the French roulette wheel. How to play crapps. If we place a straight-up bet, we have one way to win and 36 ways to lose.
ODDS FOR SUCCESS = Ways to Win / Ways to Lose = 1 / 36 https://tankgol.netlify.app/slot-machine-mask-hero-trucchi.html.
Or, the odds for success are 1:36 and the odds against success are 36:1. If we indeed emerge successful with our bet, the casino will pay us 35:1, not 36:1. The obvious difference represents the house advantage (a 1-unit profit).
If we are to place an even-money outside bet (black), we have 18 ways to win and 19 ways to lose (18 red numbers and one green single zero).
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Roulette Bets And Odds
ODDS FOR SUCCESS = Ways to Win / Ways to Lose = 18 / 19
Best Odds Roulette Strategy
Or, the odds for success are 18 to 19 and the odds against success are 19 to 18. If we indeed win, the casino will pay us 18:18 and not 18:19. Again the casino will have one unit of profit.