- How To Calculate Roulette Odds Calculator
- How To Calculate Roulette Odds In Excel
- Wizard Of Odds Roulette
- Roulette Odds Calculator Excel
A roulette player who sees what the roulette odds calculator are showing will definitely have a greater advantage when playing a roulette game. Aside from knowing a strategy that one can use for playing, it is necessary to have at least the basic knowledge of playing the game.
Random chance plays an important role of every type of gambling game. Skill is the leverage (in terms of knowledge of the rules of the game) you apply to maximize your potential for winning andminimize your potential for losing. No casino gambling game is ever determined by skill alone.
We cannot measure random chance. And gamblers frequently mistake their knowledge of games’ probability tables for predictive knowledge. Probabilities do not predict anything. If you know the probabilities for the outcome of the next round in a casinogame, you can feel more confident about your next action. That is all the probabilities guarantee you.
The casino, on the other hand, uses the probabilities to determine the maximum risk itaccepts per round in a game. The casino represents those acceptable risks in terms of the odds they give per wager.
The mathematical probability of an event happening is 1 divided by the number of possible events. You add the probabilities for identical events together to compute unique probabilities. Butbecause random chance is used to determine game outcomes, the probabilities have no effect on what happens next. And the odds do not reflect the probabilities.
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:
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French 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.
How To Calculate Roulette Odds In Excel
PROBABILITY OF SUCCESS = 12 / 12 + 25 = 12 / 37 = 0.3243, or 32.43%
| 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:
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:
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.
Let us get back to the examples concerning the French roulette wheel. 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
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).
Wizard Of Odds Roulette
ODDS FOR SUCCESS = Ways to Win / Ways to Lose = 18 / 19
Roulette Odds Calculator Excel
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.