Odds Probability Calculator

Probability of Winning Formula (A:B)

To convert odds to probability, use the plain-text formula:

PWin = A / (A + B)

Where:

• A = chances for winning
• B = chances against winning

This gives you the probability of winning as a decimal or percentage.

Probability of Losing Formula (A:B)

The probability of losing is simply:

PLose = B / (A + B)

These two formulas always add up to 1 (or 100%) because an event must either happen or not.

Example: How to Read and Convert Odds

Understanding how to read odds correctly is essential, especially in wagering or games of chance.

If you see odds of 9/2, that typically means “9 to 2 against winning.” To find the true chance of winning:

PWin = 2 / (9 + 2) = 2/11 = 0.1818 = 18.18%

PLose = 9 / (9 + 2) = 9/11 = 0.8182 = 81.82%

So, you have an 18.18% chance to win and an 81.82% chance to lose.

To see these results in action, you can also try the Odds Calculator on CalculatorCave.

Example: Lottery Odds Explained

Let’s say a lottery advertises a “1 in 500” chance of winning. That means:

• 1 chance to win
• 499 chances to lose

In terms of odds for winning, A:B = 1:499

Then,
PWin = 1 / (1 + 499) = 1/500 = 0.002 = 0.2%
PLose = 499 / (1 + 499) = 499/500 = 0.998 = 99.8%

This shows a 0.2% probability of winning — quite small, but accurate.

Example: Pick 3 Lottery

A Pick 3 lottery has 1,000 total possible outcomes (000–999). The chance of winning with one bet is 1 out of 1,000.

A:B = 1:999

PWin = 1 / (1 + 999) = 1/1000 = 0.001 = 0.1%
PLose = 999 / (1 + 999) = 999/1000 = 0.999 = 99.9%

These probabilities make it easy to see how rare a win actually is.

You can simulate such odds-based games using the Coin Flipper Calculator — a simple tool that helps visualize random outcomes and probability in action.

Example: Drawing an Ace from a Deck

Suppose you pull a card from a full 52-card deck and win if it’s an Ace.
There are 4 Aces and 48 non-Aces, so:

A:B = 4:48

PWin = 4 / (4 + 48) = 4/52 = 0.0769 = 7.69%
PLose = 48 / (4 + 48) = 48/52 = 0.9231 = 92.31%

So, you have about a 7.69% chance of winning and a 92.31% chance of losing.

Simplified odds are:

• Odds for winning: 1:12
• Odds against winning: 12:1

Implied Odds vs. True Odds

It’s important to distinguish implied odds from true odds.

• True odds represent the actual mathematical probability of winning.
• Implied odds (often used in betting) include a profit margin for the house or bookmaker.

Example: Roulette

In roulette, there are 38 possible outcomes (numbers 1–36, plus 0 and 00). Betting on a single number pays 35 to 1.

That’s odds of 1:35, giving a payout-based probability of:
PWin = 1 / (1 + 35) = 1/36 = 0.02778 = 2.78%

But the true odds are:
PWin = 1 / (1 + 37) = 1/38 = 0.02632 = 2.63%

So, you are being paid based on 36 possible outcomes when there are really 38 — giving the house an advantage.

The difference (about 0.15%) is the house edge, meaning over time you’ll lose slightly more than you win.

Why Converting Odds to Probability Matters

Understanding how to convert odds to probability allows you to make informed decisions in gambling, investments, and everyday chance-based events. Whether it’s a coin toss, a random draw, or a stock prediction, knowing the true probability helps you see the bigger picture rather than relying on emotional guesses.

If you’re curious about random events, try exploring the Random Number Generator to simulate probabilistic outcomes and see how randomness behaves in practice.

Summary: Key Formulas for Odds and Probability

Odds to Probability Conversion:
PWin = A / (A + B)
PLose = B / (A + B)

Example Simplification:

• 1:999 odds → 0.1% chance of winning
• 4:48 odds → 7.69% chance of winning
• 1:35 odds → 2.78% chance of winning (implied), 2.63% (true)

Understanding these relationships ensures clarity in games, wagers, and statistical experiments.