# Odds Probability Calculator

## Calculator Use

Convert odds into probability and percent chance of winning and losing. This calculator converts odds for winning or odds against winning into percentage chance for winning or losing. It also calculates the fractional odds.

### Probability of Winning Formula A:B

P_{Win} = A / (A + B)

Where A:B is odds for winning

### Probability of Losing Formula A:B

P_{Lose} = B / (A + B)

Where A:B is odds for winning

## How to Read Odds

It's important to understand how to read odds especially if wagering is involved. If you are using sports teams odds or betting odds and see the odds are 9/2, this is most likely odds against winning.

Enter 9 to 2 into the calculator and select "Odds against winning." It's also important to understand implied odds or betting odds which are not true statistical odds.

When playing a lottery or other games of chance be sure you understand the odds or probability that is reported by the game organizer. A 1 in 500 chance of winning, or probability of winning, may be reported as "1 in 500" or "1 out of 500." You may also see odds reported simply as chance of winning as 1:500.

These all most likely mean 1 chance of winning out of 500 total possible outcomes. Therefore, in terms of odds, this means "1 to 499 odds for winning" which is exactly the same as "499 to 1 odds for losing."

For example, a Pick 3 lottery has a total of 1000 possible outcomes, from 000 to 999. So a single bet, say 123, has a 1 in 1000 chance of winning. The chance of winning is 1 out of 1000, while the chance of losing is 999 out of 1000. Therefore, A:B = 1:999 and that is what you would enter into this calculator to find the probability.

P_{Win} = A / (A + B) = 1 / (1 + 999) = 1/1000 = 0.001 = 0.1%

P_{Lose} = B / (A + B) = 999 / (1 + 999) = 999/1000 = 0.999 = 99.9%

## Probability Formulas Explained

This calculator will convert "odds of winning" an event into a probability percentage chance of success.

Odds, are given as (chances for success) : (chances against success) or vice versa.

If odds are stated as an A to B chance of winning then the probability
**of winning** is given as P_{Win} = A / (A + B) while the probability
**of losing** is given as P_{Lose} = B / (A + B).

For example, you win a game if you pull an ace out of a full deck of 52 cards. Pulling any other card you lose. The chance of winning is 4 out of 52, while the chance against winning is 48 out of 52 (52 - 4 = 48). Entering A=4 and B=48 into the calculator as 4:48 odds are for winning you get

For **4 to 48 odds** for winning

Probability of:

Winning = (0.0769) or **7.6923%**

Losing = (0.9231) or **92.3077%**

"Odds for" winning:** 1/12 or 1:12 **(reduced from 4:48)

"Odds against" winning:** 12/1 or 12:1 ** (reduced from 48:4)

## Implied Odds vs. True Odds

Implied odds or betting odds are likely not the same as the true odds. Betting odds is a payout ratio that has the house profit margin built into it.

Take for example the game of roulette at a casino. The possible outcomes for a bet on a single number are the numbers 1 to 36 and 0 or 00 for a total of 38 possible outcomes. The payout odds for a bet on a single number is 35 to 1. This is odds of winning 1:35. This pays based on a probability of winning P_{Win} = A / (A + B) = 1 / (1 + 35) = 1/36 = 0.02778 or 2.778% (97.22% Losing).

The true odds of winning are based on 38 outcomes. P_{Win} = A / (A + B) = 1 / (1 + 37) = 1/38 = 0.02632 or 2.632% (97.37% Losing).

If you win, you get paid as if your chance of winning is 2.778% but, you really only have a chance of winning of 2.632%. This is a disadvantage for you. Putting it another way, you are being paid as if your chance of losing is only 97.22% but in reality, your chance of losing is 0.15% greater at 97.37%. You are not being compensated on the true odds because the house is taking a roughly 0.15% cut on every payout.

The probability over time, if you were paid true odds, is that you would break even. Since with implied odds or betting odds you win less often than the true odds, the probability over time is that you will always lose money.