# How to find the odds in favor

Convert stated odds to a decimal value of probability and a percentage value of winning and losing. This calculator will convert "odds for winning" an event or "odds against winning" an event into percentage chances of both winning and losing.

Be careful if you are using sports teams odds or betting odds. If you see that the Patriots super bowl odds are 9/2, that is most likely "odds against" and should be entered in the calculator with "Odds are: against winning."

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, is entered into this calculator as "1 to 500 Odds are for winning". You may also see odds reported simply as chance of winning as 500:1. This most likely means "500 to 1 Odds are against winning" which is exactly the same as "1 to 500 Odds are for winning."

## Probability Formulas:

This calculator will convert "odds of winning" for 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 PW = A / (A + B) while the probability of losing is given as PL = 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 (reduced from 4:48)

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

Odds in Favor of an Event is the ratio of Number of Favorable Choices or Successes for the event to the Number of Unfavourable Choices or Failures for the event.

⇒ Odds in Favor of an Event

 = Number of Favorable Choices : Number of Unfavorable Choices Or Number of Successes : Number of Failures = m : mc Or = m : (n − m)

Odds against an Event is the ratio of Number of Unfavorable Choices or Failures for the event to the Number of Favorable Choices or Successes for the event.

⇒ Odds against an Event

 = Number of Unfavourable Choices : Number of Favorable Choices Or Number of Failures : Number of Successes = mc : m Or = (n − m) : m

Probabilities for and against the event can be used as the antecedent and consequent of the ratio representing the odds for an event in place of favorable and unfavorable choices.

Odds in Favor of an Event

 = Number of Favorable Choices : Number of Unfavorable Choices Or Number of Successes : Number of Failures = m : mc = : = : = P(Event) : P(Eventc) Or = m : (n − m) = : = : = P(Event) : P(Eventc)

⇒ Odds in Favor of an Event = P(Event) : P(Eventc)

Probabilities against and for the event can be used as the antecedent and consequent of the ratio representing the odds against an event in place of unfavorable and favorable choices.

## Odds against an Event

Odds against an Event

 = Number of Unfavourable Choices : Number of Favorable Choices Or Number of Failures : Number of Successes = mc : m = : = : = P(Eventc) : P(Event) Or = (n − m) : m = : = : = P(Eventc) : P(Event)

⇒ Odds against an Event = P(Eventc) : P(Event)

Let Odds in Favor of the Event be x : y.

For the ratio representing odds in favor

antecedent = x and consequent = y

Odds in Favor of an Event

 = Number of Favorable Choices : Number of Unfavorable Choices Or Number of Successes : Number of Failures = m : mc

x : y = m : mc

If k is the common factor between m and mc,

Total number of possible choices

 = Number of Favorable Choices + Number of Unfavorable Choices Or Number of Successes + Number of Failures
 n = m + mc = kx + ky = k (x + y)

Probability of Occurrence of the Event

Or

Probability of Success for the Event

=
 Number of Favorable Choices or Successes for the Event Total Number of Possible Choices for the Experiment
⇒ P(E) =
=
=
=
 antecedent antecedent + consequent

Probability of Non Occurrence of the Event

Or

Probability of Failure for the Event

=
 Number of Unfavorable Choices or Failures for the Event Total Number of Possible Choices for the Experiment
⇒ P(Ec) =
=
=
=
 consequent antecedent + consequent

Where, odds in favor of an event is x : y,

Let Odds in Favor of the Event be p : q.

For the ratio representing odds in favor

antecedent = p and consequent = q

Odds against an Event

 = Number of Unfavourable Choices : Number of Favorable Choices Or Number of Failures : Number of Successes = mc : m

p : q = mc : m

If a is the common factor between mc and m,

Total number of possible choices

 = Number of Favorable Choices + Number of Unfavorable Choices Or Number of Successes + Number of Failures
 n = m + mc = qa + pa = a (q + p) = a (p + q)

Probability of Occurrence of the Event

Or

Probability of Success for the Event

=
 Number of Favorable Choices or Successes for the Event Total Number of Possible Choices for the Experiment
⇒ P(E) =
=
=
=
 consequent antecedent + consequent

Probability of Non Occurrence of the Event

Or

Probability of Failure for the Event

=
 Number of Unfavorable Choices or Failures for the Event Total Number of Possible Choices for the Experiment
⇒ P(Ec) =
=
=
=
 antecedent antecedent + consequent

Where, odds against an event is p : q,