Odds express the ratio of the probability that an event occurs to the probability
that it does not occur, or the reverse ratio, depending
on the convention. For an event with probability 
, the odds in favor are 
, while the odds against are 
.
Betting odds against winning are written in the form 
("
to 
"), with 
, and correspond to the probability
of winning 
. Therefore, given a probability 
, the odds against winning
are 
, while the odds in favor
of winning are 
.
For example, a probability of 
corresponds to odds of 
in favor and 
against.
The word odds is also used informally for a probability, as in "odds of 1 in 
"
for a probability of 
. For 
,
this means odds of 
in favor, not 
.
