Let event $E$ have probability $p$ of occurrence. Then the *odds in favor of $E$* is defined as the ratio of the probability of the event occurring against the probability of the event not occurring. $o_E = \frac{p}{1-p}$ For example, the odds of a fair coin landing heads twice on two flips $o_E = \frac{p}{1-p} = \frac{0.5 * 0.5}{1 - 0.5 * 0.5} = \frac{0.25}{0.75} = 1/3$ which can also be read as the odds of a fair coin landing heads twice are 1:3 (1 to 3). This is equivalent to saying for every one time you expect the event (two heads) to occur, you expect it to not occur three times. (It is often more common when probabilities are low to report odds against, which would be 3:1 against two heads in a row in this example). Note this is different than the probability of two heads, which is $P(HH) = p * p = 0.5 * 0.5 = 0.25 = 1/4$ To get the probability from the odds $P(E) = \frac{o_E}{o_E + 1}$