  Another useful form of Bayes' Theorem is the Odds Rule.  In the jargon of bookies, the "odds" of a hypothesis is its probability divided by the probability of its negation: O(H) = P(H)/P(~H). So, for example, a racehorse whose odds of winning a particular race are 7-to-5 has a 7/12 chance of winning and a 5/12 chance of losing. To understand the difference between odds and probabilities it helps to think of probabilities as fractions of the distance between the probability of a contradiction and that of a tautology, so that P(H) = p means that H is p times as likely to be true as a tautology. In contrast, writing O(H) = [P(H) − P(F)]/[P(T) − P(H)]  (where F is some logical contradiction) makes it clear that O(H) expresses this same quantity as the ratio of the amount by which H's probability exceeds that of a contradiction to the amount by which it is exceeded by that of a tautology. Thus, the difference between "probability talk" and "odds talk" corresponds to the difference between saying "we are two thirds of the way there" and saying "we have gone twice as far as we have yet to go."