{ localUrl: '../page/odds.html', arbitalUrl: 'https://arbital.com/p/odds', rawJsonUrl: '../raw/1rb.json', likeableId: 'SpencerJohnston', likeableType: 'page', myLikeValue: '0', likeCount: '10', dislikeCount: '0', likeScore: '10', individualLikes: [ 'AlexeiAndreev', 'EricBruylant', 'JaimeSevillaMolina', 'TimHumenny', 'AnuragKashyap', 'JulesTanneur', 'DanielRiley', 'AlisaKuznetsova', 'EneaBullari', 'StephenFox' ], pageId: 'odds', edit: '61', editSummary: '', prevEdit: '59', currentEdit: '61', wasPublished: 'true', type: 'wiki', title: 'Odds', clickbait: 'Odds express a relative probability.', textLength: '1377', alias: 'odds', externalUrl: '', sortChildrenBy: 'likes', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'AlexeiAndreev', editCreatedAt: '2016-10-24 21:03:35', pageCreatorId: 'EliezerYudkowsky', pageCreatedAt: '2016-01-26 06:21:29', seeDomainId: '0', editDomainId: 'AlexeiAndreev', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '0', isEditorComment: 'false', isApprovedComment: 'true', isResolved: 'false', snapshotText: '', anchorContext: '', anchorText: '', anchorOffset: '0', mergedInto: '', isDeleted: 'false', viewCount: '3093', text: '[summary: Odds are a tool for expressing *relative* chances. If the odds of a tree in a forest being sick versus healthy are 2 : 3, this says that there are 2 sick trees for every 3 healthy trees. (The *probability* of a tree being sick, in this case, is 2/5 or 40%.)\n\n![](https://i.imgur.com/GVZnz2c.png?0)]\n\n[summary(Technical): Odds express relative chances. If the odds for X versus Y are 2 : 3, this expresses that we think that X is 2/3 = 0.666... times as likely as Y. Clearly, odds of 6 : 9 express the same idea; odds are invariant up to multiplication by a positive factor. When an odds ratio [1rd exhausts all the possibilities], then we can convert its components to probabilities by [1rk normalizing] them so that they sum to 1. In the example above, the probabilities would be $2:3 = \\frac{2}{3+2}:\\frac{3}{3+2} = 0.4:0.6.$\n\n![](https://i.imgur.com/GVZnz2c.png?0)]\n\nOdds are a tool for expressing relative [1rf chances]. If the odds of a tree in a forest being sick versus healthy are 2 : 3, this says that there are 2 sick trees for every 3 healthy trees. (The probability of a tree being sick, in this case, is 2/5 or 40%.)\n\n![](https://i.imgur.com/GVZnz2c.png?0)\n\nOdds are expressed in the form "X to Y", e.g. "7 to 9 for X versus Y", more compactly written as $7:9$.\n\nThe representation of chances as odds is often used in gambling and [-statistics].', metaText: '', isTextLoaded: 'true', isSubscribedToDiscussion: 'false', isSubscribedToUser: 'false', isSubscribedAsMaintainer: 'false', discussionSubscriberCount: '3', maintainerCount: '2', userSubscriberCount: '0', lastVisit: '2016-02-17 11:32:15', hasDraft: 'false', votes: [], voteSummary: [ '0', '0', '0', '0', '0', '0', '0', '0', '0', '0' ], muVoteSummary: '0', voteScaling: '0', currentUserVote: '-2', voteCount: '0', lockedVoteType: '', maxEditEver: '0', redLinkCount: '0', lockedBy: '', lockedUntil: '', nextPageId: '', prevPageId: '', usedAsMastery: 'true', proposalEditNum: '0', permissions: { edit: { has: 'false', reason: 'You don't have domain permission to edit this page' }, 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