{"meta":{"copyright":"© Odds The Law (oddsthelaw.com). Precomputed dataset; all rights reserved.","generatedAt":"2026-09-17T03:14:44.369Z","description":"Exact odds for an opening 7-tile Scrabble rack drawn from a full 100-tile bag, as a multivariate hypergeometric problem -- not simulated. pointsDistribution is the exact probability of every face-value total a rack can have (blanks score 0). vowelDistribution / consonantDistribution / blankDistribution give the exact spread of each group. Scenarios are counted directly rather than by inclusion-exclusion.","rackSize":7,"rackCombinations":16007560800,"vowelTiles":42,"consonantTiles":56,"blankTiles":2},"expectedPoints":13.09,"pointsDistribution":[{"points":5,"probabilityPct":0.0651},{"points":6,"probabilityPct":1.4031},{"points":7,"probabilityPct":7.0151},{"points":8,"probabilityPct":6.1108},{"points":9,"probabilityPct":8.7699},{"points":10,"probabilityPct":11.9291},{"points":11,"probabilityPct":9.1047},{"points":12,"probabilityPct":8.8075},{"points":13,"probabilityPct":7.833},{"points":14,"probabilityPct":6.5516},{"points":15,"probabilityPct":4.9786},{"points":16,"probabilityPct":5.3953},{"points":17,"probabilityPct":4.4776},{"points":18,"probabilityPct":3.629},{"points":19,"probabilityPct":3.6825},{"points":20,"probabilityPct":2.5711},{"points":21,"probabilityPct":1.9996},{"points":22,"probabilityPct":1.5298},{"points":23,"probabilityPct":1.1862},{"points":24,"probabilityPct":0.7683},{"points":25,"probabilityPct":0.6295},{"points":26,"probabilityPct":0.5136},{"points":27,"probabilityPct":0.315},{"points":28,"probabilityPct":0.2584},{"points":29,"probabilityPct":0.1703},{"points":30,"probabilityPct":0.1093},{"points":31,"probabilityPct":0.0688},{"points":32,"probabilityPct":0.0496},{"points":33,"probabilityPct":0.0291},{"points":34,"probabilityPct":0.0176},{"points":35,"probabilityPct":0.0142},{"points":36,"probabilityPct":0.007},{"points":37,"probabilityPct":0.0042},{"points":38,"probabilityPct":0.0027},{"points":39,"probabilityPct":0.0014},{"points":40,"probabilityPct":0.0006},{"points":41,"probabilityPct":0.0004},{"points":42,"probabilityPct":0.0002},{"points":43,"probabilityPct":0.0001},{"points":44,"probabilityPct":0},{"points":45,"probabilityPct":0},{"points":46,"probabilityPct":0},{"points":47,"probabilityPct":0},{"points":48,"probabilityPct":0},{"points":49,"probabilityPct":0}],"vowelDistribution":[{"k":0,"probabilityPct":1.8783},{"k":1,"probabilityPct":10.6198},{"k":2,"probabilityPct":24.6459},{"k":3,"probabilityPct":30.427},{"k":4,"probabilityPct":21.5755},{"k":5,"probabilityPct":8.7843},{"k":6,"probabilityPct":1.9007},{"k":7,"probabilityPct":0.1685}],"consonantDistribution":[{"k":0,"probabilityPct":0.2394},{"k":1,"probabilityPct":2.4695},{"k":2,"probabilityPct":10.4479},{"k":3,"probabilityPct":23.5078},{"k":4,"probabilityPct":30.3881},{"k":5,"probabilityPct":22.574},{"k":6,"probabilityPct":8.9246},{"k":7,"probabilityPct":1.4488}],"blankDistribution":[{"k":0,"probabilityPct":86.4242},{"k":1,"probabilityPct":13.1515},{"k":2,"probabilityPct":0.4242}],"scenarios":[{"id":"no-vowels","label":"No vowel at all","probabilityPct":1.8783,"note":"Seven tiles and not one A, E, I, O or U. A blank counts as neither here -- it can become a vowel."},{"id":"no-vowels-no-blank-no-y","label":"No vowel, no blank and no Y","probabilityPct":1.1064,"note":"What a player actually means by a vowelless rack: no blank to spend and no Y to lean on either."},{"id":"one-vowel","label":"Exactly one vowel","probabilityPct":10.6198,"note":"Playable, usually, but rarely well."},{"id":"five-plus-vowels","label":"Five or more vowels","probabilityPct":10.8535,"note":"The other way a rack goes wrong, and it happens more often than an all-consonant one."},{"id":"q-no-u","label":"The Q with no U and no blank","probabilityPct":4.7618,"note":"The single most complained-about rack in the game -- and mostly a false alarm, see below."},{"id":"q-no-u-has-i","label":"The Q with no U, but an I","probabilityPct":2.2225,"note":"QI is good in both official word lists, so an I rescues the rack on its own -- though not in ENABLE, which is the public-domain list the two-letter word pages use and one of eleven two-letter words it lacks."},{"id":"q-stranded","label":"The Q with no U, no blank, no I and no A","probabilityPct":1.2579,"note":"The genuinely awkward case, once QI and QAT are accounted for. Much rarer than the folklore."},{"id":"any-blank","label":"At least one blank","probabilityPct":13.5758,"note":"Two blanks in a 100-tile bag, and you see one in about one opening rack in seven."},{"id":"both-blanks","label":"Both blanks at once","probabilityPct":0.4242,"note":"Rare enough to remember."},{"id":"any-s","label":"At least one S","probabilityPct":25.5402,"note":"Only four S tiles exist. They are worth holding for what they do -- pluralise and hook -- not for being scarce; there is one J and nobody hoards that."}]}