The data behind every figure
Nothing on this site is computed while you wait, and nothing is quoted from another site. Every number comes out of one of the 26 datasets below, generated offline by a script and then checked against something outside this project before it shipped. 21 of them are exact rather than simulated.
They are here so the figures can be checked. Any claim to be right is worth what the working behind it is worth, and the working should be visible.
Poker
Preflop hand equity
Simulated · 90 kBWin, tie and loss rates for all 169 starting hand classes, at every table size from 2 to 9 players, against random opponents played to showdown.
Checked against: AA heads-up lands near the commonly cited 85%, 72o near 32%. npm run test:poker-math re-checks both on every run.
Download JSONGenerated 15 Aug 2026Hand-type frequency (realistic folding)
Simulated · 1 kBHow often each hand category — pair through straight flush — actually reaches showdown at a table, under a model where players fold weak holdings rather than calling to the river.
Checked against: Checked against the standard five-card hand frequencies, which the no-fold variant below should approach and this one deliberately should not.
Download JSONGenerated 19 Sept 2026Hand-type frequency (everyone plays to the river)
Simulated · 1 kBThe same categories under the simpler assumption that nobody folds. Published together with the realistic model because the gap between them is the interesting part.
Checked against: Approaches the standard published five-card hand frequencies, which is the check: with no folding, showdown hands are just random seven-card draws.
Download JSONGenerated 15 Aug 2026Positional profitability
Simulated · 1 kBSimulated win rate by seat in big blinds per 100 hands, at 6-max and 9-max, under four models: flat versus positional entry ranges, each with and without a postflop in-position equity layer. The point is the decomposition, not one number.
Checked against: Seats sum to zero by construction, which is the arithmetic check. The interesting result is that the flat model shows almost no positional gradient at all — the button only pulls away once postflop in-position equity is layered in, which is the claim the dataset exists to test. The blinds lose in every variant.
Download JSONGenerated 15 Aug 2026
Blackjack
Basic strategy
Exact · 289 kBThe expected-value-maximising action for every player hand against every dealer upcard, across several rule sets, from a recursive EV engine rather than a copied chart.
Checked against: Spot-checked against the textbook chart: 5,5 doubles rather than splits, 8,8 always splits, 9,9 stands against a 7, hard 12 hits 2-3 and stands 4-6. Late surrender was checked the same way.
Download JSONGenerated 21 Sept 2026House edge by rule set
Exact · 834 BWhat the house keeps under each combination of dealer, doubling, splitting and payout rules, and what each individual rule costs you.
Checked against: Each rule’s isolated effect is checked against Wizard of Odds’ published rule-variations table, to within 0.05 points: dealer-hits-soft-17 +0.22, 6:5 payouts +1.39, no-DAS +0.14, late surrender −0.07, no-hole-card +0.11. An early version read 3.2% overall because dealer blackjack was double-counted — exactly the error this check exists to catch.
Download JSONGenerated 21 Sept 2026Third base, and what that card would have done
Exact · 3 kBWhat the card a third-base player takes would really have done to the dealer, per up-card, plus what a seat costs per hour by how many people are at the table.
Checked against: Built on a dealer recursion that removes each card from the shoe for real, rather than the frozen-composition model behind the rest of the site — a different model, and it reproduces the published six-deck dealer bust table to 0.004 percentage points, which is an independent check rather than a restatement. The expectation question itself is settled by exchangeability rather than measured: burning one card before the dealer draws moves her outcome distribution by 1.7e-16, zero to floating point.
Download JSONGenerated 21 Sept 2026Side bets
Exact · 34 kBHouse edge, hit rate and full combination breakdown for Perfect Pairs, 21+3, Royal Match and Lucky Ladies — every published pay table, at one through eight decks.
Checked against: All 58 published house edges reproduced to within 0.005 percentage points, across four bets and twelve pay tables, against Wizard of Odds. The raw combination counts match too: 144 suited king-queens and 11,868 other suited pairs in a six-deck shoe. Every enumeration is separately required to sum to C(52 × decks, n), which is what proves no hand is double-counted — the trap here being that a suited three of a kind is simultaneously a three of a kind and a flush.
Download JSONGenerated 21 Sept 2026Variance and session outcomes
Exact · 16 kBThe exact payoff distribution of a single hand, the covariance between two hands played at once, and the exact distribution of where a session finishes over a range of hand counts.
Checked against: Checked against Wizard of Odds’ variance tables, which are themselves simulations of about ten billion hands per rule set. Three rule sets are compared rather than one: variance agrees to within 0.018 and covariance to within 0.004, and every one of ours sits just below its published counterpart — a residual with a consistent sign, explained by this engine never resplitting a pair. Per-hand standard deviation across one, two and three simultaneous hands lands within 0.008 of the published figures.
Download JSONGenerated 21 Sept 2026What each mistake costs
Exact · 8 kBThe house-edge cost of every common blackjack mistake, from playing like the dealer down to each individual contested decision, with the rarity of the decision already priced in.
Checked against: Anchored on an identity rather than a published number, because the identity verifies itself: a player who mimics the dealer with a natural paying even money has no advantage left, so the entire house edge must be the probability that both hands bust. Those two figures are computed independently here and agree to 0.0008 points. The commonly published mimic-the-dealer figure of 5.48% is carried alongside for comparison.
Download JSONGenerated 21 Sept 2026Effect of removal and count indexes
Exact · 12 kBWhat removing one card of each rank does to the house edge, how closely Hi-Lo’s three whole-number tags track those effects, and the true count at which each contested hand changes its correct play.
Checked against: Effect of removal correlates at 0.998 with Wizard of Odds’ six-deck table and 0.999 with Griffin’s single-deck table in The Theory of Blackjack — two independent sources at two deck counts. The index numbers were checked against Schlesinger’s Illustrious 18: 14 of 17 playing indexes match exactly and all 17 land within one, with the insurance index of +3 falling out of pure arithmetic about a single fraction.
Download JSONGenerated 21 Sept 2026Bust odds
Exact · 3 kBThe probability of going over 21 if you take one more card on each hard total, and the probability the dealer eventually busts showing each upcard under every rule variant.
Checked against: The player figures are checkable by hand: with 13 equally likely ranks, a hard 12 busts on a 10, J, Q or K, so 4/13 = 30.77%, and each total up adds one busting rank. The dealer figures need the full recursion, and peak against a 6 as every published table shows.
Download JSONGenerated 21 Sept 2026
Yahtzee
Category odds
Exact · 2 kBExpected score and completion probability for all 13 categories under optimal single-category rerolling, plus the full score distribution and opening-roll value tiers behind each.
Checked against: P(Yahtzee) over a turn comes out at 4.60%. First-roll probabilities match exact combinatorial counts out of 6^5 = 7,776 derived independently: 6 yahtzees, 240 large straights, 300 full houses.
Download JSONGenerated 16 Sept 2026Final-score distribution
Simulated · 16 kBHow a full game actually finishes under the solved optimal policy: the distribution of final scores, percentiles, and the expected contribution and zero-rate of every category. The policy is exact and only the dice are sampled.
Checked against: Reproduces all seventeen figures Verhoeff publishes for the Optimal Solitaire Yahtzee Player -- grand total, standard deviation, median, and an expected contribution plus zero-rate for each of the thirteen categories and both bonuses. The mean also has to reproduce the exactly solved root EV of the table it plays from, which no amount of sampling error can hide.
Download JSONGenerated 21 Sept 2026Category detail
Exact · 14 kBThe per-category breakdown: expected score with one, two and three rolls available, the exact distribution of every final score, and how many genuinely distinct positions the opening roll can leave you in.
Checked against: Each distribution sums to 1 and its mean reproduces the expected score computed by a separate recursion that never builds a distribution at all.
Download JSONGenerated 16 Sept 2026Full-game optimal expected value
Exact · 8.2 MBThe expected value of the rest of a game from each of 536,448 reachable scorecard states, solved by exact backward induction over about 21 minutes.
Checked against: Optimal play from an empty card averages 254.5953 here against 254.5896 (Verhoeff, 1999) for the same joker convention — agreement to four significant figures with a result computed independently a quarter-century earlier.
Not offered as a file: 8.2 MB, and it already loads with the full-game tool that uses it.Generated 28 Aug 2026Keep-or-reroll decision table
Exact · 1.1 MBFor all 252 distinct five-dice rolls, both reroll counts and all 13 categories: which dice to keep, what that is worth, and the next-best alternatives.
Checked against: Derived from the same engine as the category odds, whose outputs are checked against independent closed forms.
Not offered as a file: 1.1 MB, and it ships with the keep-or-reroll guide.Generated 16 Sept 2026
Monopoly
Square landing odds
Exact · 6 kBLong-run probability of landing on each of the 40 squares, as the stationary distribution of a Markov chain over dice, doubles, Jail and both card decks. Counts arrivals rather than where a token rests between turns.
Checked against: Reproduces the two most-cited published facts about this problem on the first correct run: Jail is the most-landed-on square by a wide margin, and Illinois Avenue is the top non-jail square. The board and decks were cross-checked against three independent sources.
Download JSONGenerated 16 Sept 2026Property return on investment
Exact · 11 kBWhat each colour group costs to buy and build, what it earns per opponent turn at every development level, and how many turns it takes to pay for itself.
Checked against: Rents and prices come from the same cross-checked property data as the square odds. The payback ordering contradicts the folk belief that Boardwalk is the best buy, which is the point.
Download JSONGenerated 16 Sept 2026
Scrabble
Tile distribution and draw odds
Exact · 9 kBThe standard English-language 100-tile set with, for every tile, the chance it reaches an opening rack and the full distribution of how many land there.
Checked against: The distribution was taken from two independent published datasets and cross-checked letter by letter; they agree on every count and face value. Every single-copy tile comes out at exactly 7%, which needs no hypergeometric to verify.
Download JSONGenerated 16 Sept 2026Opening rack odds
Exact · 5 kBThe exact face value of an opening rack across every total it can take, the vowel and blank splits, and the probability of the racks players actually complain about.
Checked against: The rack-value DP mean equals the closed form 7 x 187/100 = 13.09, and the DP never computes a mean. 187 is the published face-value total of a full set.
Download JSONGenerated 17 Sept 2026Bingo odds
Exact · 4 kBHow often an opening rack can play all seven tiles, overall and conditioned on holding each tile, measured against the public-domain ENABLE lexicon.
Checked against: Bessoir & Pines (G4G13, 2018) get 12.92% against OWL2014 over the same 16,007,560,800 racks; ENABLE has 920 fewer seven-letter words so ours has to sit just below, and it does. The walk also asserts its own weights sum to exactly C(100,7).
Download JSONGenerated 17 Sept 2026Two- and three-letter words
Exact · 28 kBEvery two-letter word in ENABLE with the letters that hook it into a three-letter word front and back, the exact odds an opening rack can play it, its reverse where that is also a word, and its face value — plus the full three-letter list.
Checked against: ENABLE's 96 two-letter words reconcile exactly against NWL2023's 107, counted from a published enumeration: 96 + the 11 ENABLE lacks = 107, with nothing in ENABLE that NWL does not have. Every hook is round-tripped against the three-letter list, and AA's odds reproduce P(a rack holds two As) from the separately-computed tile distribution.
Download JSONGenerated 17 Sept 2026
Tennis
Tennis scoring by format
Exact · 21 kBMatch-win probability and expected match length for six formats at two serve strengths and five skill gaps, the better player’s chance in a tiebreak against a whole set, the tail of an advantage final set, and the deuce loop across every serve strength from 50% to 80%.
Checked against: A symmetric matchup comes out at exactly one half at game, tiebreak, set and match level in all six formats. The deuce closed form p² / (p² + (1 − p)²) is rebuilt from a plain point-by-point walk to 1e-12, and a game between equals is checked at its exact 6.75-point average length. No published dataset exists to match figure for figure, so the checks are identities that cannot be tuned.
Download JSONGenerated 29 Sept 2026Most points you can win and still lose
Exact · 2 kBThe largest share of total points a player can win while losing, for each of six formats, with the scoreline that achieves it.
Checked against: Solved exactly by Dinkelbach’s method over every game, tiebreak and set shape, and reproduced independently by hand: 106 of 168 points and a 6-7 6-0 6-7 loss in a best-of-three, 171 of 264 in a best-of-five. The optimal lost game is asserted to be 2-4, with no deuce.
Download JSONGenerated 29 Sept 2026Point importance
Exact · 20 kBHow much every score in a service game swings the chance of holding, for serve strengths from 50% to 85%; the chance of facing no break point in a game, a set and a match; and match-level importance at three break points under Wimbledon’s rules of the 1990s.
Checked against: Checked against Klaassen and Magnus (JASA, 2001), who model the server’s drop on a point as proportional to its match importance and print enough figures to work back to the importance each implies. At all six scores they quote, the importance computed here sits inside the range their rounding allows. Also asserted: 30-40’s importance equals the deuce win probability exactly, Morris’s game × set × match decomposition holds to 1e-12, and the no-break-point closed form is rebuilt from a plain point walk.
Download JSONGenerated 29 Sept 2026
Terms
These files are published so you can verify the figures on this site, not as a dataset to build on: they remain © Odds The Law, all rights reserved, and no licence to redistribute them is granted. If you want to use one for something, ask — the answer is likely yes.
If you quote a figure, please link the page you took it from. Two inputs are not ours and are credited where they are used: the Scrabble bingo figures are computed against the public-domain ENABLE lexicon, and board layouts, tile distributions and card decks are facts about commercially published games, cross-checked against independent public sources. Trademarks belong to their owners and are used descriptively.