Bits & Odds

Methodology

Every number on this site comes from official lottery prize data plus arithmetic you can check. This page is the arithmetic.

What the lotteries publish

For each game a state lottery publishes the prize levels, the printed odds of hitting each level, how many prizes of each level the game started with, and how many are still unclaimed. Some states publish tickets printed instead of per-tier odds; where that happens we derive the odds, and we say so below.

The formulas

For a prize tier t with published odds 1 in O, N prizes at launch and R unclaimed:

Annuity prizes are converted to their nominal total: "$1,000 a week for life" is counted as $1,000,000, and "$50,000 a year for 20 years" as $1,000,000, matching how the lotteries themselves advertise them. Free-ticket prizes are counted at the ticket price.

Known weaknesses

The tickets-remaining estimate is an unweighted average across tiers, so a top-prize tier with five prizes counts as much as a $5 tier with two million. When a game is nearly sold out the small tiers dominate reality but the average lags. We keep this method because it is the one behind every historical number on the site, and changing it would silently rewrite years of comparisons; a weighted version is planned as a separate column.

Where the tier odds come from varies by state, and it is worth being exact about it. Arizona, California, Florida, Massachusetts, New York, North Carolina, Louisiana, Oklahoma, New Mexico and South Dakota publish the odds of each prize level themselves, so on those states nothing is derived and the numbers are the lottery's own. Texas, New Jersey, Georgia, Washington, Connecticut, New Hampshire and Rhode Island publish how many tickets were printed instead, so each tier's odds are that count divided by the prizes in the tier — exact arithmetic rather than an estimate, and it reconciles with each state's own published overall odds to a fraction of a percent. One qualification to "the lottery's own": the last state in the first list types its odds tables by hand, and the odd level is mistyped (one game prints 1 in 36,000 for a prize its own table puts at 1 in 60,000). Every row of a table describes the same print run, so where one row disagrees with the rest by more than 10% we use the print run the rest describe for that level instead.

The rest are spread. Michigan publishes every prize level, with how many it started with and how many remain, but no odds for any of them, and so does Ohio; the District of Columbia does the same, adding only a top prize's odds, which on a few of its games are not odds of anything; Maryland, Virginia, Missouri and Mississippi publish a single overall figure per game and no tier breakdown; and South Carolina's per-tier odds page renders nothing at all, while warning that its figures would count tickets ordered where its prize table counts tickets delivered. West Virginia publishes a ticket count, but on most of its newer games it is a round order quantity that disagrees with its own odds and prize table, so there we use its odds wherever the two disagree. For those nine we take the state's own overall odds and spread them across the prize table by each tier's share of the prizes. The result comes out very close to the state's published overall odds, but it is derived, not quoted, and it is less precise per tier than either of the methods above.

Finally, remaining-prize counts are only as fresh as the lottery's own publishing. A prize claimed today may not appear for a day or two. Where a state's data stops updating, we show a notice on that state's pages rather than presenting old figures as current.

When a game's odds have moved too far to trust

A scratcher's tickets are packed at random, so the tickets still unsold should win about as often as the odds printed on them. If every prize tier implied the same number of unsold tickets, our any-prize odds would stay close to the printed ones. They do not always. Small prizes are claimed late — a $1 winner can sit in a drawer for months — so a game's $1 and $2 tiers keep counting as "remaining" prizes that are already in players' hands, and imply far more unsold tickets than its larger tiers do. Divide all of those prizes by the averaged ticket estimate and the odds look much better than they are. Texas's 9s In A Line (#2710) on October 13, 2026 read 1 in 3.03 against 1 in 4.45 printed, because its $1 tier implied 3.40 million unsold tickets and its $300 tier 1.28 million.

We publish those figures as the model produces them, because changing the model would rewrite every comparison on the site. But where a game's any-prize odds have moved 25% or more from the printed odds in either direction, its page says the figures lean on that disagreement, and no summary — the opening sentence of a state or ranking page, the "best" cards, the budget picker or the answers to a page's questions — names it the best of anything. 157 of the 1,652 active games are past it now.

States that publish only part of the prize table

Every formula above needs the whole prize table: every level, how many prizes it started with, and how many are left. Some lotteries publish only part of it: the top levels, or how many are left without how many were printed. Colorado publishes how many of each prize were printed, but how many are left only for the top prize. Delaware publishes only the top prize of each game, with how many were printed and how many are left. Idaho publishes how many of each prize were printed, but how many are left only for prizes of $25 and up. Indiana publishes only the upper prize levels of each game, with how many were printed and how many are left. Iowa publishes only the prizes of $50 and up for each game, with how many have been claimed and how many are left. Kansas publishes how many prizes are left at each level of a game, but not how many it started with. Kentucky publishes how many prizes are left at each level of a game, but not how many it started with. Maine publishes only the prizes of $500 and up that each game still has, with how many are left, and neither the game's top prize nor how many of any prize were printed. Minnesota publishes only the prizes of $500 and up for each game, with how many were printed and how many are left. Nebraska publishes only the top two to four prize levels of each game, and how many of each are left, but not how many were printed. Pennsylvania publishes only its top six prize levels per game, and how many of each are left, but not how many were printed. Vermont publishes only the top prize levels of each game, and how many of each are left, but not how many were printed. Wisconsin publishes only the top prize of each game, with how many were printed and how many are left. A payout computed from part of a table is not a rough payout, it is a wrong one, and wrong in a direction nobody can see from the page: the missing levels are the small, frequent prizes, so the print run the formulas infer collapses and the payout explodes. When we tried it on one state's partial table, 59 of its 81 games came out paying more than they cost.

So for these states we compute nothing. Their pages show what the lottery publishes, as published: the prize levels it lists for each game, how many of each are left (and how many were printed, where it says), its own overall odds, its own dates, and — where it publishes them — its own figures for a game as a whole (tickets printed, the share sold, prizes unclaimed in dollars), shown as its own and never combined with anything, since unclaimed dollars set against unsold tickets would be a payout by another name. There is no payout, no expected value, no current odds and no tickets-remaining estimate on any of them, and the build fails if one appears. Games are ordered by what the counts can honestly support: games with a top prize still unclaimed first, then by the share of top prizes left where the lottery publishes how many were printed, or by the size of the top prize and how many are left where it does not, with the lottery's overall odds breaking ties. Where a lottery drops a prize level from its table once it is claimed out, and publishes no top prize, its first level is only the largest prize still unclaimed; those pages are ordered by that prize and never claim a game still has its top prize.

Why some games show a payout above 100%

9 of the 1,652 active games on this site show a current payout over 100%, about one in 184. That is not a typo and not, by itself, an error: it says the prizes still unclaimed are worth more than the tickets still unsold would cost to buy. It happens late in a game's life, when most tickets have sold but the largest prizes have not been hit. It is also exactly where the averaging weakness above bites hardest, because the estimate of tickets remaining is thinnest when a game is nearly sold out. We publish the number as the model produces it, mark it on the tables, and say plainly that its precision is low. What it reliably tells you is that the game is unusually rich in unclaimed prizes. What it does not tell you is that buying it is profitable: the remaining tickets are scattered across thousands of retailers and you cannot buy them all. So a game at 100% or more is treated exactly like a game whose odds have drifted too far: it keeps its place in every table, marked, and its own page carries the caution, but no summary, "best" card, budget-picker answer or best-in-each-state list names it the best of anything.

Draw games: frequency, significance and expected value

Scratcher odds change as prizes are claimed. Draw-game odds never change at all, so the analysis is a different job: not "what is this ticket worth now" but "does anything in the history mean anything". Everything below is plain arithmetic you can reproduce.

Matrix eras — why counts start where they do

A frequency count is meaningless across a change in the pool. Ball 68 cannot be cold over a period when it did not exist. So every count is scoped to the span during which that pool's matrix was unchanged, and the era table is checked against the data two ways: every draw must fit its declared matrix, and every era must contain a draw that actually reaches its declared ceiling. A typo in either direction fails one of those checks and the build stops.

The two pools are scoped separately, because they do not move together. Mega Millions has drawn five numbers from 70 since October 2017, but the Mega Ball fell from 25 to 24 in April 2025. Scoping the main numbers to the newest game version would throw away several hundred perfectly comparable draws; scoping each pool to its own span keeps every draw that is genuinely comparable and no more.

Is a number hot?

Each number appears in a draw with probability p = k/m (k balls drawn from a pool of m), independently across draws, so over n draws its count is exactly Binomial(n, p): 

expected  = n · p
sd        = sqrt(n · p · (1 − p))
z         = (observed − expected) / sd

A z-score on its own is not a finding, because the hottest of m numbers is supposed to look extreme. The number to compare it against is the expected maximum of m standard normals, which we compute by direct quadrature of E[M] = ∫ x · m · φ(x) · Φ(x)^(m−1) dx. For a 69-number pool that is about 2.37 standard deviations. So a leader sitting 2.3 standard deviations high is not a hot number; it is an ordinary Tuesday.

For the pool as a whole we run a goodness-of-fit test against "every number equally likely". The textbook statistic divides each squared residual by the expected count; here each cell is Binomial rather than a multinomial cell, so the variance is n·p·(1−p) and the (1−p) belongs in the denominator: 

chi-square = Σ (observed − expected)² / (expected · (1 − p))     on m − 1 degrees of freedom

One approximation is worth naming: the m counts are weakly negatively correlated, because every draw contributes exactly k of them. The correlation is of order 1/(m−1) and ignoring it moves these numbers by less than their third digit.

Droughts

Gaps between appearances are geometric, so the chance a given number goes at least g draws without appearing is (1 − p)^g. We publish two different figures from that, because quoting only one is how "overdue" lists mislead: the chance for one named number right now, which is small, and the number of times a drought that long has occurred somewhere in the span, which is usually large. A number is never due.

Expected value

Prize-tier odds are exact combinatorics — C(k,j)·C(m−k,k−j)/C(m,k) for matching j of k main numbers, times the bonus-ball probability — and reproduce each operator's published table to eight significant figures. The fixed-prize expectation is the sum of probability × prize over every tier below the jackpot, including any built-in multiplier: Mega Millions has applied a random 2× to 10× to every non-jackpot prize since April 2025, averaging 3.0×, and leaving it out understates that game's return by about 67%.

The jackpot term is the part nobody else publishes, because it needs the sharing correction:

EV_jackpot = P(jackpot) · cash_value · (1 − tax) · E[1 / winners]
E[1 / winners] = (1 − e^−λ) / λ   for λ = tickets_sold · P(jackpot)

Your own ticket is the "1"; every other ticket sold is an independent chance to share. Ticket sales are the one genuinely uncertain input, and they are fitted to the footprint a game actually sells into, not borrowed from a general curve: sales respond to a jackpot in proportion to how many people the game can reach. 3 games carry a fit and there are 2 distinct curves between them — the two national games share one, because they sell to the same country off the same published national sales figures, and California SuperLotto Plus has its own.

How steeply sales answer a jackpot is the whole difference between them, and it is worth two figures rather than one, because neither curve is a single power law. Over the range it is fitted over — $20 million to $1.6 billion — Powerball's sales grow as roughly the jackpot to the power 0.87; across its top segment alone they grow as the power 1.7, which is where sharing actually starts to bite. SuperLotto Plus is flat by comparison and flat throughout: the power 0.24 over $7 million to $50 million, and 0.24 at the top, because a game sold in one state has reached everyone it can long before the number gets big. Each game's fit carries the range it was measured over, and the figure is labelled an estimate wherever it appears.

For SuperLotto Plus it is barely an estimate at all. California publishes the winner count in every prize tier of every draw, and a tier's winners divided by that tier's probability is the number of tickets that were in the drum — so the fit is a measurement of 7 anchor points built from 108 draws we hold for the game, not an extrapolation from someone else's game. Cash value is taken from each lottery's own published estimate beside the advertised jackpot: 42.4%, 42.7%, 42.6% of the annuity for the games we price. It moves with interest rates, so we re-read it rather than assuming it.

The value-over-time chart, and what we refuse to draw on it

Each point on the sawtooth is that draw's own advertised jackpot, run through the formula above. Advertised jackpots come from the California Lottery's results feed, which is the only feed we have that carries the figure for each past draw — and it carries it in the top prize tier, not in the field named for it.

A rolling jackpot can only do three things between draws: rise, be revised slightly down as the lottery re-estimates from sales, or fall to its reset once somebody wins. Any other move is a feed error, and we drop the point and leave a visible break in the line rather than draw a cliff we cannot explain — a cliff argues just as forcefully as a real one, which is exactly the problem. 2 Powerball draws in the current window are excluded on this rule. The chart's caption always says how many, and so does this sentence — both from the same count.

How much the sales estimate moves the answer

Below roughly $300 million it barely moves it at all: a win is unlikely to be shared, so the number of tickets sold hardly matters. At $300 million, halving or doubling our sales estimate changes the ticket's worth by about a cent either way.

At the top of a national game's range it matters enormously. At a $1.7 billion Powerball jackpot our estimate gives 80 cents on the dollar; halve the sales and it is $1.03, double them and it is 55 cents. So the sawtooth's low and middle ground is solid arithmetic, and its tallest peaks are our best estimate rather than a fact. The same uncertainty is why we will not name the jackpot at which the curve turns back down to a figure tighter than "somewhere in the billions" — it is an output of the sales curve, not of the prize table.

A state game is the opposite case, and it is why one of them reaches break-even. SuperLotto Plus never sells enough tickets for sharing to bite: at its largest recent jackpot, halving or doubling the sales estimate moves the ticket by a single cent. So the claim that it is worth more than a dollar above roughly $84 million does not rest on the uncertain input at all — it rests on the prize table, the odds, and California's own published cash value. What it does rest on is the tax assumption, which is why the figure is given before tax and again at the top federal rate.

Two sources where there are two sources

11 of the 139 draw games here are published by more than one official body — Pick 3 and Pick 4 and Fantasy 5 and Pick 2 and Pick 5 and Florida Lotto and Mega Millions and Powerball and Jackpot Triple Play and Millionaire for Life and Lotto America — and those are the ones we can cross-check. For them the rule is that no draw goes on the site on one source's word: a draw one feed omits is published from the others and the omission recorded, a draw two feeds contradict is settled only by a feed closer to the drawing itself, and if nothing can settle it the game does not publish at all.

The other 128 games have one official publisher, so there is no second opinion to be had and no cross-check to perform: those draws are that publisher's record, and where a feed contradicts itself we publish neither reading rather than choosing. Saying otherwise would be the easiest claim on this page to make and the least true. Every discrepancy we have found is listed on the sources page — including the 6 Powerball draws New York's open-data feed was missing until 30 September 2026, which we wrote up with the steps to reproduce.

Update cadence

We re-read all 26 states every day and store a snapshot of every prize tier, which is what makes the history charts and claim logs possible. Snapshots are never overwritten.