Keno Odds Calculator
The exact chance of catching each number of your spots, and the house edge on a keno pay table.
This prices one keno ticket against one pay table for one draw. It does not tell you which casino has the better game, because that depends on both the pay table and the draw in front of you, which is why every payout and both N and K are editable.
What a ticket actually returns
90%
of tickets return nothing at all
Typical result: nothing back on the middle ticket
The likeliest draw for this ticket
- Your spot
- Drawn
- Caught
No single result is more likely than this one: 2 of 8 caught, on 32.8% of tickets. It pays nothing. The board is a picture of that count, not a draw being run.
| Caught | Chance | Returns | Share of return |
|---|---|---|---|
| 8 of 8 | 0.00043%1 in 230,115 | 10,000 for 1 | 7.4% |
| 7 of 8 | 0.016%1 in 6,232 | 500 for 1 | 13.6% |
| 6 of 8 | 0.24%1 in 423 | 50 for 1 | 20.1% |
| 5 of 8 | 1.83% | 10 for 1 | 31.1% |
| 4 of 8 | 8.15% | 2 for 1 | 27.7% |
| 3 of 8 | 21.5% | nothing | 0.0% |
| 2 of 8 | 32.8% | nothing | 0.0% |
| 1 of 8 | 26.6% | nothing | 0.0% |
| 0 of 8 | 8.83% | nothing | 0.0% |
Exact. Every chance above is the hypergeometric probability of catching that many of your 8 spots when 20 numbers are drawn from 80, multiplied by the pay you entered. Nothing is simulated, so there is no sampling error. See how this is calculated, below.
House edge on this pay table
41.19%
That is the figure this game is judged on, and it is an average over every ticket, including outcomes almost nobody reaches. It does not say how often a ticket pays anything, and on this pay table those two numbers are not close. Change a pay in the table below and watch which of them moves.
21% of that figure is carried by outcomes rarer than 1 in 1,000. A player who does not hit one of them gets back less than the headline number, for as long as they do not hit one.
- Expected catches
- 2.00
- Catch all
- 1 in 230,115
- Return per 1 staked
- 0.588
House edge across all ten of Maryland’s published tables
Pinned to the published structure, not to any pay you edit below.
- 50.00%1 spot
- 39.87%2 spots
- 37.56%3 spots
- 41.80%4 spots
- 45.73%5 spots
- 44.37%6 spots
- 40.46%7 spots
- 41.19%8 spots(yours)
- 43.63%9 spots
- 42.88%10 spots
Every table on this ladder is a losing bet. The kindest, three spots, is still worse than almost anything else on the floor; picking it does not make keno a good wager, only a less bad one.
Pay table, for 1. Starts on a real game, edit to match yours
The pays above start on the Maryland Lottery’s published Classic Keno prize structure, retrieved 2026-09-08, so the figures describe one real game you can go and check rather than a typical one. Tables differ enormously between operators for the same number of spots, and on this one the spot count alone moves the edge by more than twelve points, so the only table worth reading anything into is the one in front of you. Edit any payout to price it.
Written and reviewed by Alexander Korsager · last reviewed September 26, 2026 · corrections
The idea
What this tool shows
A keno game draws K numbers from a field of N. When you mark k spots, the chance of catching exactly c of them is a hypergeometric probability: the number of ways to pick c from your k, times the ways to fill the other K − c draws from the N − k you didn't mark, over the total ways to draw K from N. This calculator works that out exactly for every catch count, for the draw you enter. It opens on the Maryland Lottery's real 80-number, 20-drawn Classic Keno, the same game its shipped pay table is priced for, but online and crypto-casino keno commonly run a different draw entirely, and N and K are both editable so those games can be priced honestly rather than against the wrong numbers.
The averages are humbling.Mark 10 spots and you expect to catch two and a half. Catching all ten happens about once in every 8.9 million tickets. On the Maryland Lottery table this calculator starts with, about 11% of ten-spot tickets come back with more than the dollar that went in, and the second most likely of those is a quirk worth knowing: matching none of your ten numbers pays 4, so missing everything is a better result than catching four.
Keno's house edge is the highest of any common casino game, and how high depends entirely on the pay table in front of you.This calculator starts on the Maryland Lottery's published Classic Keno structure, where the edge runs from 37.6% on a three-spot ticket to 50% on a one-spot. Published figures for casino keno are lower: the Wizard of Odds puts the usual range at 25% to 29%, which is the figure our own house-edge comparison uses. Both are a long way worse than anything else on the floor, and the size of the gap between them is the reason to price the table you are actually playing rather than trust a number from anywhere else. Enter it here to see what it costs.
Run the same arithmetic across all ten of Maryland's published tables and the edge does not climb with the spot count.It falls, then climbs, then wanders, as the ladder above shows: the kindest ticket in the game is the three-spot and the second harshest is the five-spot, two rungs apart on the same slip. Nothing about that ladder could be worked out from the outside, because it is not a property of keno. It is ten separate pricing decisions taken row by row by whoever wrote the tables, and another operator's slip will have a different shape for the same reason.
That matters because the usual answer to "how many numbers should I pick" is a rule about variance: fewer spots for frequent small returns, more spots for rare large ones. That part is true, and it answers a different question. On cost the spot count carries no information at all until the specific table has been priced, which is what the editable pays on this page are for.
There is a second figure the spot count leaves alone, and it is the one printed above as the middle ticket.Sort every outcome by what comes back, walk up that ladder adding the chances as you go, and the rung the running total reaches half on is what a median ticket returns. On all ten of Maryland's published tables the answer is the same: nothing. The one-spot catches its number once in four tries, and the ten-spot pays 4 for matching none at all, and the middle ticket still comes back empty on both. The two questions a keno slip poses therefore have opposite answers. What a ticket costs swings more than twelve points across the ten tables, and what a typical ticket returns does not move at all.
FAQ
Questions players ask
How many numbers should I pick in keno?
Not by any rule that travels between games. On the Maryland Lottery structure this tool ships with, the edge across the ten published tables reads 50.00%, 39.87%, 37.56%, 41.80%, 45.73%, 44.37%, 40.46%, 41.19%, 43.63% and 42.88% as the spot count climbs from one to ten. It falls, then climbs, then wanders, and the cheapest ticket in the game (three spots, 37.56%) sits two rungs from the second dearest (five spots, 45.73%). A spread of over twelve points inside one operator's game, arranged in no order, means the spot count on its own tells you nothing about what a ticket costs: price the table in front of you. What the spot count does decide is shape, with fewer spots giving more frequent small returns and more spots giving rare large ones, and that is a question about variance rather than about cost.
What are the odds of hitting all my numbers?
For a 6-spot, about 1 in 7,753. For an 8-spot, about 1 in 230,115. For a 10-spot, about 1 in 8,911,711. Those depend only on the draw, not on what the game pays, so they are the same wherever you play. The calculator shows the exact figure for any ticket size.
Why is keno such a bad bet?
The draws are fair, but the payouts sit a long way below the true odds, far more so than roulette or slots. The Wizard of Odds puts casino keno at a 25% to 29% house edge, and the Maryland Lottery's published tables, which this calculator starts on, work out between 37.6% and 50%. On the eight-spot the tool opens with, the edge is 41.2%: about $41 of every $100 you put through is money you should expect not to see again.
Methodology
How this is calculated
Every figure on this page is exact, and none of it is simulated. A keno game draws K numbers from a field of N, so the chance of catching exactly c of your k marked spots is the hypergeometric probability C(k, c) × C(N − k, K − c) / C(N, K).
N and K default to Maryland's real 80-number, 20-drawn Classic Keno, the game its shipped pay table is priced for, but both are editable: online and crypto-casino keno commonly run a smaller field with fewer numbers drawn, and pricing that game against 80/20 gives a confidently wrong answer no matter how carefully the pay table is transcribed.
Multiplying each catch probability by what your pay table pays for it gives the expected return per unit staked, and the house edge is what is left over. The outcome table shows each result's own probability next to the share of the total return it carries, which is the part a single house-edge figure cannot show.
Two things about that table are worth stating, because neither is visible from looking at it.
It is ordered by what an outcome returns rather than by how many numbers you caught, which is why on the nine and ten-spot tables, where matching none of your numbers pays, the zero-caught row sits partway up the ladder instead of at the foot of it.
And the middle ticket printed above the table is a median, not an average: the outcomes are walked in that same order, their chances added along the way, and the figure reported is what the rung pays when the running total first reaches half.
Nothing is interpolated between rungs, because a ticket settles on one of them rather than between two. The average sits in the panel beside it as the return per 1 staked, and on the table this page opens on those two figures are 0.588 and nothing.
The ladder of ten edges quoted above is that same calculation run once against each of the source's ten published tables at Maryland's own 80/20 draw, not a set of figures taken from anywhere: the operator publishes prizes, and what those prizes cost is left for someone to work out.
Move N or K off 80/20 and the page says so plainly, because the loaded pays stop describing the game being priced the moment the draw changes.
Common misreadings4
- The middle ticket is not the average ticket, and on keno the distance between them is the whole shape of the game. On the shipped eight-spot table the average return is 0.588 for 1 while the median is nothing, because the average is held up by rungs that almost no ticket reaches. Reading the middle ticket as what a ticket usually returns is reading it correctly. Reading the average that way is not.
- The house edge is not how often a ticket pays, and the two move independently. On the shipped 8-spot table close to nine in ten tickets return nothing at all, while about a fifth of everything that does come back is carried by outcomes rarer than 1 in 1,000. A pay table can shift either of those a long way without touching the other.
- The share-of-return column is not a chance of winning. An outcome carrying a third of the return is still an outcome you are very unlikely to see.
- Expected catches is an average, not a target. Catching exactly that many is one row of the table like any other.
Assumptions4
- A keno game drawing K numbers from a field of N, with every number equally likely and every draw independent of the last. N and K default to 80 and 20, Maryland's real Classic Keno draw, but can be changed to price a different game.
- Pays are quoted 'for 1', so a pay of 3 returns 3 for a stake of 1 and nets 2. That is the convention printed on most keno pay tables.
- The pay table the tool starts with is the Maryland Lottery's published Classic Keno prize structure, retrieved 2026-09-08 and linked beneath the pay table, priced for Maryland's own 80/20 draw. That is one real operator's game rather than a typical one, and the figures always describe whatever table is in the boxes. Real tables vary enormously between operators for the same number of spots, so enter the one in front of you before reading anything into the result, and re-enter it entirely if you change N or K away from 80/20.
- The maximum field this calculator supports is 100 numbers. C(N, K) can be larger than JavaScript can hold exactly at that size, so the combinations are computed in log space. The result is checked against exact whole-number arithmetic in the tests rather than trusted.
Limits3
- The distribution describes one ticket. It says nothing about a session of many tickets, where the results compound in a way a single ticket's table cannot show.
- Progressive or multiplier features, multi-race tickets and 'way' tickets are not modeled. Only a flat pay per catch count is.
- The source publishes pay tables for Maryland's 80/20 draw only, for 1 through 10 spots. Above 10 spots, or at any other N and K, there is no shipped pay table, so every pay starts at zero (or, if it was carried over from Maryland's table, no longer describes the game) and the figures are only as good as the pays you enter.
Evidence
The hypergeometric probabilities are standard combinatorics, and math.test.ts covers the implementation. distribution.test.ts re-derives every catch probability a second time using exact whole-number arithmetic rather than the log-space version the tool runs, so the two have to agree independently.
The shipped pay tables get a third check that does not rely on us at all: Maryland publishes an overall chance of winning for each spot count, and the tests recompute all ten from our own transcription and require them to match what the operator prints, which is what would catch a mistyped row.
That check reads the shape of a table rather than its prizes, so the ten edges quoted on this page are pinned separately, each to the two decimals it is printed at, together with the order they fall in: a prize amount edited into the wrong row would leave the published odds intact and fail there instead.
The claim that the middle ticket returns nothing is pinned across all ten tables rather than only on the one the page opens on, so it is an assertion about the operator's whole published game rather than about a single default.
A passing test means the code matches the model and the tables match the source, not that a given casino's game matches the pay table you entered.
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