The draw does not know which level you picked
Keno is a board of forty numbers. You mark up to ten of them, the game draws ten balls without replacement, and your payout depends on how many of your marks came up. The risk selector sits next to the board and looks like it changes the game. It does not touch the draw at all.
How many of your numbers hit is decided entirely by how many you marked. The probability of getting exactly h hits from k picks is the hypergeometric formula — C(k,h) × C(40−k,10−h) ÷ C(40,10) — and none of those terms contain the risk level. Mark ten numbers and this is your ticket, on every level, forever:
| HITS | CHANCE | ROUGHLY |
|---|---|---|
| 0 | 3.54% | 1 in 28 |
| 1 | 16.88% | 1 in 6 |
| 2 | 31.07% | 1 in 3 |
| 3 | 28.82% | 1 in 3 |
| 4 | 14.71% | 1 in 7 |
| 5 | 4.24% | 1 in 24 |
| 6 | 0.68% | 1 in 147 |
| 7 | 0.057% | 1 in 1,740 |
| 8 | 0.0023% | 1 in 43,303 |
| 9 | 0.000035% | 1 in 2,825,535 |
| 10 | 0.00000012% | 1 in 847,660,528 |
C(40,10) = 847,660,528 — the number of distinct draws. Exactly one of them is your ticket.
The useful number in that table is the middle. Ten picks average two and a half hits, and 51.49% of tickets land on two or fewer. Every payout table in the game is written around that fact, and each one answers the same question differently: what do you want to happen on the ordinary ticket, and what do you want on the rare one?
Four tables, one ticket
The cleanest way to see what the selector does is to mark three numbers and read all four tables side by side. Same three numbers, same draw, same chance of hitting — four different games.
| HITS | CHANCE | CLASSIC | LOW | MEDIUM | HIGH |
|---|---|---|---|---|---|
| 0 | 41.09% | — | — | — | — |
| 1 | 44.03% | ×1.00 | ×1.10 | — | — |
| 2 | 13.66% | ×3.10 | ×1.38 | ×2.80 | — |
| 3 | 1.21% | ×10.40 | ×26.00 | ×50.00 | ×81.50 |
Classic’s one-hit cell pays ×1.00 — the stake back, not a win. Low pays on 58.91% of tickets; High pays on 1.21% of them.
Low is a game where something happens most rounds and almost none of it is large. High is a game where nothing happens for an hour and then a three-hit ticket returns eighty-one times the stake. Classic sits in between with the flattest curve of the four. The one thing they have in common is the column they are all built to satisfy: the chance column, which is fixed.
The return barely moves
Each of the four levels has its own table for every pick count from one to ten, so the game ships forty payout tables. We took each one, multiplied every cell by its hypergeometric probability, and added them up. That sum is the expected return of that table — the fraction of a stake it gives back on average.
| LEVEL | RETURN RANGE | TOP MULTIPLIER | SHAPE |
|---|---|---|---|
| Classic | 98.96% – 99.04% | ×100 | Frequent small returns, capped top end |
| Low | 98.75% – 99.07% | ×1,000 | Pays often, mostly just above stake |
| Medium | 98.65% – 98.99% | ×1,000 | Fewer, larger |
| High | 98.65% – 99.01% | ×1,000 | Rare, very large |
Forty tables, all inside a 0.42-point band. The extremes are Medium and High at two picks (98.65%) and Low at nine picks (99.07%).
This is the finding worth carrying out of the article. Switching from Classic to High does not buy a worse game or a better one. It moves you along a band under half a percentage point wide, and everything that feels different about the two is happening somewhere other than the return.
What does change: how often, and how hard
Hold the pick count at six and the selector becomes measurable. The chance of any given number of hits is identical down every column; only the price of those hits moves.
| LEVEL | FIRST CELL ABOVE STAKE | CHANCE OF BEATING STAKE | TOP MULTIPLIER | VOLATILITY | RETURN |
|---|---|---|---|---|---|
| Classic | 3 hits (×3.68) | 15.28% | ×40 | 1.69 | 98.97% |
| Low | 2 hits (×1.10) | 47.40% | ×700 | 6.88 | 99.01% |
| Medium | 3 hits (×3.00) | 15.28% | ×710 | 9.67 | 98.83% |
| High | 4 hits (×11.00) | 2.58% | ×710 | 16.45 | 99.00% |
Volatility is the standard deviation of the payout, in stakes. It spans nearly a factor of ten while the return moves by 0.18 points.
A factor of ten in spread at a fixed return is the whole product. The Low table hands back small amounts constantly and the balance drifts; the High table takes the same money and holds it for a four-hit ticket that arrives once in thirty-nine attempts. Neither is generous and neither is a trap. They are different rides at the same price.
The cell everyone looks at
Ten picks on Low, Medium or High tops out at ×1,000, the largest multiplier in the game. Hitting it means all ten of your numbers came out of a draw with 847,660,528 possible outcomes. It is the single least likely thing our keno table can do, and reading it as a target rather than as decoration is the most common way players misread a paytable.
The honest version of the same table is one row up. On High with ten picks, nothing below four hits pays anything at all — and four or more hits happens on 19.69% of tickets. Four fifths of the tickets you buy on that table return zero, by design, so that the fifth can pay what it pays.
How to actually choose
Because the return is effectively fixed, the choice reduces to two questions you can answer before you sit down.
- How many rounds do you want out of this budget? Low and Classic return something on most tickets, so a fixed stake lasts longer in wall-clock terms. High burns through the same budget faster and less evenly.
- How much of a losing stretch can you sit through without changing your bet size? This is the real question. The High tables are built out of long empty runs, and the failure mode is not the table — it is raising the stake halfway through one.
That second point is where keno meets the arithmetic in risk of ruin: survival is governed by bet size relative to bankroll, and a table with a volatility of 16 needs a much smaller bet than a table with a volatility of 2 to give you the same number of rounds. Matching the stake to the level is the only decision in this game that changes anything.
What it will not do is change the price. Every level charges roughly one percent of every stake, and no combination of picks and risk settings anywhere in those forty tables gets you below that. The selector is a volatility dial that has been carefully built to be nothing else.
The board, the levels and the paytableHow keno works here, with every payout table on screen before you betKeno →
Does a higher keno risk level pay better?
No. Computed from our engine paytable, all forty tables — four risk levels across ten pick counts — return between 98.65% and 99.07% of stake. Higher risk buys larger, rarer payouts at the same average price.
Does the risk level change my chance of hitting numbers?
Not at all. Ten balls are drawn from forty regardless, so the chance of hitting a given number of your picks depends only on how many numbers you marked. The risk level only changes what each number of hits pays.
What are the odds of hitting all ten numbers in keno?
One in 847,660,528 — that is C(40,10), the number of distinct ten-ball draws from a forty-number board. It is the cell that pays ×1,000 on Low, Medium and High.
Is it better to pick more numbers or fewer?
Neither is better on return; each pick count has its own table priced to the same band. More picks means more hits on average — ten picks average two and a half — but the table demands more hits before it pays.
Can I improve my odds by choosing particular numbers?
No. Every ten-ball combination is equally likely and the draw has no memory of previous rounds, so no set of numbers is better than another. The draw is committed before you see it and can be verified after the round.
- Betkyo engine source: KENO_PAYTABLE (keno/paytable.ts), BALLS = 40 and MAX_PICKS = 10 (kenoGame.tsx), and the ten-ball draw in _shared/demoLocal.ts
- Returns and volatilities computed from those tables with the hypergeometric distribution — the standard model for drawing without replacement, in any probability text
