Keno Paytable Calculator: RTP Contributions and Volatility
Enter the full list of hit-count multipliers to see where a Keno paytable’s return comes from. Analyze each row’s RTP contribution, payout frequency and standard deviation, then compare the entered table with three generated examples using the same draw rules.
Build a Keno paytable
Choose the pool, draw size, picks and stake, then enter one hit:multiplier pair per line. List every feasible outcome explicitly, including 0× payouts. A missing row is an incomplete table, not an assumed zero.
Balanced illustrative sample for 80/20 with six picks.
Optional payout limit
Paytable results
Results use the complete entered table.
No payout limit is modeled unless entered.
Any payout includes partial returns and returned stakes. Net profit requires a return above the stake. Standard deviation (SD) measures the spread of one-round returns; it is not a loss limit or a session forecast.
Amounts exclude fees, taxes and bonuses. Values are rounded for display; operator-specific currency rounding and jackpot rules are not modeled.
RTP contribution by hit count
Analyze the table to identify the largest contribution.
Each mutually exclusive exact-hit outcome contributes probability × effective multiplier to RTP. Contributions are expressed in percentage points (pp); the final column shows the row’s share of the total. Impossible outcomes contribute zero and are excluded from the maximum return and payout frequency.
| Hits | Exact probability | Odds | Multiplier | Gross payout | RTP contribution | Share of total RTP |
|---|---|---|---|---|---|---|
| Run the calculator to analyze the paytable. | ||||||
Compare your table with sample paytables
The first row uses your entered table. The other rows generate three payout shapes for exactly the same pool, draw size and picks. Return SD measures variability in multiples of the stake, so it can be compared without changing currency.
| Table | RTP | Chance of payout | Chance of net profit | Return SD | Max effective multiplier |
|---|---|---|---|---|---|
| Run the calculator to compare sample profiles. | |||||
Comparison uses the same draw rules, stake and payout limit for every row.
Generated samples target 94% RTP before limits. Their multipliers retain 12 significant digits, and the displayed results are recalculated from those values. A cap can reduce each sample’s RTP by a different amount. “Earlier” and “later” describe where prizes begin; use the calculated SD to compare their variability.
Worked example: same RTP, different payout frequency
Pick two numbers from a 40-number pool while 10 are drawn. Exactly one hit has a 38.4615% probability; two hits have a 5.7692% probability. The following illustrative tables pay nothing for zero hits and apply no payout limit.
| Paytable | RTP | Chance of payout | Return SD | Maximum multiplier |
|---|---|---|---|---|
| A · 1.2× at one hit; 8× at two | 92.3077% | 44.2308% | 1.8423× | 8× |
| B · 16× at two hits only | 92.3077% | 5.7692% | 3.7306× | 16× |
In table A, one hit contributes 38.461538…% × 1.2 = 46.153846… percentage points. Two hits contribute another 46.153846… points. Together they produce 92.3077% RTP, with each row contributing 50% of the total return.
Table B concentrates the same return in the two-hit prize: 5.769230…% × 16 = 92.307692… percentage points. It pays less often and has a larger standard deviation, despite the identical RTP. At a 10-unit stake, each table has an expected net loss of about 0.77 per round.
How a Keno paytable changes RTP
A Keno paytable does not change the probability of hitting numbers. It changes the value assigned to each hit count. If two games use the same number pool, draw size and pick count, their hit distribution can be identical while their RTP is different.
If you only need published prize schedules rather than an RTP calculation, use the Keno payout charts. This analyzer is for turning an entire paytable into RTP, house edge and contribution by hit count.
The RTP formula is:
RTP = Σ P(h) × effective total-return multiplier(h)
Use exact probabilities, not overlapping “at least” probabilities. For a uniform draw without replacement, P(h) = C(picks, h) × C(pool − picks, drawn − h) / C(pool, drawn), where C counts combinations. This is the hypergeometric distribution.
Hit probabilities
The pool, draw size and picks determine the probability of each feasible hit count. Changing a multiplier does not change these probabilities.
Multipliers and limits
Each multiplier specifies the gross return per unit staked. An entered cap can reduce that return for individual outcomes.
Complete-table return
Add the contributions from all mutually exclusive outcomes to get RTP. Subtract 1 to get expected net return per unit staked.
Measuring paytable volatility
Let X be the effective gross-return multiplier for one round. Its mean is the paytable RTP, expressed as a decimal. The analyzer calculates variance from the entire distribution, including losing outcomes:
Variance(X) = Σ P(h) × (X(h) − RTP)²
Return SD = √Variance(X)
Currency SD = stake × Return SD
Subtracting the stake from every payout shifts the mean without changing the standard deviation. The same currency SD therefore describes one-round net profit and gross return. A higher SD means a wider spread under this measure; it does not by itself give a session loss probability.
Payout frequency and SD measure different things. A multiplier below 1× can produce frequent payouts while still losing money. For identical draw rules, moving return into rare prizes can increase SD without changing RTP, as the two-pick example shows.
Reading a payout table correctly
Total return versus profit
This input uses total-return multipliers. A 3× return on a 10-unit stake pays 30 and gives 20 net profit. A 0.5× return pays 5 and leaves a 5-unit loss. Convert net-profit odds to total return before entering them.
Zero hits can pay
If the rules award a zero-hit prize, include its multiplier on row 0. The analyzer sums the actual paying rows, including gaps between prizes, rather than assuming one continuous payout threshold.
Caps apply to every outcome
A gross-return cap includes the returned stake. A net-profit cap adds the stake to form the gross ceiling. A cap can change RTP, SD and payout frequency; the listed top multiplier alone is insufficient.
The average multiplier on paying rounds is conditional: RTP ÷ probability of any payout. It excludes zero-return rounds, so it must not be read as the expected return of every bet. When no outcome pays, that average is undefined.
When to use this paytable calculator
Use this page when you have a payout table and want to know what it means mathematically. It is useful for checking custom Keno games, comparing crypto Keno risk modes, estimating how much each hit count matters and separating hit frequency from expected value.
RTP & house edge
Estimate expected loss over repeated rounds or solve a multiplier for a target RTP.
payout math
Open the payout calculator if stake, multiplier, profit and target payout matter most.
odds breakdown
The odds calculator covers exact hits, at least hits and miss probability.
Related Keno pages
Payout charts
Read named lottery prize schedules and their stated rules when you need a payout reference.
Risk analysis
Measure dry-streak probability, miss frequency and bankroll exposure after choosing a payout structure.
Strategy guide
Compare paytables, RTP, volatility and stake sizing as one decision process.
Frequently asked questions
What is a Keno paytable?
A Keno paytable lists the prize for each hit count at a specified number of picks. This analyzer takes total-return multipliers, where 1× returns the stake and 0× pays nothing.
Does the paytable change the odds of matching numbers?
No. For a fixed pool, draw size and pick count, hit probabilities stay the same. The paytable changes payouts, RTP and the distribution of money won or lost.
How is RTP contribution calculated?
Multiply the exact probability of a hit count by its effective total-return multiplier. Sum all rows to get RTP. A row’s share of total RTP is its contribution divided by the total, when total RTP is positive.
Why can two paytables have the same RTP but different volatility?
The same expected return can be spread across frequent small prizes or concentrated in rarer large prizes. Standard deviation measures the spread of returns across every outcome, including zero payouts.
Are missing rows treated as zero payouts?
No. Every feasible hit count must appear explicitly, using 0 for a non-paying outcome. Blank, missing, duplicate, negative or malformed entries must be corrected. Impossible outcomes are excluded from payout frequency and maximum feasible return.
Are the sample paytables official?
No. They are generated mathematical examples targeting 94% RTP before limits. Multipliers retain 12 significant digits. Calculations use those entered values, and a payout cap may reduce the resulting RTP.
Does an average paid multiplier above 1× mean positive EV?
No. That average includes only paying rounds. Full EV also includes rounds that pay nothing. Positive expected net return requires full-table RTP above 100% before any unmodeled costs.
Will editing the format erase my paytable?
No. Changes to the pool, draw size or picks keep the entries for editing. Selecting or reloading a sample explicitly replaces the table. The analyzer reports missing or invalid rows for the new format.