Keno Risk Calculator: No-Payout Streaks and Bankroll
Calculate how often a round pays nothing, the chance of a consecutive no-payout run, and how many full stakes your starting bankroll can fund. Choose 80/20, 40/10 or a custom draw, then enter either a payout threshold or a list of the hit counts that pay.
Calculate Keno risk
Choose the draw rules, paying outcomes, stake, starting bankroll and planned round count. Session probabilities assume all planned rounds are played under unchanged rules, even if the starting bankroll would not fund them on its own.
Risk results
Complete the inputs to calculate risk.
Hit outcomes and payout classification
| Hits | Probability | Outcome |
|---|---|---|
| Complete the inputs to see the hit outcomes. | ||
Bankroll exposure
Planned wager volume is stake × rounds. It can exceed the starting balance when payouts are reused, and it is not an expected loss. The funding calculation below follows only an uninterrupted no-payout run from the starting bankroll.
The opening-run event starts at the first round and must finish within the planned horizon. It does not include other paths to a balance below one stake. Partial returns, later payouts, changed stakes, rewards and stopping rules are not simulated.
Frequency and hit-count variation
Expected counts are averages across completed sessions, not promised counts in one session. Hit-count standard deviation measures the spread of matches, not the spread of money returns. Use the paytable analyzer for return volatility.
Compare pick counts under one payout rule
These rows compare 1–10 picks, or fewer if the pool is smaller, under the same draw and paying-outcome rule. An impossible paying outcome contributes zero. If the current selection exceeds 10 picks, its results remain above and it is outside this comparison table.
| Picks | Expected hits | Zero-hit risk | At least 1 hit | Any payout | No payout |
|---|---|---|---|---|---|
| Run the calculator to compare pick counts. | |||||
How the risk calculation works
Let N be the pool size, D the draw size, n your picks and h the matches. A uniform draw without replacement gives the exact-hit probability P(H = h) = C(n, h) × C(N − n, D − h) / C(N, D), where C counts combinations. The SciPy hypergeometric reference gives the distribution and its feasible support.
Expected hits are nD/N. Hit-count variance is n × (D/N) × (1 − D/N) × (N − n)/(N − 1); its square root is the hit-count standard deviation. When two hit counts share the largest probability, both are shown as modes.
For a threshold t, paying outcomes are h ≥ t. For a custom hit list, only the listed feasible outcomes pay. Summing the remaining probabilities gives q, the chance of no payout. The probability that the next k rounds all pay nothing is qᵏ.
A run anywhere in the session
Overlapping windows are dependent: a run of 11 no-payout rounds contains two overlapping 10-round windows. The calculator uses a recurrence for the chance F(r) of at least one run by round r, rather than treating those windows as independent:
F(r) = 0 for r < k; F(k) = qᵏ;
F(r) = F(r − 1) + (1 − q)qᵏ[1 − F(r − k − 1)] for r > k.
This is an exact probability model for independent rounds with a constant q, evaluated numerically and rounded for display. Very small results use scientific notation. For background on run-length recurrences, see Oh, Park and Kim’s study of Bernoulli runs.
Why a session streak differs from a specific streak
Suppose each round has a 50% chance of no payout. Two specified rounds both pay nothing with probability 0.5² = 25%. Across three rounds, a two-round no-payout run can occur in rounds 1–2 or 2–3.
The exact session chance is 25% + 25% − 12.5% = 37.5%. The subtraction removes the overlap where all three rounds pay nothing. Treating the two windows as independent would give 43.75%, which overstates the chance.
To reproduce this example, choose Custom format with a pool of 2, a draw of 1 and 1 pick; set the paying threshold to 1, planned rounds to 3 and dry streak length to 2. This is a mathematical example, not an operator game.
No hits, no payout and a net loss are different
Zero hits
None of the selected numbers appear. If the table has a 0-hit prize, this can still be a paying outcome.
No payout
The hit count is classified as returning zero under the entered rule. There may still be one or more matches.
Net loss
Gross return is below the stake. For example, 0.5× pays something but loses half the stake. This tool needs only paying counts, so it does not calculate all net-loss outcomes.
To include a 0-hit prize and gaps, select Specific paying hit counts and enter a list such as 0, 2, 4-6. The hit-outcome table shows exactly how each result was classified.
What the bankroll figures can tell you
With a starting balance B and a fixed stake s, floor(B/s) consecutive no-payout rounds leave less than one full stake. For B = 200 and s = 10, that is 20 rounds. For B = 205, the same 20 rounds leave 5, which is still insufficient for another stake.
If those 20 rounds fit inside the planned horizon, the chance that the session opens with that run is q²⁰. If only 10 rounds are planned, that opening run cannot finish in the session, so the horizon-specific result is 0. It is separate from the chance of a shorter dry run elsewhere.
A full risk-of-ruin calculation would need every payout amount and a model of the changing balance and stopping rule. Losing part of a stake on paying rounds can also drain funds. The displayed opening-run probability therefore cannot be used as the total probability of exhausting a bankroll.
Compare expected net return in the RTP calculator and money-return variation in the paytable analyzer. The strategy guide explains how to read these measures together.
Related Keno tools
Hit distribution
Calculate exact hits, at-least-hit probability, zero-hit risk and the full distribution.
Payout charts
Compare prize schedules by spot count, with game-specific sources and conditions.
Payout calculator
Calculate gross return, net profit and stake amounts using a payout schedule.
Paytable analyzer
Analyze actual paying outcomes, RTP contribution and payout structure by hit count.
RTP analysis
Calculate theoretical return, house edge and expected value from a full paytable.
Strategy guide
Read paytables, RTP and risk figures while recognizing the limits of number strategies.
Frequently asked questions
What does this Keno risk calculator measure?
It calculates hit probabilities, payout and no-payout frequency, the chance of a specified no-payout block, the chance of at least one such run in a completed session, and starting-bankroll exposure. It also shows hit-count standard deviation. It does not calculate money-return volatility or the total risk of running out of funds without payout amounts.
What is the difference between a specific streak and a session streak?
A specific streak asks whether the next k rounds all pay nothing. Its probability is q to the power k. A session streak asks whether a run of at least k no-payout rounds occurs anywhere in the planned rounds. The session calculation accounts for overlapping windows.
Does the session result assume I can fund every round?
Yes. It assumes all planned rounds are completed independently under the same payout rule. It does not stop the model when a balance falls below one stake. The bankroll section separately shows what an opening no-payout run would do to the starting balance.
Can I include a zero-hit prize or non-paying gaps?
Yes. Select Specific paying hit counts and enter the counts that return a positive amount, including 0 if appropriate. You can use a list such as 0, 2, 4-6. Impossible counts contribute zero. Enter none for no paying outcomes or all for every feasible outcome.
Is a paying round necessarily profitable?
No. A payout below the stake is a net loss, and a payout equal to the stake breaks even. This calculator classifies positive returns as paying. Profit frequency and money-return volatility need the actual multipliers, which can be analyzed on the paytable page.
Why can the bankroll opening-run probability be zero?
The required uninterrupted no-payout run may be longer than the planned session, or a no-payout round may be impossible under the entered rule. A zero result for this one event does not establish zero overall financial risk. A starting balance below one stake is shown separately as already unable to fund a round.
Does picking more numbers always reduce risk?
No. More picks change the hit distribution, while the paytable determines which results pay and how much. The comparison table holds the payout rule constant to isolate probability changes; real operator tables may change with pick count.
Do earlier no-payout rounds change the next-round probability?
For independent rounds under unchanged rules, they do not. The next-round no-payout chance remains q. A previous streak does not make a payout due, and number patterns do not improve the probabilities of a fair uniform draw.