Unequal draw and pick sizes
The support starts at max(0, picks - non-winning numbers) and ends at min(picks, drawn). Impossible rows are excluded rather than displayed as fake zeros.
Probability
Lottery Outcome Table Calculator
Build the complete hypergeometric match-count table for a finite lottery draw.
FINITE OUTCOME DISTRIBUTION
Account for every possible match count before discussing a winning threshold
For lottery analysts, educators, and pool organizers who need a reproducible hypergeometric table rather than a single headline odds figure.
Per-ticket qualifying chance-
At least one qualifying ticket-
Expected matches per ticket-
Expected qualifying tickets-
Batch spend-
CURRENT DECISION RECORD
Complete match-count outcome table
Every row is regenerated from the active inputs and carried into Copy, TXT, and the page-specific PDF payload.
| Matches | Combinations | Probability (%) | Expected tickets |
|---|
CURRENT CALCULATION PROCESS
Formula, substitution, intermediate values, and reconciliation
P(X=k) = C(K,k)C(N-K,n-k) / C(N,n)
Waiting for valid inputs.
HOW TO USE
Build the complete outcome partition
- Enter the total number pool and how many winning numbers are drawn without replacement.
- Enter how many distinct numbers appear on one ticket; this may differ from the draw count in custom games.
- Set the first match count that qualifies for the outcome you are studying.
- Enter the number and cost of tickets to translate per-ticket probabilities into expected row counts and spend.
- Inspect every match row before using the qualifying total; the table is the audit trail for the sum.
FOUNDATIONS
Five ideas behind the table
- Hypergeometric model
- Matches are counted when a sample is drawn without replacement from a finite pool.
- Outcome partition
- Every possible ticket falls into exactly one match-count row, so row probabilities must sum to one.
- Combinations
- C(n,k) counts unordered selections; lottery order is ignored unless the game explicitly awards ordered outcomes.
- Expected row count
- Tickets x row probability is a long-run average, not a guaranteed number of tickets in that row.
- Qualifying tail
- The entered minimum match combines all rows at or above that threshold.
DEEP ANALYSIS
Read support, tails, and batches separately
One-ticket table versus batch chance
The table describes one ticket. The at-least-one qualifying result across many tickets uses a second complement calculation and assumes independent tickets.
Why payout is absent
Prize schedules can split tiers, add bonus balls, cap pools, or share jackpots. This page stays authoritative by modeling match counts only.
DECISION CASES
Standard and constrained supports
Six from 49
A 6-number ticket against six drawn numbers from 49 produces seven match rows from zero through six. Their probability sum and expected-match identity independently check the table.
Forced matches in a small pool
If 8 numbers are picked from a 10-number pool while 6 are drawn, at least four matches are unavoidable. Rows below four are mathematically impossible and omitted.
TERMS
Outcome-table vocabulary
- Population
- All distinct numbers eligible for the draw.
- Success states
- The drawn winning numbers within the population.
- Sample
- Numbers selected on one ticket.
- Support
- The complete set of possible match counts.
- Combination
- An unordered selection count.
- Tail probability
- The sum of probabilities at or above a stated threshold.
EVIDENCE RECORD
Inputs and lineage to preserve
Retain the pool size, draw count, ticket-pick count, qualifying threshold, ticket batch definition, rules edition, draw date, and official game-rules URL. A changed bonus-ball or ordered-draw rule creates a different sample space and requires a new table.
MODEL LIMITS
Where the match-count model stops
- Assumes unordered, distinct numbers drawn without replacement.
- Does not model bonus balls, ordered draws, multipliers, prize sharing, taxes, or rollovers.
- Batch at-least-one probability assumes ticket outcomes can be treated as independent.
- Large combination counts are evaluated in logarithmic space and displayed with practical rounding.
RELIABLE SOURCES
Combinatorics and official game context
FAQ
Questions specific to match tables
Does this include a bonus ball?
Not as a separate state. Model the main draw only unless the bonus ball is part of the same undifferentiated set.
Why are some match rows missing?
They are outside the feasible support given the pool, draw size, and ticket picks, so their probability is exactly zero.
Can repeated numbers be modeled?
No. The hypergeometric model assumes distinct selections without replacement.
Is expected qualifying tickets a forecast?
No. It is the average over many equivalent batches; an actual batch can contain none or several.
Do identical tickets count as independent?
No for diversity of selections. The batch complement assumes independent ticket outcomes and should not be used for literal duplicate tickets.
Can I add prize amounts?
Use a separate expected-value model with the official tier rules. Match probability alone is insufficient for payout value.
IMPORTANT NOTE
A match distribution is not a prize schedule
Verify bonus-ball logic, prize tiers, and duplicate-ticket dependence separately before using these probabilities in a financial analysis.