MIDNIGHT COVEN / UNDER THE SURFACE

Math & statistics.

The full distribution. Every outcome, with its selection weight.

Exact weighted corpusV2 · Current replay corpusmidnightCovenRound/v2Platform approval not confirmed

The same corpus as our recorded examples.1,000,000 complete rounds, analysed with every lookup-table weight. Replay examples on this page use these exact source files. These numbers describe the weighted corpus. The playable demo is a separate runtime. Viewing a report does not change the mathematics used by a game.

GAME MODE / BASE

Base 1× cost

One paid spin and all triggered free spins form one outcome.

RTP96.00%

AVAILABLE MAX5,000×

The bonus is a feature inside the base round. Only the base mode has a separate participation cost.

DETAILED METRICS

Weighted RTP96.00%Exact ratio 24/25

Hit probability24.86776%Any positive full-round payout

Available maximum5,000×1 in 1,982,583.04

Standard deviation6.164225×Relative to participation cost

Free-spin entry3.88691%1 in 25.7274

Break-even or better24.86776%Payout ≥ participation cost

Outcome breakdown

Zero 75.13224%Below cost 0%Break-even 0%Profit 24.86776%

Zero: 0× · Below cost: (0×, 1×) · Break-even: exactly 1× · Profit: above 1×. These groups partition all outcomes.

Average interval / any payout4.021 roundsIncludes the round containing the payout.

Average interval / profit4.021 roundsIncludes the profitable round.

Fixed-start zero streak / ≤0.1%25 roundsProbability 0.07864%

Fixed-start loss streak / ≤0.1%25 roundsProbability 0.07864%

Streak estimates assume independent, identically distributed rounds and a fixed starting point: qᵏ. They do not estimate the longest streak anywhere in a session.

HIT RATE DISTRIBUTION / BASE

Log scale

Contribution to total RTP in percentage points. Linear width, relative to the largest value.

{0}

0 pp

(0, 0.1)

0 pp

[0.1, 1)

0 pp

[1, 2)

14.758363 pp

[2, 5)

32.322934 pp

[5, 10)

19.162042 pp

[10, 20)

10.778424 pp

[20, 50)

9.257943 pp

[50, 100)

4.730576 pp

[100, 200)

2.835866 pp

[200, 500)

1.425938 pp

[500, 1000)

0.236693 pp

[1000, 2000)

0.063864 pp

[2000, 5000)

0.175162 pp

[5000, 10000)

0.252196 pp

[10000, ∞)

0 pp

Payout ranges use multiples of participation cost. The table below includes exact probabilities and counts.

Weighted payout bands · multiples of participation cost
Payout range	Corpus records	Unique payouts	Probability	Frequency	RTP contribution
{0}	753,450	1	75.13224%	1 in 1.331	0 pp
(0, 0.1)	0	0	0%	—	0 pp
[0.1, 1)	0	0	0%	—	0 pp
[1, 2)	100,802	4	10.16875%	1 in 9.834	14.7583629 pp
[2, 5)	104,915	22	10.58367%	1 in 9.4485	32.32293359 pp
[5, 10)	28,718	50	2.89703%	1 in 34.5181	19.16204225 pp
[10, 20)	8,026	100	0.80965%	1 in 123.51	10.77842368 pp
[20, 50)	3,086	298	0.31131%	1 in 321.2221	9.2579426 pp
[50, 100)	697	342	0.07031%	1 in 1,422.23	4.73057612 pp
[100, 200)	212	187	0.02139%	1 in 4,675.9	2.83586608 pp
[200, 500)	51	51	0.0051448%	1 in 19,437.09	1.42593775 pp
[500, 1000)	13	13	0.00035307%	1 in 283,226.15	0.23669273 pp
[1000, 2000)	8	8	0.00004035%	1 in 2,478,228.8	0.06386366 pp
[2000, 5000)	12	12	0.00006053%	1 in 1,652,152.53	0.1751624 pp
[5000, 10000)	10	1	0.00005044%	1 in 1,982,583.04	0.25219625 pp
[10000, ∞)	0	0	0%	—	0 pp
Total	1,000,000	1,089	100%	1 in 1	96 pp

[a, b) includes a and excludes b. Zero is its own band. Counts describe corpus records; probabilities use weights. Exact rational values are included in JSON and CSV. Contributions sum to RTP before display rounding.

MODE STATISTICS / BASE

Property	Value
Participation cost / base stake	1×
RTP / expected payout	96.00% / 0.96×
Exact expected payout	24/25
Standard deviation / variance	6.1642249762 / 37.9976695571
Minimum / available maximum	0× / 5,000×
Declared maximum	5,000×
Corpus records	1,000,000
Positive-weight / zero-weight records	1,000,000 / 0
Zero-payout records (unweighted count)	753,450
Unique reachable / all payout values	1,089 / 1,089
Total selection weight	35850652625850
Weighted payout sum (hundredths)	3441662652081600
Zero payout / below-cost payout	75.13224% / 0%
Break-even / profitable outcome	0% / 24.86776%
Loss probability (payout below cost)	75.13224%
Any payout frequency	1 in 4.0213
Profitable outcome frequency	1 in 4.0213
Available maximum probability	0.00005044%
Available maximum frequency	1 in 1,982,583.04
Most probable payout value(s)	0×
Most probable payout probability / frequency	75.13224% / 1 in 1.331
Expected free spins per paid round	0.318822
Recorded free spins (unweighted)	317,040
Recorded frames (unweighted)	1,666,806
Largest book (bytes, uncompressed)	12,329

STATISTICS VALIDATION

9 passed

Profile: jetreon-corpus-integrity/1. These are Jetreon integrity checks. External 2 Star / 3 Star requirements have not been attached to this report.

Source integrityPassed

Each book matches its lookup ID, payout and event schema; source hashes are unchanged.

Result: 1,000,000 books matched

jetreon-corpus-integrity/1 / source-integrity

Probability conservationPassed

Exact probabilities of all disjoint payout bands sum to 1.

Result: 1/1

jetreon-corpus-integrity/1 / probability-mass

RTP contribution conservationPassed

Exact band contributions sum to the mode RTP.

Result: 24/25

jetreon-corpus-integrity/1 / rtp-contribution

Configured RTPPassed

Weighted RTP equals the configured 24/25 target.

Result: 24/25

jetreon-corpus-integrity/1 / target-rtp

Base participation costPassed

Base mode costs exactly 1× the base stake.

Result: 1×

jetreon-corpus-integrity/1 / base-cost

Declared maximum is reachablePassed

A positive-weight outcome pays the configured 5,000× cap.

Result: 5000× available

jetreon-corpus-integrity/1 / declared-cap

Round payout attributionPassed

Base payout plus the paid bonus payout equals every full-round payout.

Result: 1,000,000 rounds matched

jetreon-corpus-integrity/1 / payout-attribution

Recorded mechanic examplesPassed

All examples have positive source weight and satisfy the same mechanic predicate used for these frequencies.

Result: 13 examples matched

jetreon-corpus-integrity/1 / replay-provenance

Saved local reference comparisonPassed

Normalized RTP, hit, bonus, volatility and available reference risk / payout attribution values match saved local audit statistics.

Result: Reference metrics matched; this is a local comparison

jetreon-corpus-integrity/1 / reference-statistics

Cross-mode RTP consistencyNot applicable

Compare separately priced participation modes.

Result: Only one participation mode

jetreon-corpus-integrity/1 / cross-mode

Absolute exposure and liabilityNot evaluated

Monetary values require a bet-level template and currency.

Result: No bet-level template attached

jetreon-corpus-integrity/1 / absolute-exposure

RISK & EXPOSURE

Upper-tail CVaR / 99.9% level98.514384×Mean payout in the highest-paying 0.1% probability mass.

Maximum relative exposure5,000×Gross payout per unit of participation cost.

Absolute monetary exposureNot evaluatedNo bet-level template or currency is attached.

CVaR takes exactly 0.10% of the weighted mass, splitting the boundary payout (49.1×) when needed. This measures the operator’s gross payout tail, without subtracting participation cost.

Threshold	Probability ≥ threshold	Frequency	Full tail payout E[x · 1(x ≥ t)]	Excess E[max(x − t, 0)]
40×	0.14062%	1 in 711.113	0.116467×	0.060217×
5,000×	0.00005044%	1 in 1,982,583.04	0.002522×	0×
10,000×	0%	—	0×	0×
25,000×	0%	—	0×	0×
50,000×	0%	—	0×	0×
100,000×	0%	—	0×	0×

Thresholds are inclusive. Full tail payout and excess payout have different definitions. Nested tails overlap and are not added together. All expectations are per paid round, relative to its cost.

MECHANIC STATISTICS

Paid-spin RTP contribution60.540571 pp

Free-spin RTP contribution35.459429 pp

Payouts attributed using recorded paid totals, checked against each full-round payout. Mechanic frequencies below count complete paid rounds, including their bonus; overlapping mechanics do not sum to 100%.

Free-spin entry3.88691%

The complete round contains at least one free spin.

1 in 25.7274 paid rounds · 38,608 corpus records.

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No win75.13224%

The complete round pays exactly zero.

1 in 1.331 paid rounds · 753,450 corpus records.

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Normal win24.4591%

The complete round pays more than zero and less than 20×.

1 in 4.0885 paid rounds · 242,461 corpus records.

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5+ symbol clusters24.86776%

At least one frame in the complete round records a paying cluster with 5 or more cells.

1 in 4.0213 paid rounds · 246,550 corpus records.

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Cluster cascades0.54414%

The paid spin contains at least 3 frames with positive payouts.

1 in 183.775 paid rounds · 5,395 corpus records.

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Ghost Wild spell12.06704%

The paid spin records a Ghost Wild spell cell. Free-spin spells alone are excluded.

1 in 8.287 paid rounds · 120,528 corpus records.

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Ritual seal multipliers1.23152%

At least one paying cluster in the complete round records a seal multiplier of 2× or greater.

1 in 81.2002 paid rounds · 12,246 corpus records.

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Moon flock omen0.02906%

At least one paid-spin frame records a seal value of 8 or more.

1 in 3,441.39 paid rounds · 289 corpus records.

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Seal upgrade · ×640.00218402%

At least one frame in the complete round records a seal at 64.

1 in 45,787.14 paid rounds · 53 corpus records.

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Cursed Night · 8 free spins3.88691%

The paid spin awards exactly 8 free spins.

1 in 25.7274 paid rounds · 38,608 corpus records.

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Persistent bonus seals3.35996%

A free spin after the first free spin starts with at least one nonzero seal.

1 in 29.7623 paid rounds · 33,345 corpus records.

Among rounds that enter free spins: 86.44301%.

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Portal retrigger · +3 free spins0.24762%

At least one free spin awards exactly 3 additional free spins. Smaller awards limited by the 18-spin cap are excluded.

1 in 403.8493 paid rounds · 2,494 corpus records.

Among rounds that enter free spins: 6.37054%.

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Big win0.40861%

The complete round pays at least 20× and less than 5,000×.

1 in 244.7331 paid rounds · 4,079 corpus records.

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Maximum win · 5,000×0.00005044%

The complete round pays exactly the declared 5,000× cap.

1 in 1,982,583.04 paid rounds · 10 corpus records.

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Examples use the same corpus hashes. Open an example and press Spin. A selected example does not represent the mechanic’s frequency.

HOW THE MATH WORKS

One paid round, including its bonus

A 6-column, 5-row cluster game. At least 5 matching symbols connected horizontally or vertically pay. Ghost Wilds substitute; overlapping candidate clusters are assigned in descending computed-win order so that cells are not paid twice. Winning cells clear and fresh symbols cascade in.

Winning cells charge ritual seals: 0 → 1 → 2 → 4 → 8 → 16 → 32 → 64. A cluster multiplier is the sum of seal values of 2 or more on its cells, with a minimum of 1×. Base-game seals reset before the bonus; bonus seals carry between free spins.

At least 3 Portal Scatters in the opening grid award 8 free spins, or up to 3 more during Cursed Night. Total awarded free spins cannot exceed 18. Each spin permits at most 40 paying cascades. The complete round stops at 5,000×.

Paytable and rounding

The table shows cluster base payouts before seal multipliers, in multiples of the base stake. Recorded wins use integer hundredths in 0.1× increments. Each cluster payout is limited by the remaining full-round cap.

Symbol	5–6 symbols	7–8 symbols	9–11 symbols	12+ symbols
Pumpkin	1.9×	3.8×	7.5×	15×
Raven	1.5×	3×	6×	12×
Potion	2.3×	4.5×	9×	18×
Skull	1.3×	2.6×	5.3×	10.5×
Witch Hat	1.1×	2.3×	4.5×	9×
Grimoire	2.8×	5.6×	11.3×	22.6×

Generator samples and final selection weights

The finite corpus includes ordinary and importance-sampled rare outcomes. Final integer lookup weights define probabilities; generation counts and local generator settings do not. This report covers the corpus linked to the replay library.

METHODOLOGY & DOWNLOADS

Definitions and exact arithmetic

For outcome i, pᵢ = wᵢ / Σw and xᵢ = payoutᵢ / (100 × mode cost). RTP = 100 × Σ(pᵢxᵢ). Standard deviation = √[Σ(pᵢxᵢ²) − mean²]. Hit = P(x > 0); profit = P(x > 1). Frequency = 1 / probability, including the event round.

Integer weight sums and rational RTP / band contributions are retained exactly. Zero-weight records count toward corpus size but cannot define reachable payouts. Display values are rounded; JSON retains numeric precision and exact rational band values. No confidence interval is needed for this finite weighted distribution.

No Low / Medium / High volatility label is assigned without a defined classification scale. External profiles and monetary risk remain unevaluated when their required configuration is absent.

Saved independent local audit

Saved independent local audit; not a live platform check. Reference RTP, hit probability, bonus entry, standard deviation and available risk metrics were compared after normalizing each report’s units.

titles/midnight-coven/review/math-audit-v2.jsonSHA-256 / 4ab69e01716f17a9ed3dee7420e0d63cc9e593f07955c992c9439f1089fc5d60

Source files and report identity

Generated: 08/10/2026, 17:50:41 UTC

Analyzer: jetreon-weighted-statistics/1

Analyzer SHA-256: 9f2c73724ed54a88c71a0dee8135f12138cc1710664ab1f0130e9fe777dcfb3f

Report ID: 18a20647fc672977b48acc800cb9ccaf2e26e30d699def9bce34da651137ae19

indexbuild/midnight-coven-math-v2-20261007/index.json154 bytesSHA-256 / d7de1050366cc5ac5f864fa2094a6c056483612176b804d21b62ee508eabda1e

booksbuild/midnight-coven-math-v2-20261007/books_base.jsonl.zst59,641,823 bytesSHA-256 / f7b86d815c240f7942778e9df9418eff8c19b35180cfb2aa0b518432b7046ecb

weightsbuild/midnight-coven-math-v2-20261007/lookUpTable_base_0.csv18,394,407 bytesSHA-256 / 9b8d7be5b973ba3f4b3914d9317b473f97cd09a3324317f469311cac4bae9552

exportReportbuild/midnight-coven-math-v2-20261007/report.json2,241 bytesSHA-256 / c6fdbdb8d27790087415e79bab94fa9e6af20f63bf70577e1253d09a77ea3efa

Rules description / implementation sourcetitles/midnight-coven/src/math.tsSHA-256 / 81681572df6b0cdf263e4e4907149be58cc0ba0f465ad504a86a08f2e3428edc

JSON SHA-256: 061b3e67ed3332d09b1dd10a597d62727479b5f98b891398eabe4ae04c41e79e

CSV SHA-256: 6867e054837e7c43c76138c012fdbc999f37f8d60dc3313deb570444eecbef10

All books are read with their corresponding lookup rows. IDs, payouts, schema, base/bonus payout attribution and unchanged source hashes are checked. This analysis does not re-evaluate every payline or certify platform acceptance. Full event books and lookup files are not included in the public downloads.

Download weighted JSON Download bands CSV Permanent version link