K-POP MUSE / UNDER THE SURFACE

Math & statistics.

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

Exact weighted corpusV4 · Current replay corpusneonMuseRound/v4Platform 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 probability45.66409%Any positive full-round payout

Available maximum5,000×1 in 2,037,890.35

Standard deviation13.174609×Relative to participation cost

Free-spin entry3.90512%1 in 25.6074

Break-even or better11.52005%Payout ≥ participation cost

Outcome breakdown

Zero 54.33591%Below cost 34.14404%Break-even 0.82585%Profit 10.6942%

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

Average interval / any payout2.19 roundsIncludes the round containing the payout.

Average interval / profit9.351 roundsIncludes the profitable round.

Fixed-start zero streak / ≤0.1%12 roundsProbability 0.06623%

Fixed-start loss streak / ≤0.1%57 roundsProbability 0.09336%

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)

11.298979 pp

[1, 2)

7.31689 pp

[2, 5)

10.188379 pp

[5, 10)

10.026437 pp

[10, 20)

10.134078 pp

[20, 50)

10.758646 pp

[50, 100)

7.450548 pp

[100, 200)

9.22031 pp

[200, 500)

11.1886 pp

[500, 1000)

4.75213 pp

[1000, 2000)

2.00868 pp

[2000, 5000)

1.410971 pp

[5000, 10000)

0.245352 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}	534,670	1	54.33591%	1 in 1.8404	0 pp
(0, 0.1)	0	0	0%	—	0 pp
[0.1, 1)	347,909	9	34.14404%	1 in 2.9288	11.29897884 pp
[1, 2)	54,802	10	5.37831%	1 in 18.5932	7.31689022 pp
[2, 5)	34,479	30	3.38379%	1 in 29.5526	10.18837935 pp
[5, 10)	14,638	50	1.43658%	1 in 69.6096	10.02643737 pp
[10, 20)	7,587	100	0.74459%	1 in 134.3015	10.1340781 pp
[20, 50)	3,644	298	0.35762%	1 in 279.6227	10.75864555 pp
[50, 100)	1,091	417	0.10707%	1 in 933.9552	7.45054805 pp
[100, 200)	669	473	0.06566%	1 in 1,523.09	9.2203096 pp
[200, 500)	376	347	0.0369%	1 in 2,709.96	11.18859999 pp
[500, 1000)	76	76	0.00745869%	1 in 13,407.17	4.75213005 pp
[1000, 2000)	22	22	0.00150646%	1 in 66,380.79	2.00867971 pp
[2000, 5000)	27	27	0.00050542%	1 in 197,853.43	1.4109714 pp
[5000, 10000)	10	1	0.00004907%	1 in 2,037,890.35	0.24535177 pp
[10000, ∞)	0	0	0%	—	0 pp
Total	1,000,000	1,861	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	13.1746092777 / 173.5703296197
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)	534,670
Unique reachable / all payout values	1,861 / 1,861
Total selection weight	261503720558950
Weighted payout sum (hundredths)	25104357173659200
Zero payout / below-cost payout	54.33591% / 34.14404%
Break-even / profitable outcome	0.82585% / 10.6942%
Loss probability (payout below cost)	88.47995%
Any payout frequency	1 in 2.1899
Profitable outcome frequency	1 in 9.3509
Available maximum probability	0.00004907%
Available maximum frequency	1 in 2,037,890.35
Most probable payout value(s)	0×
Most probable payout probability / frequency	54.33591% / 1 in 1.8404
Expected free spins per paid round	0.269346
Recorded free spins (unweighted)	275,715
Recorded frames (unweighted)	2,157,599
Largest book (bytes, uncompressed)	66,537

STATISTICS VALIDATION

7 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

Every book matches its lookup ID and payout; files retain their source hashes.

Result: 1,000,000 books matched

jetreon-corpus-integrity/1 / source-integrity

Probability conservationPassed

The exact probabilities of all non-overlapping payout bands sum to 1.

Result: 1/1

jetreon-corpus-integrity/1 / probability-mass

RTP contribution conservationPassed

The exact sum of band contributions equals the mode RTP.

Result: 24/25

jetreon-corpus-integrity/1 / rtp-contribution

Configured RTPPassed

Weighted RTP equals the configured target, 24/25.

Result: 24/25

jetreon-corpus-integrity/1 / target-rtp

Base participation costPassed

The 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

The paid-spin payout plus all free-spin payouts equals the full round payout.

Result: 1,000,000 rounds matched

jetreon-corpus-integrity/1 / payout-attribution

Cross-mode RTP consistencyNot applicable

Compare RTP across separately priced participation modes.

Result: Only one participation mode

jetreon-corpus-integrity/1 / cross-mode

Absolute exposure and liabilityNot evaluated

Monetary values require a specific bet-level template and currency.

Result: No bet-level template attached

jetreon-corpus-integrity/1 / absolute-exposure

RISK & EXPOSURE

Upper-tail CVaR / 99.9% level275.550335×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 (111×) 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×	0.27352%	1 in 365.6065	0.386929×	0.277522×
5,000×	0.00004907%	1 in 2,037,890.35	0.002454×	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 contribution36.547494 pp

Free-spin RTP contribution59.452506 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 entry3.90512%

The paid round contains at least one free spin.

1 in 25.6074 paid rounds · 39,829 corpus records.

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A paying base cascade45.66409%

The paid spin contains at least one paying cascade.

1 in 2.1899 paid rounds · 465,330 corpus records.

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Full-reel Wild5.91262%

At least one frame in the complete round has a merged Wild reel.

1 in 16.913 paid rounds · 59,808 corpus records.

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Initial level 1 · 6 free spins3.65845%

The paid spin awards bonus level 1.

1 in 27.3339 paid rounds · 37,309 corpus records.

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Initial level 2 · 8 free spins0.18304%

The paid spin awards bonus level 2.

1 in 546.322 paid rounds · 1,867 corpus records.

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Initial level 3 · 10 free spins0.04889%

The paid spin awards bonus level 3.

1 in 2,045.25 paid rounds · 502 corpus records.

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Initial level 4 · 12 free spins0.01473%

The paid spin awards bonus level 4.

1 in 6,790.7 paid rounds · 151 corpus records.

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Free-spin retrigger0.36096%

At least one free spin awards additional spins.

1 in 277.0378 paid rounds · 3,716 corpus records.

Among rounds that enter free spins: 9.2433%.

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Bonus level upgrade0.10273%

At least one free spin raises the active bonus level.

1 in 973.3905 paid rounds · 1,081 corpus records.

Among rounds that enter free spins: 2.63075%.

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Maximum win0.00004907%

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

1 in 2,037,890.35 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

The 5-reel, 4-row game pays on 20 lines from left to right. Three or more matching symbols pay; Wilds substitute for paying symbols. Winning symbols clear and new symbols cascade into the grid. Base cascade multipliers are 1×, 2×, 3× and then 5×.

Three, five, six or seven paying base cascades award 6, 8, 10 or 12 free spins. Free-spin bonus factors are 2×, 6×, 8× and 10×. The carried multiplier step is capped at 30; the factor applies to that step. Retrigger thresholds begin at four free-spin cascades, and a stronger award can upgrade the remaining bonus. The full-round payout is capped at 5,000×.

Paytable and rounding

Raw line pays for 3 / 4 / 5 matching symbols are in twentieths of the base stake. The base scale is 0.47266439855548 and the free-spin scale is 0.16854447986270668, applied before the cascade multiplier. Cumulative payouts are rounded across the paid round to 0.1× increments.

Symbol	3 / 4 / 5 · raw twentieths
Perfume	12 / 40 / 120
Swimsuit	10 / 30 / 100
Headphones	8 / 25 / 80
Platform boot	6 / 20 / 65
Sneaker	5 / 16 / 50
Mini handbag	4 / 12 / 40
Sunglasses	3 / 10 / 30

Generator samples and final selection weights

The corpus is a finite set of complete outcomes. Final lookup weights define the probability of each recorded round; raw occurrence counts do not. The v4 export includes separately weighted rare outcomes, including cap-reaching rounds. Their generation frequency is not a natural-frequency estimate.

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.

Source files and report identity

Generated: 08/10/2026, 17:25:00 UTC

Analyzer: jetreon-weighted-statistics/1

Analyzer SHA-256: 37b91a1eb36256885306232a64f01a40b0451bbdbf2d7ce978a2de693a6e5f66

Report ID: af23202cba4f2121bf85d15f822f3e4dba35f2fd851f22683e5a595ba315fce9

indexrelease/kpop-v4-math-2026-10-06/index.json154 bytesSHA-256 / d7de1050366cc5ac5f864fa2094a6c056483612176b804d21b62ee508eabda1e

booksrelease/kpop-v4-math-2026-10-06/books_base.jsonl.zst80,201,491 bytesSHA-256 / 4ad815c376d0f546e90f10036aeec2c9379167628212235f63a69c6e1db764ab

weightsrelease/kpop-v4-math-2026-10-06/lookUpTable_base_0.csv19,486,348 bytesSHA-256 / d48bfecb44ffe6e2882aa2b00e52c5f0ad00ffc065ecb5e269e6935454131a39

exportReportrelease/kpop-v4-math-2026-10-06/report.json2,666 bytesSHA-256 / 513dc7a457f83bf69dc05a6af9592b14f67e182ceca0a450b84ada6bb0472fe3

JSON SHA-256: 866652059c822f0e171d77ba3ebf011f27b3ec613a7a66a210e525e6e06fb228

CSV SHA-256: 5719aa89c4eb3e7e18e15d1c46729d53e126e1fd4f7f244b39db17be58d3f632

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.

Separate local-generator simulation

This older unweighted simulation is a different dataset: 1,000,000 cycles, seed 20261006. Observed RTP: 97.12524%, 95% interval 94.73506% – 99.51542%. Its sampling uncertainty does not apply to the exact weighted report above.

Source: titles/neon-muse/public/math-report.json
SHA-256: 85ff4210ea4f408d09def2bfb4d9462ba2ec99356d2fde7f2caa28530b9abbf5

Download simulation JSON

Download weighted JSON Download bands CSV Permanent version link