HIGHLAND CHEERS / UNDER THE SURFACE

Math & statistics.

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

Exact weighted corpusV1 · Current replay corpushighlandCheersRound/v1Platform 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 probability64.79061%Any positive full-round payout

Available maximum5,000×1 in 1,969,380.96

Standard deviation6.54552×Relative to participation cost

Free-spin entry2.06593%1 in 48.4044

Break-even or better16.46375%Payout ≥ participation cost

Outcome breakdown

Zero 35.20939%Below cost 48.32686%Break-even 1.8815%Profit 14.58225%

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

Average interval / any payout1.543 roundsIncludes the round containing the payout.

Average interval / profit6.858 roundsIncludes the profitable round.

Fixed-start zero streak / ≤0.1%7 roundsProbability 0.06708%

Fixed-start loss streak / ≤0.1%39 roundsProbability 0.08977%

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)

18.055196 pp

[1, 2)

11.695249 pp

[2, 5)

12.313768 pp

[5, 10)

8.108203 pp

[10, 20)

13.664822 pp

[20, 50)

24.271972 pp

[50, 100)

6.679784 pp

[100, 200)

0.452345 pp

[200, 500)

0.022067 pp

[500, 1000)

0.032912 pp

[1000, 2000)

0.06503 pp

[2000, 5000)

0.384765 pp

[5000, 10000)

0.253887 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}	361,956	1	35.20939%	1 in 2.8402	0 pp
(0, 0.1)	0	0	0%	—	0 pp
[0.1, 1)	475,870	9	48.32686%	1 in 2.0692	18.05519641 pp
[1, 2)	88,190	10	8.95611%	1 in 11.1656	11.69524865 pp
[2, 5)	42,931	30	4.35985%	1 in 22.9366	12.31376789 pp
[5, 10)	12,570	50	1.27654%	1 in 78.3366	8.1082027 pp
[10, 20)	9,255	100	0.93989%	1 in 106.3955	13.66482188 pp
[20, 50)	8,111	300	0.82371%	1 in 121.4019	24.27197227 pp
[50, 100)	1,018	373	0.10338%	1 in 967.2794	6.6797843 pp
[100, 200)	39	39	0.00396064%	1 in 25,248.47	0.45234519 pp
[200, 500)	10	10	0.00005078%	1 in 1,969,380.96	0.02206683 pp
[500, 1000)	10	10	0.00005078%	1 in 1,969,380.96	0.03291186 pp
[1000, 2000)	8	8	0.00004062%	1 in 2,461,726.2	0.06503008 pp
[2000, 5000)	22	22	0.00011171%	1 in 895,173.16	0.38476507 pp
[5000, 10000)	10	1	0.00005078%	1 in 1,969,380.96	0.25388689 pp
[10000, ∞)	0	0	0%	—	0 pp
Total	1,000,000	963	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	6.5455199719 / 42.8438317024
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)	361,956
Unique reachable / all payout values	963 / 963
Total selection weight	427697552492700
Weighted payout sum (hundredths)	41058965039299200
Zero payout / below-cost payout	35.20939% / 48.32686%
Break-even / profitable outcome	1.8815% / 14.58225%
Loss probability (payout below cost)	83.53625%
Any payout frequency	1 in 1.5434
Profitable outcome frequency	1 in 6.8577
Available maximum probability	0.00005078%
Available maximum frequency	1 in 1,969,380.96
Most probable payout value(s)	0×
Most probable payout probability / frequency	35.20939% / 1 in 2.8402
Expected free spins per paid round	0.169737
Recorded free spins (unweighted)	167,929
Largest book (bytes, uncompressed)	36,274

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: 12 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% level75.045219×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 (51.2×) 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×	0.20798%	1 in 480.8059	0.123568×	0.040374×
5,000×	0.00005078%	1 in 1,969,380.96	0.002539×	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 contribution49.801394 pp

Free-spin RTP contribution46.198606 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 entry2.06593%

The complete round contains at least one free spin.

1 in 48.4044 paid rounds · 20,400 corpus records.

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No win35.20939%

The complete round pays exactly zero.

1 in 2.8402 paid rounds · 361,956 corpus records.

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Normal win63.85925%

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

1 in 1.5659 paid rounds · 628,816 corpus records.

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Pub owner Wild19.27508%

At least one paid or free spin has a paying line whose hasWild flag is true.

1 in 5.188 paid rounds · 189,855 corpus records.

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Round on the House34.45995%

The paid spin records a positive cash-pint collection. Free-spin collections alone are excluded.

1 in 2.9019 paid rounds · 339,358 corpus records.

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Golden pint · double collection5.16142%

At least one paid or free spin records a collection with a golden factor of exactly 2.

1 in 19.3745 paid rounds · 50,881 corpus records.

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Highland cow anticipation9.86254%

The paid-spin grid contains exactly 2 Highland cow Scatters.

1 in 10.1394 paid rounds · 99,040 corpus records.

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Last Orders! · 8 free spins2.06593%

The paid spin awards exactly 8 free spins.

1 in 48.4044 paid rounds · 20,400 corpus records.

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Tray multiplier upgrade2.06583%

At least one free spin ends with a tray multiplier higher than its starting multiplier.

1 in 48.4068 paid rounds · 20,399 corpus records.

Among rounds that enter free spins: 99.99508%.

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Tray multiplier · ×51.58689%

At least one free-spin collection records the maximum tray multiplier of 5×.

1 in 63.0162 paid rounds · 15,683 corpus records.

Among rounds that enter free spins: 76.81266%.

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Cow retrigger · +3 free spins0.14153%

At least one free spin awards exactly 3 additional free spins. Smaller awards limited by the 16-spin cap are excluded.

1 in 706.5804 paid rounds · 1,443 corpus records.

Among rounds that enter free spins: 6.85051%.

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Big win0.93131%

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

1 in 107.3759 paid rounds · 9,218 corpus records.

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Maximum win · 5,000×0.00005078%

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

1 in 1,969,380.96 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 5-reel, 3-row game with 20 paylines. Three or more matching symbols pay from left to right. The Pub owner Wild substitutes for paying symbols. Amber pints may carry cash values of 0.1×, 0.2×, 0.5×, 1×, 2× or 5×.

A Serving tray collects all cash pints once per spin; extra trays do not duplicate the collection. A golden pint doubles the entire cash-pint subtotal once. The tray multiplier starts at 1×; a successful free-spin collection raises it for the next spin, up to 5×.

At least 3 Highland cow Scatters award 8 Last Orders free spins, or up to 3 more during the bonus. Total awarded free spins cannot exceed 16. Line wins and collections share a 5,000× full-round cap.

Paytable and rounding

The table shows line payouts in multiples of the base stake. Recorded paid spin totals use integer hundredths in 0.1× increments. At the cap, the paid spin total can be smaller than its raw line-plus-collection total. RTP attribution therefore uses the capped spin totals, not raw collection amounts.

Symbol	3 matching	4 matching	5 matching
Amber pint	0.1×	0.5×	1.5×
Highland whisky	0.2×	0.6×	2.1×
Steak pie	0.2×	0.9×	3.1×
Cheese board	0.3×	1.2×	4×
Bagpipes	0.4×	1.5×	5.5×
Golden stag	0.6×	2.4×	7.3×

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.

release/highland-cheers-math-v1/audit-report.jsonSHA-256 / febf5c456fbb5087bb9df21043469b799f7d157b829f44e13fdd5d04a357f5ee

Source files and report identity

Generated: 08/10/2026, 17:50:55 UTC

Analyzer: jetreon-weighted-statistics/1

Analyzer SHA-256: 9f2c73724ed54a88c71a0dee8135f12138cc1710664ab1f0130e9fe777dcfb3f

Report ID: 9edbb20d3e7303e10f718f8039647d0c83fafb3667108d619c26caf4518c6698

indexrelease/highland-cheers-math-v1/index.json154 bytesSHA-256 / d7de1050366cc5ac5f864fa2094a6c056483612176b804d21b62ee508eabda1e

booksrelease/highland-cheers-math-v1/books_base.jsonl.zst46,283,083 bytesSHA-256 / 1ef287d6eb7e5fddaf6497bc51782b043ce77b7177cbb5762cbe42df83978559

weightsrelease/highland-cheers-math-v1/lookUpTable_base_0.csv19,707,676 bytesSHA-256 / 42d4001ed658a3068ad10fb2d9e0b23b3e5c7a5847ff1038177c105312e28335

exportReportrelease/highland-cheers-math-v1/export-report.json773 bytesSHA-256 / 2fa9010b0e7fe1b6c4af5e9db97295eb0477384e7cd5fa9b2ff50a468cb6d271

Rules description / implementation sourcetitles/highland-cheers/src/math.tsSHA-256 / 07255aefbaec50866bd2ab51a07953ad357ea64fca66c03f46eb5e11f614fd62

JSON SHA-256: 691addc8899277120b6b1180edb489199151b6ac546a3ff04e30d6142422ad0a

CSV SHA-256: 13641717301b4658ee36b5f024a079c30dc7c1536d0c1608a100aead1a4dbe2c

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