NUTTY STASH / UNDER THE SURFACE

Math & statistics.

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

Exact weighted corpusV1 · Current replay corpusnuttyStashRound/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 probability31.45541%Any positive full-round payout

Available maximum5,000×1 in 5,352,127.19

Standard deviation8.497309×Relative to participation cost

Free-spin entry2.29368%1 in 43.5981

Break-even or better15.2081%Payout ≥ participation cost

Outcome breakdown

Zero 68.54459%Below cost 16.24731%Break-even 2.36598%Profit 12.84212%

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

Average interval / any payout3.179 roundsIncludes the round containing the payout.

Average interval / profit7.787 roundsIncludes the profitable round.

Fixed-start zero streak / ≤0.1%19 roundsProbability 0.07647%

Fixed-start loss streak / ≤0.1%42 roundsProbability 0.09792%

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)

7.723216 pp

[1, 2)

8.499817 pp

[2, 5)

14.529189 pp

[5, 10)

12.791213 pp

[10, 20)

16.643738 pp

[20, 50)

12.702775 pp

[50, 100)

0.29265 pp

[100, 200)

0 pp

[200, 500)

22.29407 pp

[500, 1000)

0.408503 pp

[1000, 2000)

0.021409 pp

[2000, 5000)

0 pp

[5000, 10000)

0.093421 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}	494,669	1	68.54459%	1 in 1.4589	0 pp
(0, 0.1)	0	0	0%	—	0 pp
[0.1, 1)	260,873	8	16.24731%	1 in 6.1549	7.72321581 pp
[1, 2)	105,943	10	6.59819%	1 in 15.1557	8.49981669 pp
[2, 5)	79,715	30	4.96469%	1 in 20.1422	14.52918885 pp
[5, 10)	30,301	50	1.88716%	1 in 52.9896	12.79121321 pp
[10, 20)	19,079	100	1.18825%	1 in 84.1574	16.6437375 pp
[20, 50)	7,683	294	0.4785%	1 in 208.9858	12.70277486 pp
[50, 100)	83	66	0.00516928%	1 in 19,345.04	0.29265 pp
[100, 200)	0	0	0%	—	0 pp
[200, 500)	1,370	340	0.08532%	1 in 1,172	22.29407034 pp
[500, 1000)	248	167	0.00077228%	1 in 129,486.95	0.40850331 pp
[1000, 2000)	6	6	0.00001868%	1 in 5,352,127.19	0.02140862 pp
[2000, 5000)	0	0	0%	—	0 pp
[5000, 10000)	30	1	0.00001868%	1 in 5,352,127.19	0.0934208 pp
[10000, ∞)	0	0	0%	—	0 pp
Total	1,000,000	1,073	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	8.4973094371 / 72.2042676701
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)	494,669
Unique reachable / all payout values	1,073 / 1,073
Total selection weight	635407536891225
Weighted payout sum (hundredths)	60999123541557600
Zero payout / below-cost payout	68.54459% / 16.24731%
Break-even / profitable outcome	2.36598% / 12.84212%
Loss probability (payout below cost)	84.7919%
Any payout frequency	1 in 3.1791
Profitable outcome frequency	1 in 7.7869
Available maximum probability	0.00001868%
Available maximum frequency	1 in 5,352,127.19
Most probable payout value(s)	0×
Most probable payout probability / frequency	68.54459% / 1 in 1.4589
Expected free spins per paid round	0.247786
Recorded free spins (unweighted)	399,683
Largest book (bytes, uncompressed)	8,442

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% level235.141595×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 (43.7×) 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×	0.11136%	1 in 898.0079	0.239892×	0.195349×
5,000×	0.00001868%	1 in 5,352,127.19	0.000934×	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 contribution51.335851 pp

Free-spin RTP contribution44.664149 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 entry2.29368%

The complete round contains at least one free spin.

1 in 43.5981 paid rounds · 36,999 corpus records.

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No win68.54459%

The complete round pays exactly zero.

1 in 1.4589 paid rounds · 494,669 corpus records.

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Normal win30.8856%

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

1 in 3.2378 paid rounds · 495,911 corpus records.

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Wild substitution17.30202%

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

1 in 5.7797 paid rounds · 278,074 corpus records.

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Acorn Toss15.94692%

The paid spin records an Acorn Toss cell. Free-spin tosses alone are excluded.

1 in 6.2708 paid rounds · 179,627 corpus records.

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Scatter anticipation14.7575%

The paid-spin opening grid has at least two tree-hollow Scatters, and that spin awards no free spins.

1 in 6.7762 paid rounds · 136,462 corpus records.

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8 free spins2.29368%

The paid spin awards exactly 8 free spins.

1 in 43.5981 paid rounds · 36,999 corpus records.

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Stash collection2.27255%

At least one free spin collects stash points and its opening grid contains a Basket.

1 in 44.0035 paid rounds · 36,651 corpus records.

Among rounds that enter free spins: 99.07863%.

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Stash opens · extra Wilds2.14308%

At least one spin opens the stash and records at least 3 extra Wild cells.

1 in 46.6617 paid rounds · 34,587 corpus records.

Among rounds that enter free spins: 93.43432%.

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Stash bonus · +3 free spins2.14308%

At least one free spin opens the stash and awards exactly 3 extra free spins.

1 in 46.6617 paid rounds · 34,587 corpus records.

Among rounds that enter free spins: 93.43432%.

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Repeated stash opening1.8396%

At least two distinct spins open the stash in the same complete round.

1 in 54.3595 paid rounds · 29,710 corpus records.

Among rounds that enter free spins: 80.20315%.

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Big win0.56979%

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

1 in 175.5045 paid rounds · 9,390 corpus records.

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Base maximum win · 5,000×0.00001246%

The complete round pays 5,000× and contains only the paid spin.

1 in 8,028,190.78 paid rounds · 20 corpus records.

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Bonus maximum win · 5,000×6.2281e-6%

The complete round pays 5,000× and contains at least one free spin.

1 in 16,056,381.56 paid rounds · 10 corpus records.

Among rounds that enter free spins: 0.00027153%.

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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. Golden-acorn Wilds substitute for paying symbols. Acorn Toss can turn one non-Scatter cell into a Wild before evaluation.

Three or more tree-hollow Scatters award 8 free spins. During free spins, each Wild charges the stash by 1 point and each Basket by 2. Every 6 points releases up to 3 extra Wilds into eligible cells; additional completed thresholds can release more. The remainder carries forward.

The first stash opening awards 3 extra free spins, once per round. The maximum is 11 free spins. Payouts stop when the complete round reaches 5,000×.

Paytable and rounding

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

Symbol	3 matching	4 matching	5 matching
Blackberries	0.2×	0.8×	2.5×
Pine cone	0.3×	1×	3.5×
Oak leaf	0.4×	1.5×	5×
Mushroom	0.5×	2×	6.5×
Apple	0.7×	2.5×	9×
Hazelnuts	1×	4×	250×

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/nutty-stash/review/math-audit-v1.jsonSHA-256 / 1a3da877a637277aceb5fdaae3f351490deb9298c889a7bb6a7fc76aa176be90

Source files and report identity

Generated: 08/10/2026, 17:50:35 UTC

Analyzer: jetreon-weighted-statistics/1

Analyzer SHA-256: 9f2c73724ed54a88c71a0dee8135f12138cc1710664ab1f0130e9fe777dcfb3f

Report ID: 5f17939578ea35ec36a87753ab36893e14fc48e88d0abeeb3602bdaf5d181706

indextitles/nutty-stash/math-output/v1-2026-10-07/index.json154 bytesSHA-256 / d7de1050366cc5ac5f864fa2094a6c056483612176b804d21b62ee508eabda1e

bookstitles/nutty-stash/math-output/v1-2026-10-07/books_base.jsonl.zst56,902,183 bytesSHA-256 / 58f8d577705149657cbb67b2bf58ae6646896292b76b22b7c2a059ddbe377264

weightstitles/nutty-stash/math-output/v1-2026-10-07/lookUpTable_base_0.csv19,668,560 bytesSHA-256 / 96c5bc8c71f839fe5ecbab1bbebda9e98c3b67febf4e0827ae4d1d0c4110cd34

exportReporttitles/nutty-stash/math-output/v1-2026-10-07/report.json1,590 bytesSHA-256 / 35f1798f500a52771a4fb9c5c6f724884cd4138cffc7e3ffbdde906108e2bc55

Rules description / implementation sourcetitles/nutty-stash/src/math.tsSHA-256 / fb115810a08cd802fae01a01bbbc546f7517228a417fa97a6a96e351aadf729f

JSON SHA-256: 7e27ffbac20c03d6401cec7e6565892e8f4db826e28a9bbfa9cfa3961b45f5c7

CSV SHA-256: 90679a141fa8e96bd568c28987667bd3b4a897554d62be81294e3c14e2b4c41a

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