# Plinko Settings Tested — method and data guide

Study completed 19 September 2026. Model `wyl-discrete-plinko-3`; protocol `plinko-bankroll-1`. All values are virtual credits, not money. Targets 101% and 105% are experimental model settings, not casino offers.

## Design

Rows 8/12/16 × Risk Low/Medium/High × Target RTP 97/99/100/101/105 = 45 base configurations. Each has the same 1,000 reproducible seeds. Each full reference contains 10,000 drops. Five paired games start with 20/50/100/500/1,000 credits and use prefixes of that reference at a fixed bet of 1. There are 45,000 evaluated full references and 225,000 limited games, not 225,000 independent experiments. Within each Rows setting, paths are shared across Risk/RTP. Across Rows, the grouping of PRNG bits differs.

Seeds were fixed before the run: SHA-256 of `plinko-bankroll-1:main:<index>`, first four bytes unsigned big-endian, rejecting zero, duplicates and pilot/warmup seeds. The public `seeds.json` preserves the original list. xorshift32 with the low bit of each step supplies left/right decisions; it is a finite deterministic generator, not proof of independent random samples. No new outcomes or bootstrap simulations were generated for this article.

## Accounting and stopping

A game stops before a wager only when balance < 1. Balance exactly 1 can bet. Wager subtraction precedes payout addition. Completing the 10,000th drop counts as completion even if another bet could not be funded. No replacements, excluded failed games, top-ups or bet changes.

Money uses integer millionths (scale 1,000,000), with a BigInt payout product and half-up rounding to a millionth. At bet 1, the archived payouts are exact in this scale. String totals in JSON are integer ledger units; divide by 1,000,000 for virtual credits. Display rounding never affects results.

P/L = returned − wagered. Ending balance = starting balance + P/L. Profitable means P/L > 0, losing < 0, break-even = 0. All 1,000 starts remain in every denominator. Completion and profitability are different outcomes.

For cumulative P/L S_t after t drops, required starting balance is max(1 − S_t), t = 0…9,999. This is the lowest pre-bet funding threshold, not peak-to-trough drawdown. Completion matches starting balance >= this threshold in all saved games. It is known only after observing the full sequence and is not a deposit recommendation or future guarantee.

## Statistics

Target RTP is an input. Theoretical RTP = sum(slot probability × archived multiplier); binomial slot probabilities use fair left/right branches. Rounding the table makes theoretical RTP differ from its target. Observed RTP = sum returned / sum wagered, not the mean of individual game RTPs.

Nearest-rank percentiles describe outcomes; p5–p95 is the central 90% range, not a 95% confidence interval. Saved bootstrap intervals use 2,000 resamples of whole seed blocks, preserving pairing. Proportion intervals use Wilson's method. No multiple-comparison correction was applied. Seed-half agreement is a sensitivity check, not an independent replication. Sample rankings were selected after looking at the complete grid. Rare-tail estimates and near-fair means are uncertain; resampling cannot supply missing rare hits.

In the ideal independent-drop model, expected stopped-game P/L = (theoretical RTP − 1) × expected executed drops, at bet 1 and bounded horizon. Bankroll does not change the per-drop edge, but changes exposure. Full fixed-distance expected P/L is independent of starting funds. Finite pseudorandom results need not exactly match ideal expectation.

## Maximum multiplier supplement

Only 16 Rows / High is included. Maxima at Targets 97/99/100/101/105 are 1267×/1293×/1306×/1319×/1371×, respectively, in slots 0 and 16 only. Multipliers are gross payouts, including the wager.

The same 1,000 full paths give 10,000,000 unique drops: 161 left-edge hits, 151 right-edge hits, 312 combined; 272 games with at least one hit, 728 without. The five RTP rows reuse these paths. They do not create 50 million independent observations. Limited-game counts use saved executed-drop cutoffs, including the last executed drop. Rates divide by actual drops across all starts. Paired balance rows overlap and must not be pooled as independent hits. Separate completed/early-stopped slices are outcome-conditioned and are not unbiased slot-probability estimates.

These are observed counts recovered in the completed supplement, not theoretical expectations. The ideal either-edge probability 1/32,768 is reported separately. Archived replay matched 5,000 original target-specific sequence hashes and verified 25,000 limited games. No replay was required for the article.

## Validation and scope

The original audit checked completeness, accounting, all 1,755 contrasts, and independently recalculated 135 full references / 675 limited games. The editorial audit reread every raw seed block and checked all 450,000 paired bankroll observations. Original source checksums were rechecked before packaging the article. The edge supplement had a separate count audit from saved event indices.

This is WYL's own discrete model, not a proprietary provider implementation, casino audit or real-money player sample. Its numbers do not establish any casino's RNG, multipliers, RTP or player results. No claim of equivalence is made. The full private raw archive stays outside the web document root. Public files below are deliberate aggregate exports.

## Files

- `comparison.json`: all 225 combinations, core counts, quantiles, means, saved mean and Wilson intervals, turnover, observed/theoretical RTP and required balance. Exact mean derived from integer total net / 1,000.
- `summary.csv`: original complete 225-cell summary, including supplementary quantiles and ledger totals.
- `full-sequences-summary.json`: 45 unrestricted reference aggregates and reserve statistics.
- `paired-bankroll.json`: all 450 paired contrasts; direction is B minus A. Quantiles of paired differences are not differences of marginal quantiles.
- `editorial-evidence.json`: full matrix coverage counts, exception lists and seed-half checks for the nine findings.
- `theoretical-rtp.csv`: exact payout-table RTP and full-distance expectation.
- `edges.json`: full and limited edge counts, separate completed/early-stopped slices, and explicitly separate theoretical reference.
- `bankroll-edges.csv`, `bankroll-edges-by-stop-status.csv`: tabular edge counts and actual-drop denominators.
- `seeds.json`: the original seed list.
- `provenance.json`: versions and SHA-256 identities of the source aggregates; names identify archived inputs, not public raw-data URLs.
- `SHA256SUMS`: checksums of all files in this public package (excluding the checksum file itself).


## Detailed evidence behind the article

These are the exact statistical details retained when the main article was simplified. The article rounds money to one decimal and RTP to a readable precision; the data and the figures below retain their original precision. None of the calculations or saved results changed.

In the ideal independent-drop model: expected game P/L = (theoretical RTP − 1) × expected drops played, with RTP written as a ratio and a bet of 1. The expected P/L of a fixed, fully funded 10,000-drop sequence does not depend on the starting balance.

The sample shows both directions. At Target 97%, all 87 non-tied balance comparisons had lower mean P/L with more funds; the other 3 tied. At experimental Target 105%, 59 had higher mean P/L and 31 tied, with none lower. All 87 negative comparisons at 97% stayed negative in both halves of the seeds; 58 of the 59 positive comparisons at 105% stayed positive in both halves.

Near 100%, small sample differences are much less reliable. For 16 Rows / High / Target 100%, moving from 100 to 1,000 credits raised mean P/L by 21.9805 credits, but the paired 95% interval ran from −32.7504 to +77.7376. The median paired change was −24.8: 425 games did better, 509 did worse and 66 tied. Bigger balance was a clear completion benefit, not a demonstrated profit benefit here.

Across the actual payout tables, the 210 balance comparisons with a negative edge had 192 lower sample means, 10 higher and 8 ties. The 210 with a positive edge had 159 higher, 8 lower and 43 ties. All 30 exactly fair comparisons had intervals that included zero. Choose a balance to control affordable play, not to change the edge; do not treat a small observed gain near 100% as proof.

At experimental Target 105%, all 45 combinations had positive mean P/L, yet 11 had a losing median. Eight used High Risk and three used Medium. None used Low Risk or a 1,000-credit balance. Ten of those 11 still had a positive mean and a negative median in both halves of the sample; ten had a mean interval entirely above zero. At Target 100%, none of the 17 positive means had an interval entirely above zero. At Target 101%, 12 of the 16 mean/median splits held in both seed halves.

Increasing Target RTP raised mean P/L in all 450 limited-game comparisons and all 90 full-sequence comparisons. Every limited-game mean difference had a positive saved 95% interval and stayed positive in both seed halves. This was the broadest profit effect in the study.

Completion rose in 348 of those 450 comparisons, tied in 101, and fell in one. At 16 Rows / High / balance 100, Target 99% → 100% took completion from 68 to 66 out of 1,000, and profitable games from 66 to 65, while mean P/L rose by 6.713 credits. The completion-difference interval included zero (−0.6 to +0.2 percentage points). Do not turn this small exception into a rule against higher RTP.

A balance of 1,000 still missed that 95% completion mark in 7 of 45 configurations: 12 Rows / High at Targets 97% and 99%, plus 16 Rows / High at all five targets. Their p95 required balances were 1,221 and 1,087.3 credits for those two 12-Row settings; for the five 16-Row settings they were 1,828.1, 1,645.3, 1,645.5, 1,558.4 and 1,330.1 credits, in target order.

At 8 Rows / Low / Target 97% / balance 100, every game stopped early. P/L ran from −99.3 at p5 to −99.1 at p95. That narrow band described almost everyone losing nearly 100 credits. At the opposite extreme, 16 Rows / High / Target 105% / balance 20 had 976 early stops and p5–p95 of −19.9 to −19.1. Rare results above p95 lifted its mean to +15.3866, but the mean’s interval included zero.

We ranked all 225 combinations by exact total P/L divided by 1,000 starts. These are the top five cells, including the tie for fourth. All used experimental Target 105%. The table is a result of this sample, not a universal ranking.

That is a choice between different observed distributions, not proof of a best setting. The leader’s 95% mean interval was +474.9817 to +546.6893; the Low Risk comparison’s was +499.3168 to +508.3970. Those intervals overlap, and the leader was selected after inspecting the whole grid. The 8-Row High tie is exact because both balances finished the same sequences. No result here guarantees future profit.

Across the full 10,000,000 drops, the left edge landed 161 times and the right edge 151 times: 312 hits, an observed rate of 0.00312%. There were 272 games with at least one hit and 728 with none, out of 1,000 full games. Hits and games with hits are different counts because one game can hit more than once.

The ideal 50/50 model puts either edge at 1 in 32,768 drops, or about 0.00305176%. That is a theoretical probability, separate from our observed counts. Rare hits and different stopping points can move observed rates around. Restricting the analysis to early-stopped games would also select games by their outcomes, so those conditional rates are not a fair estimate of the slot probability.

Study date: 19 September 2026. Model: wyl-discrete-plinko-3. Protocol: plinko-bankroll-1. We used 1,000 reproducible seeds fixed before inspecting results, with no seed selection, replacements or top-ups. Each of the 45 Rows × Risk × Target combinations had 1,000 full reference sequences; each reference was paired with five starting balances. That gives 45,000 full reference sequences and 225,000 limited-balance games. At the same Rows, Risk and RTP changes reuse slot paths; different Rows group the random bits differently.

All 1,000 starts count in each cell. Funds exactly equal to the bet allow a drop; funds strictly below 1 stop the game before the next bet. Completing drop 10,000 counts as completion even if the remaining balance could not fund another drop. Balances and multipliers use integer millionths, with half-up payout rounding to a millionth. At bet 1, the archived table payouts are represented exactly. Display rounding never determines a stop.

The full reference is a counterfactual sequence with unlimited funding, not a suggestion to borrow or keep depositing. If St is cumulative P/L after t drops, the minimum required starting balance is max(1 − St) over t = 0…9,999. The final post-drop balance is excluded. We checked that this threshold predicts every saved completion result.

Means include early stops. Medians and percentiles use nearest rank. p5–p95 describes the middle 90% of sample results; it is not a confidence interval for the mean. Saved 95% mean and paired-difference intervals used 2,000 bootstrap resamples of whole seed blocks; proportions have Wilson intervals in the downloadable summary. There was no correction for multiple comparisons. Seed-half checks are sensitivity checks, not independent replications. Sample leaders and small differences near 100% should not be read as significance rankings.

The model uses deterministic xorshift32 streams. Different seeds do not prove independence, and reusing streams intentionally links the configurations. A bootstrap cannot invent rare outcomes absent from the sample. The ideal independent-drop expectation explains the direction of the edge; finite pseudorandom samples need not reproduce it exactly. These virtual-credit results exclude real-money conditions and do not establish any casino’s payouts, RNG, RTP or player results. The transferable principles are the distinction between return per bet and total exposure, and the need to count every start.

The completed dataset passed ledger, completeness and paired-result checks; an independent audit recomputed 135 full sequences and 675 limited games. The edge supplement recovered the original 16-Row paths from archived seeds and matched all 5,000 target-specific sequence hashes. This article uses those saved results. No new simulations were run for the article.

## Reproducibility download

[Full reproducibility package](full-reproducibility-package.zip) collects the full-precision JSON/CSV summaries, all saved paired contrasts (bankroll, factors, and full-versus-stopped), seeds, original manifest, supporting audit tables, archived model/experiment source, protocol and checksums. No simulation is needed to read the results. Private raw session files and operational logs remain outside this public package.

Inside the ZIP, SHA256SUMS covers every payload file. The live public SHA256SUMS additionally covers the ZIP itself. The package README explains this separation; neither manifest hashes itself. The technical detail above and the unchanged machine-readable files retain the evidence behind the rounded article examples.