Plinko — The Return Solved in Closed Form, Not Simulated

Twelve fair binary decisions produce a binomial distribution across thirteen slots. Multiply each slot’s probability by its multiplier and the return is exact — no simulation needed, and none used. The first time this page’s own arithmetic ran, it reported 1410.82%.

Format: Drop · 12 rows · 13 slots  ·  Demonstrates: Exact arithmetic that caught its own author’s error before deploy

Play it freeRun the audit yourself

The machine

The 1410% error

The multiplier array was assembled backwards on the first pass, which put the 40× jackpot in the centre slot — the one the ball reaches 924 times in 4,096 — and buried the 0.3× out at the 1-in-4,096 edges. The return on that board is 1410.82%, and the page printed exactly that figure the first time it rendered locally.

It was fixed before anything was deployed. The array was rebuilt edge-to-centre-to-edge, recomputed at 96.3281%, and checked against a hand calculation.

The reason this is worth a section on a game page: a hand-typed label would have said 96% over a broken board, and it would have kept saying it. Nothing about the game looks wrong from the outside. The ball drops, the multipliers sit there in the interface, the payouts arrive. The only thing that surfaced the fault was the rule that no published number on this platform is typed by a human — every one of them is computed from the constants the game actually runs, in front of the reader.

The methodology caught its own author. That is the whole argument, and it is recorded in the error ledger rather than quietly patched.

What did not ship, and is not claimed

Earlier drafts of this page described a commit-reveal fairness scheme: a hashed server seed shown before the drop, a player-supplied client seed, a verifier that reconstructs the path afterwards. None of it was built, so the description has been removed rather than left standing as an aspiration.

The fairness claim this game does make is narrower and checkable: the board is a fair binomial, the multipliers are published above, and the resulting return is arithmetic the reader can redo on paper. Twelve coin flips is not a difficult probability problem, which is precisely why it makes a good demonstration.

The mathematics

Basis: exact. Computed at page load, not sampled — there is no error bar because there is no estimate.

Twelve rows, each a fair left-or-right decision, so the ball’s landing slot is binomial over
4,096 equally likely paths. There is exactly one path to each
edge slot and 924 to the centre. No simulation is needed and none is used.

The 40× edge slots are what the eye goes to, and together they contribute
1.9531% — less than the 1× slots do at
24.1699%. A one-in-4,096 outcome paying forty
times cannot carry a game, and this table is why.

This is the page the project is built on. An earlier build of this game
published a 1410% return: the multipliers had been summed rather than weighted by their
probabilities. The error is recorded in full in the error ledger,
and the table above is the correction — every row weighted, the column summing to
96.3281%.

What the gate does before the game loads

Nine states have enacted statutory bans on the sweepstakes casino model, and six more closed their markets by enforcement without passing anything. Every one of those instruments turns on redeemable value. This platform has none, so it stays lawful in all fifty — but the geo-gate still names the statute, because a compliance claim that cannot be checked against a citation is a marketing claim.

Select New Jersey and the gate blocks the lobby citing A5447/S4282. Select Oklahoma and it plays, with an amber banner recording that SB 1589 takes effect on 1 November 2026. The distinction between an enacted ban and a ban in force is the sort of thing operators discover late; here it is in the interface, fed by the same weekly-verified database as the state tracker.

Gold Coins cannot be purchased, redeemed, transferred, or exchanged for anything. They have no value of any kind. 18+.