Euclidean Remainder Volume Claim: Original Demo & Rules

How Scoring Works

The game reveals twelve independent fair binary steps to form three four-bit blocks. Each completed block is decoded as a value from 0 to 15, and 1 is added to obtain integers a, b, and c, each ranging from 1 to 16.

The raw terminal statistic is the product of the modulo operations: (a modulo b), (b modulo c), and (c modulo a). The global minimum of 0 is subtracted from this result. Before capturing a stake, the player preselects a linear, squared, or cubed reward weight to weight that score.

Live Quote & Payout

The live gross quote is calculated as 0.97 times the conditional expected terminal weight divided by the initial expected terminal weight. This quote may rise, fall, or become zero during the round.

• Manual Collect: You can collect the current quote at any time.
• Auto-Cashout: You can set automatic collection thresholds at 1.25, 1.75, or 2.5. If an earlier threshold is crossed, the round settles before a later zero event. A quote of zero resolves before cashout at the same event.
• Final Step: If the round reaches step 12, the surviving current quote is collected.

Controls & Modes

Selectable stakes are 10, 20, 50, or 100 play coins, with a default of 20. Once a round is active, settings, restoration, and starting another round are locked.

Before capturing a stake, you choose the reward weight curve: linear, squared, or cubed. Automatic collection can be turned off or set to one of the preset thresholds.

Settlement & Persistence

One captured stake is used per round. At settlement, the floor of the gross return plus stored fractional carry is credited; the remainder persists. In zero-return rounds, the fractional carry remains unchanged.

• Fractional Carry: Persists in browser localStorage across settlement, refill, and reload. Refilling does not clear it.
• Unfinished Reload: If you reload during an active round, the captured stake remains deducted. The round ends without refund, payout, continuation, or resume.
• Settled Balance: Persists locally, including zero.

Wallet & Restoration

The demo starts with a balance of 1000 virtual coins. A manual idle-only restoration is available when the balance is below 10, setting it exactly to 1000. This is distinct from adding coins or automatic replenishment.

Virtual coins have no cash value. No account login or payment flow is implemented in this demo.

Mathematical Evidence & RTP

The following table shows simulation measurements for different modes and thresholds. These are supporting sample observations, not the mathematical payout law. The expected RTP is 97% across all tested policies.

Frequently asked questions