Bounded Diophantine Solutions Claim: Mechanics & Math

Game Structure and Decoding

The game consists of twelve independent fair binary steps. These steps reveal three four-bit blocks. Each completed block is decoded as a number from 0 to 15. To obtain the variables a, b, and c, 1 is added to each decoded block value, resulting in integers ranging from 1 to 16.

The core statistic is the number of integer pairs (x, y) where both x and y are between 1 and 16, satisfying the equation a*x + b*y = 16*c. This raw terminal statistic is the basis for the reward calculation.

Reward Modes and Scoring

Before each round, you must preselect a reward weight curve: linear, squared, or cubed. The score function is defined as function score(mask){return statistic((mask>>8)+1,(mask>>4&15)+1,(mask&15)+1)-CFG.min;}, where CFG.min is the global minimum statistic value.

The live gross quote is calculated as 0.97 times the conditional expected terminal weight divided by the initial expected terminal weight. This quote can rise, fall, or become zero. The specific mode chosen affects the distribution of outcomes, but the expected RTP remains consistent at 97% across policies in the mathematical evidence.

Controls, Stakes, and Settlement

Stakes are selectable at 10, 20, 50, or 100 play coins, with 20 being the default. Once a stake is captured, the settings, refill, and starting another round controls are locked until settlement.

Settlement occurs when you manually collect the current quote, when a preset auto-threshold is crossed, or when the quote hits zero. If the quote hits zero, it resolves before cashout if they occur at the same event. The final step 12 collects the current quote for surviving rounds. At settlement, the floor of (raw gross return + stored fractional carry) is credited; any remainder persists. Zero-return rounds leave the fractional carry unchanged.

Auto-Collection and Stopping Rules

Automatic collection can be set to off, 1.25, 1.75, or 2.50. An earlier crossed auto-threshold settles the round before a later zero event. If zero resolves first at the same event, it takes precedence. The process prioritizes prior crossed events before later crashes; the surviving terminal step 12 collects the current quote if no earlier resolution occurs.

Mathematical Evidence and RTP

The following table presents simulation measurements from 1,000,000 rounds for each curve and policy. These are supporting sample observations, not the mathematical payout law. The expected RTP is consistently 97%.

Wallet, Persistence, and Demo Identity

The demo wallet starts with an initial balance of 1000 virtual coins. Restoration is manual and idle-only: if the balance drops below 10 while idle, it is SET to exactly 1000. Refilling does not clear the fractional carry, which persists in browser localStorage across settlement, refill, and reload.

If you reload during an unfinished round, the captured stake remains deducted, and the round ends without refund or continuation. Default stake (20) and first preset are restored after reload. Virtual coins have no cash value, and no account login or payment flow exists in this demo. Storage includes virtual-coin balance and fractional payout carry in browser localStorage.

Frequently asked questions