Determinant Windows: Exact Rules and Virtual Return

Three whole-matrix determinant scores

Each round draws three independent 2 by 2 matrices. Their four entries are independent uniform digits from 0 to 3. With entries a,b on the top row and c,d below, the raw score is the absolute value of a times d minus b times c. A zero determinant scores zero; a negative determinant contributes its positive absolute value.

Each whole matrix uses one third of the captured total stake. The three matrix returns are added. No individual cell row is paid separately, and there are no paylines, wild symbols or matching-symbol bonuses. Low weighting takes the square root of a positive score, Medium keeps it and High squares it. Zero remains zero.

Exact weighting and expected gross return

There are 256 equally likely digit arrangements per matrix. Each weighting has its own mean calculated over those arrangements. The gross multiplier for one matrix is 0.96 times its transformed score divided by that mean. Applying it to one third of the stake and adding the three credits gives 96% expected gross virtual return for the round.

The raw determinant is not the final payout. For [1,2;3,0], the determinant is minus six and the raw score is six. The unnormalised Low, Medium and High weights are the square root of six, six and thirty-six. Each still needs its own normalising factor. A zero result remains zero in every mode, so weighting changes amounts without changing positive-result frequency.

Expected gross return is neither net profit nor a promised wallet balance. The stake was deducted before settlement. Random matrices remain random even though their probabilities can be enumerated exactly. Timing, patterns and prior results do not establish an advantage.

Captured rounds and persistent free coins

A new browser wallet starts with 1,000 free virtual coins. Balance and fractional-credit carry persist in localStorage; refresh does not restore coins. Free refill is optional and available only below the minimum stake when the game is idle. It sets balance to 1,000 and preserves carry.

Stake and weighting are captured when a round starts. Controls and refill are locked during settlement and an automatic queue. Automatic play runs at most ten rounds. Stop prevents future rounds while an active round finishes. Insufficient balance prevents a new stake rather than creating debt. Coins have no cash value or transfer facility.

Category names do not define this model

Game category names alone do not specify probabilities. A reel game may use symbol arrangements; a wheel game uses its defined outcome set; a crash game needs its stopping and return rules; a number draw needs its actual draw distribution and reward table. Those descriptions are not a catalogue attributed to Dorodango.

Our particular simulator evaluates whole-matrix determinants. It has no live dealer, wheel, cashout curve, sports market or lottery ticket. Do not apply a generic industry percentage, assumed payline rule or commercial comparison to it. Only its explicit digit model and normalisation determine its expected virtual return.

Adult use and stopping time

The simulator is for adults aged 18 or older under this site rule. That does not establish the legal gambling age or authorisation for any service in Peru or another jurisdiction. The guide makes no claim that a craft query represents a gambling platform.

Choose a stopping time outside the game and take breaks. A free refill does not require another round, and lost virtual coins do not need recovery. Close the page if use displaces other activities or causes distress. Qualified local support may be appropriate; no diagnosis, treatment promise or authenticated helpline is supplied here.