The virtual coins have no cash value.
How Real-Binary Gap Works
Nine independent fair bits fill a 3 × 3 matrix by rows, giving 512 equally likely boards. Its raw reward is the matrix rank over real numbers minus its rank over GF(2), where addition is modulo two. Rank counts independent rows or columns; the real rank is determined by exact integer minors.
Only six boards have reward 1; the other 506 have reward 0. Select power 1, 2 or 3 before drawing. All powers give identical payouts here, because both 0 and 1 are unchanged by these powers. Their exact means are all 6/512 = 0.01171875. Gross multiplier is 0.96 × reward**power / mean: 81.92 when reward is 1, otherwise zero. Expected gross return is 96%, not a promised session result.
Select stake 10, 20, 50 or 100 virtual coins. Defaults are stake 20 and power 1. The whole stake is deducted and saved when a draw starts. At settlement, add previous carry to stake × gross multiplier, credit the floor, and save the fractional remainder. A zero-return draw preserves carry. Gross returns include the stake and are not profit.
For example, rows (0,1,1), (1,0,1), (1,1,0) have real rank 3 and binary rank 2, so reward is 1. With stake 20 and zero carry, the gross amount is 1638.4: credit 1638 and retain carry 0.4. The resulting balance from 1000 is 2618 after the captured stake.
Modes and Probabilities
Nine independent fair bits fill a 3 × 3 matrix by rows, giving 512 equally likely boards. Its raw reward is the matrix rank over real numbers minus its rank over GF(2), where addition is modulo two. Rank counts independent rows or columns; the real rank is determined by exact integer minors.
Only six boards have reward 1; the other 506 have reward 0. Select power 1, 2 or 3 before drawing. All powers give identical payouts here, because both 0 and 1 are unchanged by these powers. Their exact means are all 6/512 = 0.01171875. Gross multiplier is 0.96 × reward**power / mean: 81.92 when reward is 1, otherwise zero. Expected gross return is 96%, not a promised session result.
Saved simulations contain one million rounds per power, three million in total. Measurements are sample observations, not the payout law. The same theoretical distribution can have different sample measurements.
| Power | Expected gross return | Measured (1M rounds) |
|---|---|---|
| 1 | 96% | 96.62464% |
| 2 | 96% | 96.33792% |
| 3 | 96% | 96.33792% |
Controls and Stakes
The wallet starts with 1000 virtual coins without cash value. While idle and below 10, you can manually set the whole-coin balance to exactly 1000. This replaces the low balance, does not add 1000, and preserves carry. Current balance, including zero, and carry persist on reload.
Stake, power and restoration lock during drawing; sound remains available. There is no Auto, Stop, early cash-out or automatic queue. An unfinished reload gives no refund, payout or resume. Its captured stake remains deducted, and selections reset to stake 20 and power 1.
Select stake 10, 20, 50 or 100 virtual coins. Defaults are stake 20 and power 1. The whole stake is deducted and saved when a draw starts. At settlement, add previous carry to stake × gross multiplier, credit the floor, and save the fractional remainder. A zero-return draw preserves carry. Gross returns include the stake and are not profit.
For example, rows (0,1,1), (1,0,1), (1,1,0) have real rank 3 and binary rank 2, so reward is 1. With stake 20 and zero carry, the gross amount is 1638.4: credit 1638 and retain carry 0.4. The resulting balance from 1000 is 2618 after the captured stake.
Wallet and Persistence
The wallet starts with 1000 virtual coins without cash value. While idle and below 10, you can manually set the whole-coin balance to exactly 1000. This replaces the low balance, does not add 1000, and preserves carry. Current balance, including zero, and carry persist on reload.
Stake, power and restoration lock during drawing; sound remains available. There is no Auto, Stop, early cash-out or automatic queue. An unfinished reload gives no refund, payout or resume. Its captured stake remains deducted, and selections reset to stake 20 and power 1.
Privacy and Storage
The current balance and fractional carry are stored in localStorage. Clearing browser cached files alone may leave the wallet intact; removing this site’s localStorage clears the saved balance and carry. Local wallet storage does not establish anonymity or exclude other processing.
The published page requests Google Fonts stylesheets and font files and Statinside44 site-counter resources. These observations are not an exhaustive privacy audit and do not establish retention, sale, anonymity or security guarantees.
Responsible Use and Audience
This guide targets an 18+ audience. This is its own policy, not a universal legal age, implemented age gate or statement of local legality. You can choose personal time or virtual-coin limits, pause between draws and decide not to restore the wallet. No timer, account blocking or self-exclusion is offered.
The demo does not clinically train behaviour or make losses safe. Seek appropriate local qualified help if your play concerns you.
Frequently asked questions
What is the exact payout formula?
The reward is the rank over the real numbers minus the rank over GF(2). This raw reward is raised to power 1, 2, or 3 (depending on mode) and normalized by its exact mean over all equally likely complete draws. The displayed multipliers are gross coin returns, not profit.
Can I cash out early?
No. There is no Auto, Stop, or cash-out feature. One whole stake is captured per complete draw.
What happens if I reload the page mid-game?
An unfinished reload gives no refund, payout or resume. The captured stake stays deducted; current balance and carry persist. Selections reset to stake 20 and power 1.
