Orbit Sum: Worked Probability and Payout Examples

How the Modulo-7 System Works

Orbit Sum uses two independent pointers that each draw a number from 0 to 6 uniformly. These two numbers are added together and then taken modulo 7 to produce a final result between 0 and 6. You select an arc of 1, 2, or 3 positions starting from zero. If the final result falls within your chosen arc, you win. The payout depends on the arc size: a 1-position arc pays 6.72x, a 2-position arc pays 3.36x, and a 3-position arc pays 2.24x. Any result outside your arc returns zero. The game resets to a default stake of 25 upon reload, discarding any unfinished round without refund.

Expected Return and Simulation Data

The expected return to player (RTP) for all arc choices is 96%. This is calculated because the sum modulo 7 is uniformly distributed, and the payout multiplier is inversely proportional to the arc size. Simulation data from one million rounds confirms this theoretical expectation. For a 1-position choice, the simulated RTP was 95.77%. For a 2-position choice, it was 95.91%. For a 3-position choice, it was 95.90%. These figures align closely with the 96% theoretical model.

Wallet Mechanics and Stake Rules

The demo starts with a virtual balance of 1000 coins. When you start a round, the stake is deducted once at the beginning and persists before any animation. Payouts are computed in hundredths. Any fractional carry is kept separately, and only whole coins are credited to your balance. You can manually refill your balance to 1000 only when idle and your balance falls below 10. If you reload the page, any unfinished round is discarded without refund. Controls are disabled while the round is active.

Frequently asked questions