How Our Original Cycle Surplus Simulator Works

Each round samples ten independent fair binary choices, one for every possible undirected edge between five labelled vertices. Every one of the 1024 edge patterns has equal probability. Count present edges E and connected components C, including isolated vertices. The raw reward is E minus 5 plus C. A forest has reward zero, while the complete five-vertex graph has reward six. Random selection determines the graph; the component calculation then scores that selected graph.

Choose linear, squared or cubed weighting before a round. For power p, the gross credit is the captured whole stake times 0.96 times raw reward raised to p, divided by its exact mean across all 1024 graphs. Those means are 1.365234375, 3.30859375 and 9.685546875 respectively. All three modes have exact unrounded expected gross credit of 96% of stake. There are 291 zero-reward and 733 positive-reward graphs. Changing the power changes positive credit sizes, while leaving those outcome frequencies unchanged. Expectation is not a promise about a session or a commercial game.

The wallet begins with 1000 free virtual coins. One captured stake prices the whole graph; there are no row stake shares. Settled wallet balance and fractional-credit carry persist in browser localStorage. When idle with fewer than ten coins, manual refill sets the balance to 1000 and preserves carry. It does not add 1000. Refill and settings are locked during settlement and an active automatic queue. Reloading does not reset a settled wallet. An unfinished round ends on reload without a refund; keep active play open until settlement.

Automatic play schedules at most ten rounds. Stop cancels future scheduled rounds and allows the active round to settle. It does not restore a stake already committed. The selected stake and weighting are captured for a round, and controls cannot change them during settlement. The optional queue does not change the distribution of graphs or expected return. You can leave after settlement without refilling or starting another round.

This independent guide has not established an operator, official business address, licence or application associated with the RTM1 query. A matching name or logo is a lead rather than evidence of ownership. The guide provides its own original simulator, Cycle Surplus, and no account or payment facility. Its rules do not reproduce or certify an external game.