Uniform connected hazard trees
Choose 3, 4 or 5 hazards on a 4×4 grid. Shared horizontal or vertical edges connect all hazards into a single graph, and that graph has no cycle. A solid 2×2 hazard block forms a cycle and is excluded. Straight connected rows of three hazards are permitted. The 52, 104 or 196 legal layouts respectively are equally likely; one is fixed for the entire round.
Corner and inner-cell example
With 3 hazards, a corner is initially safe in 47 of 52 layouts, whereas an inner cell is safe in 36 of 52. From 20×0.97 coins, a safe corner gives about 21.464 coins and a safe inner cell about 28.022. Coordinates matter from the first reveal; unrestricted 13/16 or 12/15 formulas do not apply.
Expected return and variance
Exact expected return is 97% for permitted stopping policies. The initial 3% reduction is applied once; conditional safe-branch compensation preserves expectation. Choosing coordinates or stopping changes risk and variance, not this expectation. A short session is not guaranteed to match it.
Collecting and automatic settlement
Collect is available after a safe reveal. Proven hazards are unavailable; proven-safe cells have probability 1 and add no value. A choice with next value above 1000 times stake is unavailable. When no eligible uncertain choice remains, the current value is banked automatically. The guard is not a promise that 1000×stake can be reached.
Wallet persistence and refill
Settled balance and fractional payout carry persist in localStorage. Reloading during a round ends it without refunding its already deducted stake. Outside a round, refill restores 1000 coins when balance is below the smallest stake; it does not add 1000 or reset fractional carry. Hazard count, stake and refill are locked during play.
Frequently asked questions
Is this an operator website?
This independent DuoGaming guide supplies its own free Open Circuit Mines demo. Operator identity, domains, licence, apps, payments, support and commercial game equivalence have not been independently verified. No operator account or commercial link is supplied here.
What is the public layout rule?
Choose 3, 4 or 5 hazards on a 4×4 grid. Shared horizontal or vertical edges connect all hazards into a single graph, and that graph has no cycle. A solid 2×2 hazard block forms a cycle and is excluded. Straight connected rows of three hazards are permitted. The 52, 104 or 196 legal layouts respectively are equally likely; one is fixed for the entire round.
How is the live value calculated?
Live value starts at 0.97 times the virtual stake. A safe reveal divides it by that cell’s exact conditional safe probability among the remaining compatible legal layouts. A hazard ends the round with zero return. Reveals change knowledge, not the hidden layout.
Explore the free Open Circuit demo and its exact conditional cell odds.
