Connected hazards with exactly one cycle
Choose 4, 5 or 6 hazards on a 4×4 board. Shared horizontal or vertical edges connect all hazards into one graph with exactly one independent cycle. There are respectively 9, 48 or 144 equally likely legal layouts, and one stays fixed throughout the round. At 4 hazards the only legal shapes are the nine filled 2×2 squares.
Initial and updated conditional odds
With 4 hazards, a corner is initially safe in 8 of 9 layouts, an edge cell away from a corner in 7 of 9, and a central cell in 5 of 9. From a 20-coin stake, a safe corner gives 20×0.97/(8/9)=21.825 coins; a safe centre gives 34.92 coins. Observations update compatible layouts, so later probabilities can rise or fall. Initial odds are coordinate-specific rather than uniformly 12/16.
Value from compatible layouts
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.
Collect and eligible choices
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.
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.
Frequently asked questions
Is this an operator website?
This independent S667 query guide supplies its own free Loop Circuit Mines demo. The query can refer to technical products; an established casino business is not authenticated here. No operator identity, domains, licence, apps, payments, support or commercial game equivalence have been verified. No operator account or commercial link is supplied.
What is the single-cycle rule?
Choose 4, 5 or 6 hazards on a 4×4 board. Shared horizontal or vertical edges connect all hazards into one graph with exactly one independent cycle. There are respectively 9, 48 or 144 equally likely legal layouts, and one stays fixed throughout the round. At 4 hazards the only legal shapes are the nine filled 2×2 squares.
How is 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.
Do first-cell coordinates affect odds?
With 4 hazards, a corner is initially safe in 8 of 9 layouts, an edge cell away from a corner in 7 of 9, and a central cell in 5 of 9. From a 20-coin stake, a safe corner gives 20×0.97/(8/9)=21.825 coins; a safe centre gives 34.92 coins. Observations update compatible layouts, so later probabilities can rise or fall. Initial odds are coordinate-specific rather than uniformly 12/16.
When can I collect?
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.
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