Colour Census: Graph Patterns and Gross Credits

Colour Census draws ten independent fair binary switches, one for each unordered pair among five labelled vertices. A present edge constrains its two endpoints to have different colours. The software counts all 243 assignments of three labelled colours to the five vertices and uses the number of valid assignments as its raw score. The player does not manually assign colours or choose which edges are present.

With no edges present, every assignment is valid and the score is 243. A complete five-vertex graph has score zero: five pairwise adjacent vertices cannot all use different colours drawn from a set of only three. These are outcomes of our specific simulator. They do not describe a BossPay product, and the illustration of a bending jig is decorative rather than an additional game rule.

There are 1024 equally likely edge-switch patterns. Exactly 66 have score zero, so a positive raw score occurs in 958 of 1024 patterns. This is a positive gross-credit probability, not the probability of profit after subtracting the stake. Linear, square and cube weighting leave zero scores at zero and positive scores positive. They change the credit amounts, not which draws have a positive raw result.

For mode exponent p equal to 1, 2 or 3, the gross-credit multiplier is 0.96 × score^p / mean(score^p). The exact means are 34.2216796875, 2058.7587890625 and 177666.3544921875 respectively. Thus every mode has an expected gross credit of 96% of the captured stake. That is a distribution average, not a claim that 96% of rounds win or that a session ends with 96% of its starting balance.

Choose a stake and weighting before pressing Draw. One whole stake is debited once for the entire graph. There are no separate rows, paylines or row shares. Settings and refill remain locked while the draw settles and throughout an active automatic queue. Auto schedules up to ten rounds, subject to sufficient balance. Stop cancels future rounds; it does not refund or change an already drawn result.

A new browser wallet starts at 1000 virtual coins. Settled integer balance and fractional payout carry are saved in localStorage. A gross credit is added to any saved fraction; the integer part is credited and the remaining fraction is carried forward. These coins have no cash value, deposits, withdrawals or prizes. Storage belongs to this browser and origin, not to an account or an external payment balance.