Column Run Total Three: Rules and Math

The game draws a four-by-four board uniformly from all boards with the selected mine count. This draw is restricted by a public support rule: across all columns, there are exactly three nonempty occupied runs in total. Draws are uniform over this support, not over all unconstrained boards. Each safe reveal filters the support space, making the game distinct from standard mines variants.

The gross cashout is calculated as 96 percent of the captured stake times the initial support size divided by the current compatible support size. Known certain mines are disabled, and cells with zero conditional safe probability are also disabled. If a safe reveal would exceed the 1000 times stake cap, it is disabled. The gross return includes the stake, differing from net profit.

A mine ends the round with zero gross return. Manual bank becomes available only after at least one safe reveal. When no eligible reveal remains, the current quote is banked automatically. Captured stake and mine count remain locked throughout the round. No refill occurs during an active round, and there is no automatic queue for plays.

The wallet starts with an initial balance of 1000 virtual coins. A captured whole stake is deducted once at the start. Manual restoration is available only when idle and the balance falls below 10, setting the integer wallet to 1000. Fractional carry persists across settlement and reloads. An unfinished reload ends without refund or resume.

The source-bound mathematical proof gives an exact expected gross return to player rate of 96 percent across various mine counts. For example, with three mines, measured RTPs hover around 96 percent. The maximum gross multiplier observed is 384 for three mines and 921.6 for five mines. These figures distinguish exact expectation from measured estimates in simulation collections.

Z93 is an unverified query identity; this guide’s original demo does not certify another service. The game uses browser localStorage for settled demo balance and fractional carry. A declared Google Fonts stylesheet exists, but actual request capture is pending. No account or payment form establishes anonymity, and no local age gate is confirmed.