How Fifo Residence Works

The game operates over twelve time indices, labeled 0 through 11. The revealed bit selects one of these actions at each index:

• Enqueue: If the revealed bit is zero, enqueue the current index.
• Serve: If the revealed bit is one, serve the oldest waiting item, if any; add its waiting time to the raw score.

The raw score is the sum of the elapsed times for all served items. Items that remain in the queue when the game ends contribute zero to the score.

Twelve independent fair bits (0 or 1) are revealed in order. These bits determine the specific sequence of events, creating 4,096 equally likely complete outcomes. The score is then raised to a selected power:

• Power 1: Raw score
• Power 2: Squared score
• Power 3: Cubed score

The live gross bank quote is calculated using a conditional expected value. The formula is:

Exact Unconditional Means:

• Power 1: 10.29248046875
• Power 2: 146.80419921875
• Power 3: 2574.92626953125

The quote can rise or fall as bits are revealed because it averages all remaining possible word completions. If the conditional potential becomes zero, the game settles with a gross of zero. Any bounded stopping rule that uses only revealed bits and settles by phase 12 yields an expected gross return of 96% before integer rounding.

Raise each possible final score to the selected power before taking its conditional mean; raising the mean itself to the power would be a different formula. Reloading an unfinished round abandons its debit and is not a settlement covered by the 96% expectation.

Stake: One whole captured stake per round. There are no row shares.

Power Selection: Preselect Power 1, 2, or 3 before the round begins.

Automatic Reveal Cap: Choose a cap of 4, 8, or 12 revealed phases. When the cap is reached, the current quote is automatically banked.

Manual Bank: Available immediately while the round is live. This settles the current conditional quote.

Locking: Once the round starts, the captured stake, power selection, and reveal cap are locked until settlement. Sound controls remain available.

Each semantic reveal follows a 650ms interval. The following stopping conditions apply:

• Manual Bank: Settles the current conditional quote immediately.
• Auto-Bank: Triggers at the selected cap (4, 8, or 12). It banks the current quote.
• Zero Potential: If the conditional future potential drops to zero, the game settles immediately with a gross of zero, even if the cap has not been reached.

Hidden future bits are not exposed before their scheduled reveal. All unused future bits are averaged exactly when calculating the quote. Actions use no information about hidden bits.

Initial Balance: 1000 virtual coins.

Refill Rule: A manual refill is available when idle. If the balance is below 10, the system sets the balance to exactly 1000. This is a reset, not an addition.

Fractional Carry: Fractional carry persists across settlement, refill, and reload.

Reload Behavior: If you reload the page during an unfinished trace (round), the captured debit is lost. There is no refund or resume capability for unfinished rounds.

Controls: Stake, mode, and refill buttons are locked while active and until settlement; this game has no automatic queue of rounds.

The game uses 12 independent fair bits, resulting in 4,096 equally likely complete words. The expected gross return is exactly 96% for all supported stopping policies.

Worked Examples:

• Word [0,0,0,0,0,0,0,0,0,0,0,0]: Raw Score = 0
• Word [0,0,0,0,0,0,1,1,1,1,1,1]: Raw Score = 36

Simulation Data: Each power/cap sample contains 1,000,000 rounds; exact enumeration and conditional averages establish the 96% gross expectation. Measured RTPs vary slightly due to sampling (e.g., Mode 0, Cap 8 measured RTP: 96.095%).