3NN Fifo Residence: Unverified Identity & Demo Rules

Fifo Residence operates over twelve time indices (0 to 11). At each index, a fair bit (0 or 1) is revealed. The rules are:

• Zero (0): Enqueues its current index into a waiting queue.
• One (1): Serves the oldest waiting item from the queue if one exists.

The raw score is the sum of elapsed times for all served items. Unserved items contribute zero to the score. The game uses a FIFO queue structure, meaning the first item to enter the queue is the first to be served by a '1'.

There are three scoring modes based on the raw score:

• Power 1: Raw score (mean: 10.29248046875)
• Power 2: Squared score (mean: 146.80419921875)
• Power 3: Cubed score (mean: 2574.92626953125)

Each mode has its own exact unconditional mean used to price the payout. The total number of equally likely complete words is 4096 (2^12).

The live gross bank quote is calculated as:

0.96 × captured whole stake × conditional mean of the final raw score raised to the selected power / unconditional mean for that power

• The quote can rise or fall as bits are revealed.
• If the conditional potential ends with zero (e.g., queue empty and no future items can be served), the gross settles to zero.
• Fractional carry persists across settlement, refill, and reload.

The exact unconditional means are:

The expected gross return under supported stopping policies is exactly 96% before integer rounding. This is not a guarantee of net profit for any session.

• Stake: One whole captured stake per round. No row shares.
• Preselection: Select raw-score power (1, 2, or 3) and automatic reveal cap (4, 8, or 12).
• Locking: Captured stake, power, and cap are locked during the live round. Sound remains available.
• Manual Bank: Available immediately while live. No Auto10 queue.
• Refill: Idle-only refill. If balance is below 10, manual refill sets balance to exactly 1000 and preserves fractional carry.

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

• Manual Bank: Settles the current conditional quote immediately.
• Auto-Bank Cap: The selected cap (4, 8, or 12) automatically banks the current quote at that phase. If the zero conditional potential settles to zero earlier, it banks then.

No hidden future bit is exposed before its reveal. All unused future bits are averaged exactly when calculating the live quote. Actions use no information about hidden bits.

Initial Balance: 1000 virtual coins.

Refill Rule: Manual idle-only restoration sets the balance to exactly 1000 if it falls below 10. This preserves fractional carry.

Fractional Carry: Persists across settlement, refill, and reload.

Settled Balance: Persists locally, including zero balances.

Unfinished Reload: If you reload an unfinished trace, it ends without refund or resume. The captured debit is lost.

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

Exact Mean Values:

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

Worked Examples:

Simulation Data (1,000,000 rounds per power/cap combination):

Policy for all modes: Bank at cap or earlier zero conditional value.