The core mechanic involves a queue where 'zero' enqueues the current index and 'one' serves the oldest waiting item. The score is the sum of elapsed times for served items. You can select one of three raw-score powers (1, 2, or 3), each with a different exact unconditional mean. The live gross bank quote is calculated as 0.96 times the captured stake times the conditional expected terminal powered score divided by its unconditional mean. This quote can rise or fall as bits are revealed.
Scoring and Powers
The game reveals twelve independent fair bits in order. Each bit contributes to the FIFO queue. The raw score is the sum of elapsed times for items served. Unserved items contribute zero. You must preselect a power for the raw score:
- Power 1: Raw score. Exact unconditional mean: 10.29248046875.
- Power 2: Squared score. Exact unconditional mean: 146.80419921875.
- Power 3: Cubed score. Exact unconditional mean: 2574.92626953125.
The quote averages all remaining possible words at each prefix. If zero future potential ends, the gross settles to zero.
Banking and Controls
Each semantic reveal follows a 650ms interval. You have two banking options:
- Manual Bank: Available immediately while live. It settles the current conditional quote.
- Automatic Bank: You select a reveal cap of 4, 8, or 12. The game automatically banks the current quote when that many bits are revealed. If zero conditional potential occurs earlier, it banks immediately.
Once you start a trace, the captured stake, power selection, and reveal cap are locked until settlement. Sound remains available throughout. Unused future bits are averaged exactly; actions use no information about hidden bits.
Payout and Settlement
The live gross bank quote is calculated as:
| Formula |
|---|
| 0.96 × captured whole stake × conditional mean of the final raw score raised to the selected power / unconditional mean for that power |
The expected gross under supported stopping policies is 96%. This is not a guarantee of net profit. Fractional carry persists across settlement. If you reload an unfinished trace, the captured debit is lost.
Wallet and Persistence
The demo wallet uses browser localStorage for settled balance and fractional carry. The initial balance is 1000. If the balance falls below 10 while idle, you can manually refill it, which sets the balance to exactly 1000 and preserves fractional carry. This is a manual restoration, not an automatic replenishment.
Settled balances persist locally, including zero balances. Unfinished reloads end without refund or resume. There is no account login flow or payment processing in this demo.
Mathematical Evidence
The following table shows measured RTP from simulation, distinct from the exact 96% expected gross RTP.
| Mode | Auto Cap | Measured RTP (%) |
|---|---|---|
| 0 | 4 | 96.05% |
| 0 | 8 | 96.10% |
| 0 | 12 | 95.96% |
| 1 | 4 | 96.08% |
| 1 | 8 | 96.03% |
| 1 | 12 | 95.77% |
| 2 | 4 | 95.99% |
| 2 | 8 | 96.13% |
| 2 | 12 | 96.08% |
Worked Examples
Example 1: A word of all zeros [0,0,0,0,0,0,0,0,0,0,0,0] results in a raw score of 0. Example 2: A word [0,0,0,0,0,0,1,1,1,1,1,1] results in a raw score of 36. These examples illustrate the scoring based on the specific bit sequence.
Frequently asked questions
How does the FIFO queue work?
At twelve time indices 0..11, zero enqueues its current index and one serves the oldest waiting item if any. The score is the sum of elapsed times for served items.
What happens if I reload during a round?
Reloading an unfinished trace ends the round without refund or resume. The captured debit is lost.
Is the 96% RTP guaranteed?
No. The expected gross under supported stopping policies is 96%, but this is not a guarantee of net profit. Measured RTP may vary slightly in simulations.
