Mirror Subsequences: Rules and Expected Return

The game begins by drawing two independent uniform two-digit tickets ranging from 00 to 99, retaining leading zeros. These two tickets are concatenated in order to form a four-digit sequence. The core scoring function identifies the longest palindromic subsequence within this sequence, preserving the original position order while allowing for character deletions. Note that contiguous substring length is not used for scoring.

The raw score is calculated as the maximum of zero and the length of this longest palindromic subsequence minus two. For example, if the four digits are 0, 0, 0, 0, the longest palindromic subsequence is length four, resulting in a raw score of two. If the digits are 0, 1, 2, 3, the longest palindromic subsequence is length one, resulting in a raw score of zero.

One whole captured stake covers both tickets simultaneously. Before starting the draw, the player chooses one of three score modes: score, score squared, or score cubed. Each mode is separately normalized over all 10,000 equally likely ordered ticket pairs to achieve a 96% expected gross return. The powers one, two, and three do not alter which raw scores are zero; they only scale the payout for non-zero scores.

The gross return for a round is calculated using the formula: Gross = 0.96 × captured whole stake × raw^p / meanForPower(p), where p is 1, 2 or 3 and the corresponding means are 0.281, 0.301 and 0.341. The exact mean values for the three modes are 0.281 for linear, 0.301 for squared, and 0.341 for cubed.

Settlement normally occurs after 480 ms of animation; reduced-motion mode can settle on the first animation callback. During this time, and throughout any active auto-queue, the stake, mode selection, and refill controls are locked, though sound remains available. The expected gross return is 96%, which is a mathematical expectation over many rounds and not a guarantee of net profit in a single session. Saved sample data from one million rounds per mode is consistent with this separate mathematical calculation, with observed returns ranging between 96.0171% and 96.1718% depending on the mode.

The interface offers several control modes to manage gameplay flow. Auto10 queues at most ten captured draws in advance. If a player presses Stop, it cancels future draws in the queue while allowing the current draw to settle. There is no early settlement control during a draw.

Settings, refill, and restoration controls are locked until settlement is complete and the queue finishes. This ensures that the mathematical state of the round is finalized before further actions can be taken. Sound controls remain available during active settlement and queueing to provide audio feedback without affecting the game logic.

The demo uses a local virtual wallet with an initial balance of 1,000. Fractional carry persists across settlement, refill, and reload, meaning small decimal differences in balance are preserved rather than rounded to zero. The settled balance persists locally, including when it reaches zero.

Players can manually restore their balance when idle and the balance falls below 10. This action sets the balance to 1,000 and preserves any existing fractional carry. It is not automatic and does not add the reset amount to the current balance; it replaces it. Reloading the page or browser ends an unfinished draw without refund or resume of progress. A saved wallet does not mean a round or all progress resumes upon reload.

The game's mathematics are based on 10,000 equally likely ordered ticket pairs. The expected gross return is exactly 96% for all three modes. This is a long-term mathematical expectation, not a win probability or a target to recover over one session.

Simulation evidence from one million rounds per mode shows measured returns close to the expected value. For powers one, two and three, the measured gross returns were approximately 96.0171%, 96.1649% and 96.1717%, respectively. These sample observations support the separate mathematical calculation and illustrate that measured results vary. The demo credits whole coins at settlement and carries the fractional remainder forward.

This demo is an independent virtual-coin browser application. It does not identify an outside gaming operator. The brand 3star and website 3star.cc are unverified in this context, meaning no official address, license, or corporate history is confirmed by this guide. The demo has no account flow, no cashier, and no cash value for virtual coins.

Privacy is managed via browser localStorage, which stores the settled demo balance and fractional carry. This does not establish anonymity or exclude other processing. The template declares a Google Fonts stylesheet, but actual browser request capture is pending. Clearing cached files is distinct from removing this site's localStorage. The intended audience policy is 18+, but this is a guide policy, not an implemented age gate.