Run Merge Grammar: Rules and Virtual Demo

The game begins by generating twelve independent fair bits, which produce an ordered list of maximal equal-bit run lengths. The score is determined by counting the number of complete ordered full binary parenthesizations of this run list that satisfy a specific structural constraint: every internal node must have strictly smaller total length on its left side than on its right side. Leaves retain their original order, and every run is used exactly once. If there is no valid complete tree, the raw score is zero.

Raw Score Examples

The raw score is then raised to a power (1, 2, or 3) depending on the selected mode. The exact unconditional means for raw-score powers 1, 2, and 3 are 0.626953125, 1.927734375, and 7.5, respectively.

The game operates with a single whole captured stake, with no row shares. Players can preselect a raw-score power (one, two, or three) and an automatic reveal cap of 4, 8, or 12. Once the round starts, the captured stake, power, and cap are locked until the round ends. Sound controls remain available throughout.

Banking and Stopping

A manual bank option is available immediately while the round is live. Each semantic reveal follows a 650ms interval. The selected cap automatically banks the current quote if reached. If the zero conditional potential is reached, the game settles zero earlier than the cap. No hidden future bits are exposed before their scheduled reveal.

Auto Queue

There is no Auto10 queue. During a live round, you can bank manually, or the selected reveal cap banks automatically. Refill functionality is available only when idle.

The live gross bank quote is calculated as 0.96 times the captured whole stake, multiplied by the exact conditional mean of the terminal powered score divided by its own unconditional mean. All 4096 equally likely complete words are enumerated. The quote can rise or fall during the reveal process. If the zero conditional potential settles, the payout is zero.

Exact RTP vs. Measured Estimates

The expected gross return under bounded stopping rules is 96%, before integer settlement with preserved fractional carry. This does not guarantee net profit in a specific session. Below is the mathematical evidence comparing exact gross RTP against simulation measurements:

The policy for all modes is to bank at cap or earlier if zero conditional value is reached.

The demo wallet initializes with a balance of 1000 virtual coins. Fractional carry persists across settlement, refill, and reload.

Restoration

A manual idle-only restoration sets the balance to exactly 1000. This is eligible only when the balance is below 10 and the user is idle. It does not add coins or automatically replenish; it sets the balance to the specific threshold. Settled balance persists locally, including zero balances. However, if an unfinished round ends on reload, it ends without refund or resume. Busy controls (Stake, mode, refill) are locked while active.

The source uses browser localStorage for settled demo balance and fractional carry. This does not establish anonymity or exclude other processing. The template declares a Google Fonts stylesheet, though actual browser request capture is pending; this is not a claim that other requests or processing are absent. Clearing cached files may leave local storage where that storage is actually used.

The 18+ designation is this guide's own intended audience policy, not a claim about local law or an implemented age gate. Responsible use includes optional pauses, setting personal time or virtual-coin limits, and finding appropriate local qualified help. The demo does not clinically train behavior or make losses safe. There are no account-level blocking, timer, or self-exclusion tools in this specific demo interface.