A Query Does Not Establish an Operator
This independent guide has not established an operator, official business address, licence, application, support channel or financial service associated with 333PK. A matching search name or logo is a lead rather than evidence of ownership. The guide offers its own original browser simulator, Shortcut Closure, with free virtual coins and no account. Those original rules do not reproduce or certify a separate product.
Four Ordered Vertices and Six Fair Edges
Each round samples six independent fair binary choices for the forward edges 0 to 1, 0 to 2, 0 to 3, 1 to 2, 1 to 3 and 2 to 3. Edges only go from a lower label to a higher one. All 64 edge patterns have equal probability. The raw reward counts ordered pairs connected by a directed path but lacking their direct edge. It counts pairs rather than the number of different paths between them. A pair with an existing direct edge never contributes, even if an additional indirect route also connects it.
Three Powers and Exact Mean Normalization
Choose linear, squared or cubed weighting before a round. For selected power p, gross credit equals the whole captured stake times 0.96 times raw reward raised to p, divided by its exact mean over the 64 graphs. Those means are 0.484375, 0.734375 and 1.328125 respectively. The reward distribution is zero in 40 patterns, one in 18, two in five and three in one. Each mode has exact unrounded expected gross credit of 96% of stake. Zero stays zero; all modes have 24 positive-reward graphs out of 64. Changing a power changes credit sizes, not positive-result frequency. Expectation does not guarantee a session result.
Whole Stakes, Saved Wallet and Manual Refill
The wallet begins with 1000 free virtual coins. One captured whole stake prices the graph; there are no row stake shares. Settled wallet balance and fractional-credit carry persist in browser localStorage. Idle balance below ten permits manual refill to 1000 while retaining carry. Refill does not add 1000 and is locked during settlement and an active automatic queue. Reloading does not reset the saved wallet. An unfinished round is not resumed on reload: its already debited stake is not automatically refunded and a pending credit can be lost. Keep active play open until settlement.
Local Storage and Third-Party Requests
The guide has no login, identity-document or payment form. Google Fonts and Statinside requests, as well as server or CDN logs, may expose IP, device and request information. Complete third-party processing, retention, cookie lifetimes and anonymity are not established. Saved virtual values use localStorage; ordinary cache or history deletion may leave it intact. An absence of account forms cannot establish that no personal information is processed or that all requests are limited to essential functionality.
Time Limits and the Guide’s Own Age Rule
The guide restricts its simulator to adults aged eighteen and over by its own rule. Legal age and activity requirements vary by location; no legal determination is supplied. Choose a stopping time and take breaks away from the game. Free coins create no obligation to refill or continue. If play feels uncomfortable or competes with ordinary responsibilities, pause. Qualified local help can be sought through independently identifiable health or public-service sources; this guide supplies no diagnosis or verified named treatment service.
Frequently asked questions
Is a business behind the query established?
No operator, official address, licence or application associated with 333PK has been independently established by this guide.
What is the raw reward?
Count ordered pairs connected by a directed path but lacking their direct edge, on four ordered vertices with six possible forward edges.
Why does a complete graph score zero?
Every connected pair already has its direct edge, so there is no missing shortcut to count.
Does 96% mean a winning frequency?
No. It is exact unrounded expected gross credit in each normalized mode. Positive raw reward occurs in 24 of the 64 equally likely patterns.
When can I refill?
While idle with fewer than ten coins, manual refill sets the balance to 1000 and preserves fractional carry.
