Five vertices and graph bridges
Bridge Inspector draws an undirected graph on five vertices, labelled 1 to 5. Ten independent fair switches choose the ten possible links, one for each pair of vertices. Each link is equally likely to be present or absent, so all 1,024 graphs are equally likely. A bridge is a present link whose removal increases the number of separate connected components. Isolated vertices count as components too.
A chain with only links 1–2, 2–3, 3–4 and 4–5 has four bridges: removing any one splits the chain. A five-vertex cycle has no bridges because another path remains around the cycle. A single link 1–2 has one bridge even though vertices 3, 4 and 5 are isolated. A graph with no links also has no bridges and returns zero.
How the three Powers calculate a return
The score is the number of bridges, from 0 to 4. Power 1 uses that count, Power 2 its square, and Power 3 its cube. The gross multiplier is 0.96 × that powered score divided by its own average over all 1,024 graphs. All Powers draw from the same graphs with the same probabilities; the selected Power changes the payout mapping, not the chance of a particular graph. No bridges means zero return in every Power.
Each Power has exactly 96% expected gross return before whole-coin wallet credits and carry. That average follows from applying the 0.96 factor to a powered score normalized by its own mean. It is not a promised return for a round or session. A gross return includes what is paid back from the stake, rather than being additional profit. Integer credits and carry mean that an individual wallet credit need not equal 96% of its stake.
Start and complete one draw
Choose a stake of 10, 20, 50 or 100 and a reward Power of 1, 2 or 3 before pressing Draw link switches. A fresh page selects stake 20 and Power 1, with sound off. The chosen stake is deducted once at the start, and both stake and Power are fixed for that draw. Stake, Power, draw and restoration controls are locked until settlement; sound remains available. There is no early collection or automatic queue.
Integer wallet and fractional remainder
A new wallet starts at 1,000 free virtual coins. Settlement multiplies the captured stake by the full multiplier and adds the saved fractional remainder. Only the whole-number part is credited to the wallet; the new remainder is saved for a later settlement and is never credited separately. The multiplier shown on screen is rounded to four decimal places, but the calculation uses the full value. A zero return credits no coins and retains the existing remainder.
Restore balance is available only when no draw is active and the balance is below 10. Pressing it sets the wallet to exactly 1,000; it does not add 1,000 or run automatically. The fractional remainder is preserved. A balance of exactly 10 is not eligible.
Saved deductions and reload defaults
The wallet is saved when the stake is deducted and again when the result is credited. Reloading during an unfinished draw loses that draw without refund or resume, so its already deducted stake stays deducted. The saved wallet, including zero, and fractional remainder remain if browser storage is retained. Reload returns stake to 20, Power to 1 and sound to off; the result meters show a dash.
Scope, storage and audience
This independent OK12 guide explains its own free browser demo. No outside operator, business ownership, licence, official account address, payment service or app has been established here. A matching name or search result does not verify an outside service or connect it to this demo.
The browser stores the virtual wallet and a separate fractional remainder in localStorage for this site. The page also requests Google Fonts resources and loads the Statinside measurement script for counter ID 44, with a measurement image when JavaScript is disabled. These identified requests are not a complete network audit. Local storage and the lack of a login do not establish anonymity or promise that no personal data are processed.
The guide is intended for adults aged 18 and over. That label does not enforce an age check or establish local legality. Virtual coins have no cash value, cannot be withdrawn and are not prizes.
Frequently asked questions
What is a bridge?
A present link is a bridge if removing it increases the number of connected components. Isolated vertices count as components. The score counts these bridges, from 0 to 4.
How many vertices and possible graphs are there?
There are five labelled vertices and ten possible undirected links. Independent fair switches give all 1,024 graphs equal probability in every Power.
What do Powers 1, 2 and 3 change?
They use the bridge count, its square or its cube, each divided by its own exact mean and multiplied by 0.96. The graph probabilities and bridge-count rule do not change.
What are the stakes and defaults?
Stakes are 10, 20, 50 and 100. A fresh page or reload selects stake 20, Power 1 and sound off. Stake and Power stay selected between completed draws.
Is 96% a guaranteed session return?
No. It is the exact expected gross return before integer wallet credits and carry for each Power. Individual results vary and can return zero.
Can I collect early or queue draws automatically?
No. Each draw captures one stake and settles once. There is no early collection or automatic queue.
What is fractional carry?
It is the saved remainder after settlement credits only the whole-number part of stake times multiplier plus old carry. It is retained for a later settlement and is never credited separately.
When can I restore my balance?
Only while idle with a balance below 10. Restore balance sets the wallet to exactly 1,000 free coins and preserves fractional carry. A balance of 10 is not eligible.
What happens on reload during a draw?
The unfinished draw cannot resume and its already deducted stake is not refunded. Saved wallet and carry remain if storage is retained; settings return to defaults and result meters show a dash.
Do I need an account, and can I withdraw coins?
The demo has no login, registration, deposit or withdrawal flow. Its free virtual coins have no cash value and are not prizes.
What storage and external requests are identified?
The browser stores wallet and carry in localStorage. The page requests Google Fonts and Statinside measurement for counter ID 44. These observations do not establish anonymity or a complete processing policy.
Can I change settings while a draw is active?
Stake, Power, the draw button and restoration are locked until settlement. Sound remains available. There are no other game choices during the draw.
Read the reward-Power guide or try the free demo. Play the free demo
