Guide

Distance Chord: fixed hazards and exact cell prices

II789 is a search name here without a confirmed commercial identity. This guide hosts its own Distance Chord game. It confirms no outside operator, affiliation, official domain, licence, payment service or app. Similar naming does not establish a shared publisher.

Play the free demo
Free demo gameVirtual coins, no cash value

The following rules concern this original demo alone. Its calculations do not establish the mathematics, security, legality or catalogue of another product. There are no monetary deposits or customer accounts in the demo.

The sum of all hazard-pair distances

Choose 3, 4 or 5 hazards on the 4×4 board. Rows and columns are indexed 0–3. Distance between two cells is the absolute row difference plus the absolute column difference.

Count every unordered hazard pair once. The sum of all these distances must be divisible by three; individual pairs need not be divisible by three. Legal supports contain 188 layouts for three hazards, 469 for four and 1,444 for five. A layout is sampled uniformly once at the start and stays fixed. One captured stake covers the whole round.

Each choice uses its own conditional probability

After the opened safe cells are known, let N be the number of legal layouts consistent with that history. For an unopened cell let K be the number of those layouts where it is safe. Its safe probability is K/N. Each eligible cell shows that probability; it is not a generic remaining-safe-cells ratio.

The quote starts at 0.97. A safe reveal changes quote q to q×N/K, using the probability of that very chosen cell before revealing it. A hazard ends the round with zero return. Collect returns captured stake times quote, with fractional carry. The identity (K/N)×(q×N/K)=q explains 97% expected gross return for choices using revealed information. This is not a win probability or a guaranteed session return.

Known hazards and proven-safe choices

If K=0 the cell is a known hazard and cannot be chosen. If K=N it is proven safe, so choosing it does not change the quote. A next quote above 1,000× is disabled. If no eligible uncertain choice remains, the round settles automatically; otherwise collection is available after one safe reveal.

The layout constraint can make different cells have different probabilities. After a safe reveal, a particular cell’s chance may rise or fall; risk does not necessarily increase uniformly across the board. Choices change which results are reached, without changing the stated expected gross return.

Captured settings and visible cell probabilities

While idle, choose hazard count and 10, 20, 50 or 100 virtual coins. Start shelves captures those settings and deducts one stake. Hazard count, stake and refill controls stay locked during the round. Collection is unavailable before the first safe reveal.

There is no Auto queue, timed crash or cashout threshold setting. Each click reveals one eligible cell immediately. Sound is optional. The game does not animate a moving hazard or require a reflex action; the hidden layout remains fixed.

Local virtual balance and fractional carry

The initial balance is 1,000 free virtual coins without monetary value or prize entitlement. The settled balance and fractional payout carry are kept in local browser storage when available. A fraction is carried into later settlements rather than discarded on each payout.

Restore balance is available only while idle and below the minimum stake of 10. It sets the balance to 1,000, rather than adding 1,000, and preserves the fraction. It is a manual button, not an automatic reset or a refund for an interrupted round.

Independent guide and Distance Chord

II789 is a search name here without a confirmed commercial identity. This guide hosts its own Distance Chord game. It confirms no outside operator, affiliation, official domain, licence, payment service or app. Similar naming does not establish a shared publisher.

The following rules concern this original demo alone. Its calculations do not establish the mathematics, security, legality or catalogue of another product. There are no monetary deposits or customer accounts in the demo.

Frequently asked questions

Does the search name confirm an operator?

II789 is a search name here without a confirmed commercial identity. This guide hosts its own Distance Chord game. It confirms no outside operator, affiliation, official domain, licence, payment service or app. Similar naming does not establish a shared publisher. The following rules concern this original demo alone. Its calculations do not establish the mathematics, security, legality or catalogue of another product. There are no monetary deposits or customer accounts in the demo.

How are hazard-pair distances combined?

Choose 3, 4 or 5 hazards on the 4×4 board. Rows and columns are indexed 0–3. Distance between two cells is the absolute row difference plus the absolute column difference. Count every unordered hazard pair once. The sum of all these distances must be divisible by three; individual pairs need not be divisible by three. Legal supports contain 188 layouts for three hazards, 469 for four and 1,444 for five. A layout is sampled uniformly once at the start and stays fixed. One captured stake covers the whole round.

How is the selected cell priced?

After the opened safe cells are known, let N be the number of legal layouts consistent with that history. For an unopened cell let K be the number of those layouts where it is safe. Its safe probability is K/N. Each eligible cell shows that probability; it is not a generic remaining-safe-cells ratio. The quote starts at 0.97. A safe reveal changes quote q to q×N/K, using the probability of that very chosen cell before revealing it. A hazard ends the round with zero return. Collect returns captured stake times quote, with fractional carry. The identity (K/N)×(q×N/K)=q explains 97% expected gross return for choices using revealed information. This is not a win probability or a guaranteed session return.

What happens to proven-safe cells?

If K=0 the cell is a known hazard and cannot be chosen. If K=N it is proven safe, so choosing it does not change the quote. A next quote above 1,000× is disabled. If no eligible uncertain choice remains, the round settles automatically; otherwise collection is available after one safe reveal. The layout constraint can make different cells have different probabilities. After a safe reveal, a particular cell’s chance may rise or fall; risk does not necessarily increase uniformly across the board. Choices change which results are reached, without changing the stated expected gross return.

Read the pair-distance rules and try the original free virtual-coin demo. Play the free demo