The 4×4 board has labels 1 through 16 in row order. Choose 3, 4 or 5 hazards before starting. Each safe reveal eliminates layouts containing that tile, so future safe probabilities depend on the layouts still possible.
Board and Hazard Selection
The game board is a 4×4 grid containing labels 1 to 16. Before a round starts, you must choose the number of hazards: 3, 4, or 5. This choice determines the size of the support (the total number of valid hazard configurations).
| Hazards | Support Count | Description |
|---|---|---|
| 3 | 53 | Uniformly sample from 53 valid subsets |
| 4 | 181 | Uniformly sample from 181 valid subsets |
| 5 | 379 | Uniformly sample from 379 valid subsets |
These counts are exact. The labels printed on the board are not clues to a hidden independent grid; they are used solely to calculate the LCM constraint.
The LCM Congruence Rule
A subset of hazards is valid only if the sum of the LCM of every pair of labels in that subset is divisible by 11. This constraint reduces the total possible combinations of hazard positions to the specific support counts listed above.
- Uniform Sampling: Within the valid support, all configurations are equally likely.
- Posterior Probability: As you reveal safe tiles, the probability of subsequent tiles being safe updates based on the remaining valid configurations. This is not a simple ratio of safe tiles to total tiles.
Pricing and Gross Return
The price of each unrevealed safe tile is calculated as the Current Gross Value divided by the exact posterior probability of that tile being safe.
- Initial Value: The initial gross quote is 97% of the captured stake: 19.4 at stake 20 and 97 at stake 100.
- Reveal Pricing: When you reveal a safe tile, the Current Gross Value is divided by the posterior safe probability of that tile.
- Probability 1: If the chosen tile’s safe probability before revealing it is 1, the gross value remains unchanged.
Worked Example (3 Hazards):
| Parameter | Value |
|---|---|
| Stake | 20 play coins |
| Initial Gross | 19.4 |
| Printed Label | 4 |
| Posterior Safe Probability | 0.8113207547169812 |
| Gross After Reveal | 23.91162790697674 |
Gross return includes the stake. The example’s net gain before integer credit and carry is about 3.91162790697674 play coins; it is not a guarantee of a safe reveal.
Controls and Modes
Stakes: Selectable stakes are 10, 20, 50, or 100 play coins. The default stake is 20.
Controls: Settings, restoration, and starting another round are locked while a round is active. You cannot change the hazard count or stake mid-round.
Collection: You can only collect after at least one safe reveal. Once collected, the round ends.
Stopping Rules and Auto-Bank
Manual Stop: You may collect at any time after the first safe reveal.
Auto-Bank: The game automatically banks (collects) only when no eligible uncertain choice remains. A choice is ineligible if its gross return exceeds 1000 times the captured stake. Equality (gross = 1000 × stake) is allowed and does not trigger auto-bank if other choices remain.
Settlement and Wallet Persistence
Settlement: At settlement, the floor of (raw gross return + stored fractional carry) is credited to your balance. The remainder persists as fractional carry.
Fractional Carry: This value persists in browser localStorage across settlement, refill, and reload. Refilling the wallet does not clear it.
Zero-Return Rounds: If you hit a hazard and get zero return, the fractional carry remains unchanged.
Unfinished Reload: If you reload the page during an unfinished round, the captured stake remains deducted. The round ends without refund, payout, continuation, or resume.
Frequently asked questions
What is the support count for 3 hazards?
The support count for 3 hazards is exactly 53. This means there are 53 valid subsets of 3 tiles whose LCM pair sums are divisible by 11.
How is the gross value calculated after a safe reveal?
Divide the current gross quote by the tile’s safe probability before the reveal. With three hazards, label 4 has probability 43/53 before any reveal. At stake 20, the quote changes from 19.4 to approximately 23.91162790697674 after safely revealing label 4. Gross return includes the stake.
Does the fractional carry reset when I refill my wallet?
No. The fractional carry persists in browser localStorage across settlement, refill, and reload. Refilling the wallet does not clear it.
