Two hexadecimal reels
Each independent uniform reel produces 0–9 or A–F, with A–F representing 10–15. Read n = 16 × first + second + 1: the 256 reel pairs give the integers 1–256 with equal probability. For each prime power p^e in n, calculate p^(2e−2) × (p²−1), then multiply those terms. The empty product for n = 1 is 1. Subtract 1 from the statistic to obtain the reward score.
Three reward curves
Before starting, choose linear, squared or cubed score weights. Let weight be score, score² or score³. The gross multiplier is 0.96 × weight divided by the exact mean weight over all 256 integers. Multiply that multiplier by the captured stake for raw gross return. The whole reel pair uses one stake; there are no row bets, bonuses or intermediate collection. A gross return is the full credited return, rather than net gain after the stake debit.
Whole coins and fractional carry
At settlement, floor(raw gross return + stored fractional carry) is credited. The remainder is saved for future rounds. A zero return leaves valid carry unchanged. For reels 0 and 0, n = 1, statistic = 1 and score = 0, so every curve returns zero. For reels 0 and 1, n = 2, statistic = 3 and score = 2; the selected curve weights are 2, 4 and 8.
Local virtual wallet
A new wallet begins with 1,000 play coins. Balance, including zero, and fractional carry are saved in browser localStorage when storage is available. Restoration is manual, available only while idle with a balance strictly below 10, and sets the balance to exactly 1,000. It does not add 1,000 and does not clear carry. A balance of 10 does not qualify.
Reloading an unfinished round
Starting has already deducted the captured stake. Reloading before settlement ends that round without refund, payout or resumption. The saved balance and carry remain; settings return to stake 20 and linear. A saved wallet is not a saved active round. Clearing cached files is different from deleting this site’s localStorage; removing localStorage removes the stored wallet, with no account recovery.
Exact expectation and measured samples
All three curves have exact expected gross return 24/25, or 96% of stakes. This is a distribution average, not a promise for a session or a win probability. Existing simulations of this unchanged game code used 1,000,000 rounds per curve and measured 95.9783%, 96.0854% and 96.1369% for linear, squared and cubed weights. These are sample measurements. The exact sums of weights over 256 outcomes are 4,674,440; 156,701,861,706; and 6,380,283,699,274,598.
Frequently asked questions
Are play coins worth money?
No. They have no cash value or redemption flow.
Can an unfinished round resume?
No. Reloading before settlement leaves the captured stake deducted and ends the round without refund or payout. Balance and carry remain saved when storage is available.
When can I restore the balance?
Only manually while idle with balance strictly below 10. Restoration sets it to exactly 1,000 and preserves fractional carry.
