What the queried name establishes
34r is the query name used by this independent guide. The name and 34r.info address do not establish an official company, licence, app or affiliation. This site explains its own original browser demo; information about an outside service remains unverified.
What this demo can establish
The demo exposes two hexadecimal reels, three reward curves, four stakes and a conditional restoration button. Its finite set of 256 integers allows independent checking of the arithmetic and gross multipliers. These checks concern this guide’s own game; they do not establish another product’s fairness, reputation or payments.
Two hexadecimal reels and one integer
Unitary Totient Reels draws two independent uniform values from 0 to 15. The symbols 0–9 represent themselves and A–F represent 10–15. Read the first value as a and the second as b: the integer is n=16a+b+1, uniformly distributed from 1 to 256. For each full prime power p^e in n’s factorization, use p^e−1; multiply those factors. With no prime factors, the product is 1. Subtract 1 to obtain the reward score. This is the unitary totient statistic, not the ordinary Euler totient.
Exact expectation and a worked outcome
Averaging each curve’s gross multiplier over all 256 equally likely integers gives exactly 0.96, or 96% expected gross return per coin staked. This is neither the chance of winning nor a promised session result. For symbols 0 and B, n=12; its prime powers are 4 and 3, the statistic is (4−1)(3−1)=6 and the reward score is 5. Linear weight is 5, square weight 25 and cube weight 125. Symbols 0 and 0 give n=1, statistic 1 and score 0, so every curve returns zero.
Gross return and fractional settlement
The exact sums of the 256 weights are 22,945 for linear, 3,024,331 for square and 479,301,235 for cube. Each mean is its sum divided by 256. The gross multiplier is 0.96 × weight / mean. Multiply that multiplier by the captured stake to get the raw gross return. Add existing fractional carry, credit the whole-number part and save the remainder. Net wallet change is credited coins minus the stake deducted earlier. A zero-score result pays zero and leaves carry unchanged.
Storage and page requests
The game saves its virtual balance and fractional carry locally. The page loads Google Fonts and includes a Statinside visitor counter. These observations do not establish complete collection practices, server logging, retention periods, data sharing or security guarantees. Having no account form does not prove that no personal data are processed. Removing local game storage does not establish deletion of any server or third-party records.
Frequently asked questions
Does this demo prove an outside licence or official service?
No. The name, domain and arithmetic checks do not verify an outside company, licence, app or commercial relationship.
How is the reward score calculated?
Multiply p^e−1 for the full prime powers in the selected integer’s factorization, using 1 for an empty product, then subtract 1. For n=12 the statistic is 6 and score is 5. It is not the ordinary Euler totient.
Can virtual coins be withdrawn?
No. The coins have no cash value and this demo provides no deposits, withdrawals or exchange service.
