Two polynomials with four coefficients each
Eight independent fair bits form two polynomialsA andB, each with four coefficients for degrees0 through3. Ordinary integer multiplication produces seven coefficientsc0 throughc6. Raw score=sum of c_k*(c_k−1)/2 over those seven coefficients. One whole captured stake prices both polynomials and the full draw.
Coefficientc_k counts active multiplication terms landing at degreek. Its contribution counts unordered pairs of distinct active terms. Coefficients are integer counts, not reduced modulo2. This is not a root count, rank, XOR or count of distinct coefficient values. The program calculates automatically.
When both input polynomials have four coefficients equal1, the product coefficients are1,2,3,4,3,2,1. Their pair contributions0,1,3,6,3,1,0 sum to14. If either input polynomial is all zero, the product and score are zero. Players do not select coefficients or alter score through stopping time.
Scores0,1,2,3,5,6,8,14 occur161,48,16,18,4,4,4,1 times. There are95 positive and161 zero outcomes. Mode changes preserve positive frequency. Positive gross credit can be smaller than stake. Previous outcomes do not change new independent inputs.
For p=1,2,3, gross multiplier=0.96*rawScore^p/mean(rawScore^p). Exact means are0.875,3.7890625,26.6328125. Each mode has96% expected unrounded gross credit, not winning frequency, net profit or a guaranteed final wallet. Zero stays zero. Powers are not multiplication by2 or3. Choose the mode before drawing, not after calculating score.
Whole stake and mode are captured before drawing with one upfront debit. Settlement lasts480ms. Settings and refill lock during settlement and an active auto queue. Auto schedules at most10 rounds with sufficient balance. Stop cancels future rounds while the current round settles. No early cashout, coefficient selection or reroll exists.
A new browser wallet starts at 1000 virtual coins. Settled integer balance and fractional payout carry are saved in localStorage. A gross credit is added to any saved fraction; the integer part is credited and the remaining fraction is carried forward. These coins have no cash value, deposits, withdrawals or prizes. Storage belongs to this browser and origin, not to an account or an external payment balance.
Only an idle balance below ten offers Free refill. Clicking it sets the balance to 1000; it does not add 1000 to the existing balance. The fractional carry is preserved. Refill is unavailable during settlement or an active automatic queue. Changing the stake cannot force a refill while the balance is ten or more. A previously saved zero balance remains zero after reload until the user clicks the available refill.
Reload preserves saved balance and fractional carry when browser storage remains available. A draw debits its stake before the short settlement animation: leaving or reloading during that unfinished animation can discard its pending credit. Reload after settlement preserves the completed result. Clearing cache alone may not delete localStorage; removing site storage can erase the wallet. Private browsing and browser settings can change storage availability and retention.
Exact means and expected gross credit
For p=1,2,3, gross multiplier=0.96*rawScore^p/mean(rawScore^p). Exact means are0.875,3.7890625,26.6328125. Each mode has96% expected unrounded gross credit, not winning frequency, net profit or a guaranteed final wallet. Zero stays zero. Powers are not multiplication by2 or3. Choose the mode before drawing, not after calculating score.
The finite virtual wallet
A new browser wallet starts at 1000 virtual coins. Settled integer balance and fractional payout carry are saved in localStorage. A gross credit is added to any saved fraction; the integer part is credited and the remaining fraction is carried forward. These coins have no cash value, deposits, withdrawals or prizes. Storage belongs to this browser and origin, not to an account or an external payment balance.
Captured settings and future auto rounds
Whole stake and mode are captured before drawing with one upfront debit. Settlement lasts480ms. Settings and refill lock during settlement and an active auto queue. Auto schedules at most10 rounds with sufficient balance. Stop cancels future rounds while the current round settles. No early cashout, coefficient selection or reroll exists.
Frequently asked questions
Y7777 query and our original simulator?
Y7777 is the search subject of this independent guide. No business identity, official address, app, licence, support or financial service is established here. Coefficient Collisions is our original virtual-coin simulator, not a commercial replica or a test of outside software.
Two polynomials with four coefficients each?
Eight independent fair bits form two polynomialsA andB, each with four coefficients for degrees0 through3. Ordinary integer multiplication produces seven coefficientsc0 throughc6. Raw score=sum of c_k*(c_k−1)/2 over those seven coefficients. One whole captured stake prices both polynomials and the full draw.
Count active product pairs, not repeated coefficient values?
Coefficientc_k counts active multiplication terms landing at degreek. Its contribution counts unordered pairs of distinct active terms. Coefficients are integer counts, not reduced modulo2. This is not a root count, rank, XOR or count of distinct coefficient values. The program calculates automatically.
All-one inputs score14?
When both input polynomials have four coefficients equal1, the product coefficients are1,2,3,4,3,2,1. Their pair contributions0,1,3,6,3,1,0 sum to14. If either input polynomial is all zero, the product and score are zero. Players do not select coefficients or alter score through stopping time.
