The game uses twelve independent fair left/right steps to define positions from x_0=0 through x_12. Scoring is based on the divisor function τ applied to specific position values, not on standard multipliers or peg layouts. This section explains how the scoring works, the exact payout structure, and what distinguishes it from conventional Plinko categories.
Exact Scoring Mechanics
The core of Divisor Gap Ribbons Plinko is a comparison of divisor counts across symmetric rows. For each i from 1 to 5, the game compares τ(abs(x_i)+1) and τ(abs(x_(12-i))+1). The score is the sum of the absolute differences between these values across all pairs.
| Concept | Description |
|---|---|
| Path Definition | Twelve independent fair left/right steps define positions x_0 through x_12. |
| Scoring Basis | Compares τ(abs(x_i)+1) and τ(abs(x_(12-i))+1) for i=1..5. |
| Raw Score | Summed absolute differences of these divisor counts. |
| Final Reward | Raw score minus the exact minimum statistic (0) over all 4096 paths. |
The score function is defined as: Add the five absolute differences between divisor counts at paired positions (rows 1 and 11, 2 and 10, 3 and 9, 4 and 8, 5 and 7). Count the positive divisors of the absolute position plus one in each case; the minimum path total is zero.
τ(n) means the number of positive integer divisors of n; for example τ(1)=1 and τ(4)=3. Left moves by −1 and right by +1, beginning at zero.
Reward Modes and Weights
Before capturing the stake, you must choose a reward weight mode. This choice affects the gross multiplier calculation. There are three distinct modes:
- Linear (Mode 0): Weight sum of 10544.
- Squared (Mode 1): Weight sum of 38512.
- Cubed (Mode 2): Weight sum of 166352.
The gross multiplier is calculated as 0.96 times the chosen weight divided by its exact 4096-path mean. No interim collection occurs during the round.
Payout and Settlement
Each round captures one stake. At settlement, the floor(stake × gross multiplier + stored fractional carry) is credited to the balance. Any remainder persists in the fractional carry.
- Zero-return rounds leave the fractional carry unchanged.
- The fractional carry persists in browser localStorage across settlement, refill, and reload.
Exact calculations give an expected RTP of 96% for all modes; simulations of 1,000,000 rounds per mode provide sample measurements, with measured RTPs closely aligning (e.g., 96.0006% for Linear, 95.9777% for Squared, 96.0022% for Cubed).
Controls and Modes
Stakes are selectable at 10, 20, 50, or 100 play coins, with 20 as the default. Settings, restoration, and starting another round are locked while a round is active. You must choose the linear, squared, or cubed reward weight before the captured stake is locked.
No intermediate collection is possible. The round must complete to settle the score and distribute the reward.
Wallet and Persistence
The demo wallet starts with an initial balance of 1000. Restoration is manual and idle-only: if the balance falls below 10 while idle, it is set to exactly 1000. Refilling does not clear the fractional carry.
- Settled balance persists locally, including zero.
- Unfinished rounds on reload end without refund, payout, continuation, or resume. The captured stake remains deducted.
- After reload, controls reset to default stake 20 and the first preset.
Distinction from Conventional Categories
Unlike conventional Plinko, which relies on geometric peg layouts and fixed multipliers, Divisor Gap Ribbons Plinko uses a mathematical scoring function based on divisor counts τ(n). The score is derived from the symmetry of the path (x_i vs x_12-i) rather than physical landing zones. The gross payout is strictly tied to the chosen weight mode and the exact 4096-path mean, giving an exact expected RTP of 96%; individual rounds and finite sessions vary across all modes.
Frequently asked questions
What is the minimum score in Divisor Gap Ribbons Plinko?
The subtracted minimum statistic over all 4096 paths is exactly 0. The final reward score is nonnegative.
How does the fractional carry work?
The fractional carry persists in browser localStorage across settlement, refill, and reload. It is added to the raw gross return at settlement, and the floor of this sum is credited. The remainder persists for the next round.
Can I resume an unfinished round after reloading the page?
No. An unfinished round ends without refund, payout, continuation, or resume. The captured stake remains deducted, and controls reset to default settings.
